Identifying differentially abundant microbes is a common goal of microbiome studies. Multiple methods are used interchangeably for this purpose in the literature. Yet, there are few large-scale studies systematically exploring the appropriateness of using these tools interchangeably, and the scale and significance of the differences between them. Here, we compare the performance of 14 differential abundance testing methods on 38 16S rRNA gene datasets with two sample groups. We test for differences in amplicon sequence variants and operational taxonomic units (ASVs) between these groups. Our findings confirm that these tools identified drastically different numbers and sets of significant ASVs, and that results depend on data pre-processing. For many tools the number of features identified correlate with aspects of the data, such as sample size, sequencing depth, and effect size of community differences. ALDEx2 and ANCOM-II produce the most consistent results across studies and agree best with the intersect of results from different approaches. Nevertheless, we recommend that researchers should use a consensus approach based on multiple differential abundance methods to help ensure robust biological interpretations. Many microbiome differential abundance methods are available, but it lacks systematic comparison among them. Here, the authors compare the performance of 14 differential abundance testing methods on 38 16S rRNA gene datasets with two sample groups, and show ALDEx2 and ANCOM-II produce the most consistent results. Marker gene sequencing, such as 16S rRNA gene sequencing, is the most common form of microbiome profiling and enables the relative abundances of taxa to be compared across different samples. A frequent and seemingly simple question to investigate with this type of data is: which taxa significantly differ in relative abundance between sample groupings? Newcomers to the microbiome field may be surprised to learn that there is little consensus on how best to approach this question. Indeed, there are numerous ongoing debates regarding the best practices for differential abundance (DA) testing with microbiome data3. This approach has been heavily criticized because excluding data could reduce statistical power and introduce biases. In particular, using rarefied count tables for standard tests, such as the t-test and Wilcoxon test, can result in unacceptably high false positive rates4. Nonetheless, microbiome data is still frequently rarefied because it can simplify analyses, particularly for methods that do not control for variation in read depth across samples. For example, LEfSe5 is a popular method for identifying differentially abundant taxa that first converts read counts to percentages. Accordingly, read count tables are often rarefied before being input into this tool so that variation in sample read depth does not bias analyses. Without addressing the variation in depth across samples by some approach, the richness can drastically differ between samples due to read depth alone.One area of disagreement is whether read count tables should be rarefied  to correct for differing read depths across samples6. Importantly, this filtering must be independent of the test statistic evaluated (referred to as Independent Filtering). For instance, hard cut-offs for the prevalence and abundance of taxa across samples, and not within one group compared with another, are commonly used to exclude rare taxa7. This data filtering could be especially important for microbiome datasets because they are often extremely sparse. Nonetheless, it remains unclear whether filtering rare taxa has much effect on DA results in practice.A related question to whether data should be rarefied is whether rare taxa should be filtered out. This question arises in many high-throughput datasets, where the burden of correcting for many tests can greatly reduce statistical power. Filtering out potentially uninformative features before running statistical tests can help address this problem, although in some cases this can also have unexpected effects such as increases in false positives8 and edgeR9 are both tools that assume read counts follow a negative binomial distribution. To identify differentially abundant taxa, a null and alternative hypothesis are compared for each taxon. The null hypothesis states that the same setting for certain parameters of the negative binomial solution explain the distribution of taxa across all sample groupings. The alternative hypothesis states that different parameter settings are needed to account for differences between sample groupings. If the null hypothesis can be rejected for a specific taxon, then it is considered differentially abundant. This idea is the foundation of distribution-based DA tests, including other methods such as corncob10 and metagenomeSeq11, which model microbiome data with the beta-binomial and zero-inflated Gaussian distributions, respectively.Another contentious area is regarding which statistical distributions are most appropriate for analyzing microbiome data. Statistical frameworks based on a range of distributions have been developed for modeling read count data. For example, DESeq212, meaning that sequencing only provides information on the relative abundance of features and that each feature’s observed abundance is dependent on the observed abundances of all other features. This characteristic means that false inferences are commonly made when standard methods, intended for absolute abundances, are used with taxonomic relative abundances. Compositional data analysis (CoDa) methods circumvent this issue by reframing the focus of analysis to ratios of read counts between different taxa within a sample14. The difference among CoDa methods considered in this paper is what abundance value is used as the denominator, or the reference, for the transformation. The centered log-ratio (CLR) transformation is a CoDa approach that uses the geometric mean of the read counts of all taxa within a sample as the reference/denominator for that sample. In this approach all taxon read counts within a sample are divided by this geometric mean and the log fold changes in this ratio between samples are compared. An extension of this approach is implemented in the tool ALDEx215. The additive log-ratio transformation is an alternative approach where the reference is the count abundance of a single taxon, which should be present with low variance in read counts across samples. In this case the ratio between the reference taxon chosen (denominator) and each taxon in that sample are compared across different sample groupings. ANCOM is one tool that implements this additive log-ratio approach16.Finally, it has recently become more widely appreciated that sequencing data are compositional17. It is unsurprising that distribution-based methods perform best when applied to simulated data based on that distribution. Nonetheless, simulated data with no expected differences has been valuable for evaluating the false discovery rate (FDR) of these methods. Based on this approach it has become clear that many of the methods produce unacceptably high numbers of false positive identifications19. Similarly, based on simulated datasets with spiked taxa it has been shown that these methods can drastically vary in statistical power18.Regardless of the above choices, evaluating the numerous options for analyzing microbiome data has proven difficult. This is largely because there are no gold standards to compare DA tool results. Simulating datasets with specific taxa that are differentially abundant is a partial solution to this problem, but it is imperfect. For example, it has been noted that parametric simulations can result in circular arguments for specific tools, making it difficult to assess their true performance19. In contrast, both ANCOM and limma voom21 have been implicated as both accurately and poorly controlling the FDR, depending on the study19. To further complicate comparisons, different sets of tools and dataset types have been analyzed across evaluation studies. This means that, on some occasions, the best performing method in one evaluation is missing from another. In addition, certain popular microbiome-specific methods, such as MaAsLin222, have been missing from past evaluations. Finally, many evaluations limit their analysis to a small number of datasets that do not represent the breadth of datasets found in 16S rRNA gene sequencing studies.Although these general observations have been well substantiated, there is less agreement regarding the performance of tools across evaluation studies. Certain observations have been reproducible, such as the higher FDR of edgeR and metagenomeSeq. Similarly, ALDEx2 has been repeatedly shown to have low power to detect differencesGiven the inconsistencies across these studies it is important that additional, independent evaluations be performed to elucidate the performance of current DA methods. This is particularly important as these tools are typically used interchangeably in microbiome research. Accordingly, herein we have conducted additional evaluations of common DA tools across 38 two-group 16S rRNA gene datasets. We first present the concordance of the methods on these datasets to investigate how consistently the methods cluster and perform in general, with and without the removal of rare taxa. Next, based on artificially subsampling the datasets into two groups where no differences are expected, we present the observed false postive rate for each DA tool. Lastly, we present an evaluation of how consistent biological interpretations would be across diarrheal and obesity datasets depending on which tool was applied. Our work enables improved assessment of these DA tools and highlights which key recommendations made by previous studies hold in an independent evaluation. Furthermore, our analysis shows various characteristics of DA tools that authors can use to evaluate published literature within the field.To investigate how different DA tools impact biological interpretations across microbiome datasets, we tested 14 different DA testing approaches . As expected, we found that the number of ASVs identified by all tools positively correlated with the effect size between test groups with Spearman correlation coefficient values ranging between 0.35–0.72 with unfiltered data Fig.  and 0.31pth Fig. . We alsoWe next investigated whether the significant ASVs identified by the tested DA tools were, on average, at different relative abundances. The clearest outliers were ALDEx2 (median relative abundance of significant ASVs: 0.013%), ANCOM-II (median: 0.024%), and to a lesser degree DESeq2 (median: 0.007%), which tended to find significant features that were at higher relative abundance in the unfiltered datasets  on CLR data . The precision score of all tools at this threshold was low on both relative abundance (range: 0–0.01) and CLR data (range: 0–0.2). This result is unsurprising as in practice we would expect DA tools to identify features that are below a discriminatory threshold of 0.9 AUC.As the above analysis has the potential to penalize tools that call a higher number of ASVs that are of lower discriminatory values we also investigated the ability of the tested DA methods to identify ASVs above specific AUC thresholds  , edgeR, , corncob , metagenomeSeq  and DESeq2  had the highest number of ASVs only identified by that particular tool as being in the top 20. On average only a small number of ASVs were amongst the top 20 ranked of all tools in both the filtered  and unfiltered  datasets  we would expect tools to not identify any ASVs as being differential abundant. Through this approach we were able to infer the false positive characteristics of each tool. In other words, we determined what percentage of tested ASVs was called as significant by each tool even when there is no difference expected between the sample groups.t-test (rare) consistently identified no ASVs as significantly different in the unfiltered data analyses. However, both MaAsLin2 and Wilcoxon (rare) found no significant features in the majority of tested datasets (6/8 and 7/8 respectively). Two clear outliers in the filtered data analyses were edgeR (mean: 0.69–27.9%) and LEfSe (mean: 3.4–5.1%) which consistently identified more significant hits compared with other tools , and that most tools identified only a small percentage of significant ASVs, regardless of filtering procedure. The exceptions were the two limma voom methods, which had high FDRs with unfiltered data, and edgeR and LEfSe, which had high FDRs on the filtered data. Although these tools stand out on average, we also observed that in several replicates on the unfiltered datasets, the Wilcoxon (CLR) approach identified almost all features as statistically significant Fig. . This waWe investigated the outlier replicates for the Wilcoxon (CLR) approach and found that the mean differences in read depth between the two tested groups were consistently higher in replicates in which 30% or more of ASVs were significant . We ran all DA tools on each individual filtered dataset and restricted our analyses to the 218 genera found across all datasets. Like our ASV-level analyses, the tools substantially varied in terms of the number of significant genera identified. For instance, ALDEx2 identified a mean of 17.6 genera as significant in each dataset (SD: 17.4), while edgeR identified a mean of 46.0 significant genera (SD: 12.9). Tools that generally identify more genera as significant are accordingly more likely to identify genera as consistently significant compared with tools with fewer significant hits. Accordingly, inter-tool comparisons of the number of times each genus was identified as significant would not be informative.p < 0.001) of consistency in calling significant genera in the observed data. In contrast, edgeR produced results that were only 1.10-fold more consistent compared with the random expectation (p = 0.002).Instead, we analyzed the observed distribution of the number of studies that each genus was identified as significant in compared with the expected distribution given random data. This approach enabled us to compare the tools based on how much more consistently each tool performed relative to its own random expectation. For instance, on average edgeR identified significant genera more consistently across studies compared with ALDEx2 . However, this observation was simply driven by the increased number of significant genera identified by edgeR. Indeed, when compared with the random expectation, ALDEx2 displayed a 1.35-fold increase (p < 0.05)  approach, ALDEx2, and the limma voom (TMMwsp) approach performed significantly better than expected by chance (p < 0.05). The MaAsLin2 (rare) approach produced by far the most consistent results based on these datasets .We conducted a similar investigation across five obesity 16S rRNA gene datasets, which was more challenging to interpret due to the lower consistency in general , and LEfSe output a high number of significant ASVs on average. In contrast, ALDEx2 and ANCOM-II tended to identify only a relatively small number of ASVs as significant. We hypothesize that these latter tools are more conservative and have higher precision, but with a concomitant probable loss in sensitivity. This hypothesis is related to our observation that significant ASVs identified by these two tools tended to also be identified by almost all other differential abundance methods, which we interpret to be ASVs that are more likely to be true positives. Furthermore, it was clear that in most, but not all, cases these two methods tended to identify the most discriminatory ASVs that were found by other tools. We believe that the lower number of ASVs identified by these approaches could be due to multiple reasons. ALDEx2’s conservative nature is most likely due to its Monte Carlo Dirichlet sampling approach which down weights low abundance ASVs. On the other hand, ANCOM-II’s conservative nature could be attributed to its large multiple testing burden. Furthermore, the variance in the number of features identified could also be attributed to pre-processing steps several tools use to remove potential ASVs for testing. This includes corncob that does not report significance values for ASVs only found in one group or ANCOM-II’s ability to remove structural zeros. While it is unclear why some methods have much higher significance rates than other tools it could be due to several reasons. These include LEfSe’s choice not to correct significance values for false discovery or Wilcoxon (CLR)’s inability to consider differences in sequencing depth between metadata groupings. It should be noted that in some cases authors haven chosen to apply FDR Given that ASVs commonly identified as significant using a wide range of approaches are likely more reliable, it is noteworthy that significant ASVs in the unfiltered data tended to be called by fewer tools. This was particularly evident for both limma voom approaches and the Wilcoxon (CLR) approach. Although it is possible that many of these significant ASVs are incorrectly missed by other tools, it is more likely that these tools are simply performing especially poorly on unfiltered data due to several reasons, such as data sparsity.17. We believe that this issue is most likely driven by the inability for TMM normalization methods to deal with highly sparse datasets as filtering the data resulted in performance more in line with other DA methods9. It is important to acknowledge that our randomized approach for estimating FDR is not a perfect representation of real data; that is, real sample groupings will likely contain some systematic differences in microbial abundances—although the effect size may be very small—whereas our randomized datasets should have none. Accordingly, identifying only a few significant ASVs under this approach is not necessarily proof that a tool has a low FDR in practice. However, tools that identified many significant ASVs in the absence of distinguishing signals likely also have high FDR on real data.This issue with the limma voom approaches was also highlighted by high false positive rates on several unfiltered randomized datasets, which agrees with a past FDR assessment of this approach18 Although metagenomeSeq also has been flagged as such18, that was not the case in our analysis. This agrees with a recent report that metagenomeSeq  appropriately controlled the FDR, but exhibited low power26. There have been mixed results previously regarding whether ANCOM appropriately controls the FDR17, but the results from our limited analysis suggest that this method is conservative and controls the FDR while sometimes potentially missing true positives, as evident in our discriminatory analysis.Two additional problematic tools based on this analysis were edgeR and LEfSe. The edgeR method has been previously found to exhibit a high FDR on several occasionst-test (rare) approach, LEfSe, and edgeR. The random expectation in this case was quite simplistic; it was generated based on the assumption that all genera were equally likely to be significant by chance. This assumption must be invalid to some degree simply because some genera are more prevalent than others across samples. Accordingly, it is surprising that the tools produced only marginally more consistent results than expected.Related to this point, we found that ANCOM-II performed better than average at identifying the same genera as significantly DA across five diarrhea-related datasets despite only identifying a mean of four genera as significant per dataset. Nonetheless, the ANCOM-II results were less consistent than ALDEx2, both MaAsLin2 workflows, and limma voom (TMM). The tools that produced the least consistent results across datasets (relative to the random expectation) included the 1. Despite these complicating factors, it is noteworthy that the MaAsLin2 workflows and ALDEx2 produced more consistent results than expected based on these datasets.Although this cross-data consistency analysis was informative, it was interesting to note that not all environments and datasets are appropriate for this comparison. Specifically, we found that the consistency of significant genera across five datasets comparing obese and control individuals was no higher than expected by chance for most tools. This observation does not necessarily reflect that there are few consistent genera that differ between obese and non-obese individuals; it could instead simply reflect technical and/or biological factors that differ between the particular datasets we analyzed27. One goal of our work was to validate the recommendations of another recent DA method evaluation paper, which found that limma voom, corncob, and DESeq2 performed best overall of the tools they tested19. Based on our results, we do not recommend these tools as the sole methods used for data analysis, and instead would suggest that researchers use more conservative methods such as ALDEx2 and ANCOM-II. Although these methods have lower statistical power19, we believe this is an acceptable trade-off given the higher cost of identifying false positives as differentially abundant. However, MaAsLin2 (particularly with rarefied data) could also be a reasonable choice for users looking for increased statistical power at the potential cost of more false positives. We can clearly recommend that users avoid using edgeR (a tool primarily intended for RNA-seq data) as well as LEfSe  for conducting DA testing with 16S rRNA gene data. Users should also be aware that limma voom and the Wilcoxon (CLR) approaches may perform poorly on unfiltered data that is highly sparse. This is particularly true for the Wilcoxon (CLR) approach when read depths greatly differ between groups of interest.We believe the above observations regarding DA tools are valuable, but many readers are likely primarily interested in hearing specific recommendations. Indeed, the need for standardized practices in microbiome analysis have recently become better appreciatedMore generally, we recommend that users employ several methods and focus on significant features identified by most tools, while keeping in mind the characteristics of the tools presented within this manuscript. For example, authors may want to present identified taxonomic markers in categories based on the tool characteristics presented within this paper or the number of tools that agree upon its identification. Importantly, applying multiple DA tools to the same dataset should be reported explicitly. Clearly this approach would make results more difficult to biologically interpret, but it would provide a clearer perspective on which differentially abundant features are robust to reasonable changes in the analysis.A common counterargument to using consensus approaches with DA tools is that there is no assurance that the intersection of the tool outputs is more reliable; it is possible that the tools are simply picking up the same noise as significant. Although we think this is unlikely, in any case running multiple DA tools is still important to give context to reporting significant features. For example, researchers might be using a tool that produces highly non-overlapping sets of significant features compared with other DA approaches. Even if the researchers are confident in their approach, these discrepancies should be made clear when the results are summarized. This is crucial for providing accurate insight into how robust specific findings are expected to be across independent studies, which often use different DA approaches. Similarly, if researchers are most interested in determining if signals from a specific study are reproducible, then they should ensure that they use the same DA approach to help make their results more comparable.7. Although statistical arguments regarding the validity of independent filtering are beyond the scope of this work, intuitively it is reasonable to exclude features found in only a small number of samples (regardless of which groups those samples are in). The basic reason for this is that otherwise the burden of multiple-test correction becomes so great as to nearly prohibit identifying any differentially abundant features. Despite this drawback, many tools identified large numbers of significant ASVs in the unfiltered data. However, these significant ASVs tended to be more tool-specific in the unfiltered data and there was much more variation in the percentage of significant ASVs across tools. Accordingly, we would suggest performing prevalence filtering  of features prior to DA testing, although we acknowledge that more work is needed to estimate an optimal cut-off rather than just arbitrarily selecting one4.How and whether to conduct independent filtering of data prior to conducting DA tests are other important open questions regarding microbiome data analysis4.Another common question is whether DA tools that require input data to be rarefied should be avoided. It is possible that the question of whether to rarefy data has received disproportionate attention in the microbiome field: there are numerous other factors affecting an analysis pipeline that likely affect results more. Indeed, tools that took in rarefied data in our analyses did not perform substantially worse than other methods on average. More specifically, the most consistent inter-tool methods, ANCOM-II and ALDEx2, are based on non-rarefied data, but MaAsLin2 based on rarefied data produced the most consistent results across datasets of the same phenotype. Accordingly, we cannot definitively conclude that DA tools that require input data to be rarefied are less reliable in general. It should be noted that we are referring only to rarefying in the context of DA testing: whether rarefying is advisable for other analyses, such as prior to computing diversity metrics, is beyond the scope of this work19. However, we believe this does not provide the full picture of how these DA tools perform. This is because it has been highlighted that in many scenarios simulations can led to circular arguments where tools that are designed around specific parameters perform favorably on simulations using those parameters17. Without better knowledge of the range of data structures that microbiome sequencing can result in these types of simulation analyses can be difficult to interpret. As such we believe that it was important to test these methods on a wide range of different real-world datasets in order to gain an understanding of how they differed from one another. By doing so we have highlighted the issues of using these tools interchangeably within the literature. Indeed, the question ‘which taxa significantly differ in relative abundance between sample groupings?’ may be too simple and need further parameterization before it can be answered. This includes information such as what type of abundance the authors are comparing and the tools they plan to use within their analysis. Unfortunately, the variation across tools implies that biological interpretations based on these questions will often drastically differ depending on which DA tool is considered.Others have investigated the above questions by applying simulations to various DA methods, which has yielded valuable insightsIn conclusion, the high variation in the output of DA tools across numerous 16S rRNA gene sequencing datasets highlights an alarming reproducibility crisis facing microbiome researchers. While we cannot make a direct simple recommendation of a specific tool based on our analysis, we have highlighted several issues that authors should be aware of while interpreting DA results. This includes that several tools have inappropriately high false discovery rates such as edgeR and LEfSe and as such should be avoided when possible. It is also clear from our analysis that some tools designed for RNA-seq such as limma voom methods cannot deal with the much higher sparsity of microbiome data without including a data filtration step. We have also highlighted that these tools can significantly differ in the number of ASVs that they identify as being significantly different and that some tools are more consistent across datasets than others. Overall, we recommend that authors use the same tools when comparing results between specific studies and otherwise use a consensus approach based on several DA tools to help ensure results are robust to DA choice.64 . Abundance tables of ASVs for each sample were then output into tab-delimited files. Rarefied tables were also produced for each dataset, where the rarefied read depth was taken to be the lowest read depth of any sample in the dataset over 2000 reads (with samples below this threshold discarded).Thirty-eight different datasets were included in our main analyses for assessing the characteristics of microbiome differential abundance tools. Three additional datasets were also included for a comparison of differential abundance consistency across diarrhea and obesity-related microbiome datasets. All datasets presented herein have been previously published or are publicly available70 implemented in VSEARCH (v2.17.1)68. Both the UCHIME2 and UCHIME3 de novo approaches were applied in addition to the UCHIME2 reference-based chimera checking approach. For this latter approach we used the SILVA v138.1 short-subunit reference database71. We used the default options when running these algorithms.Chimeric ASVs were identified with the UCHIME2 and UCHIME3 chimera-checking algorithmsWe created a custom shell script  that ran each differential abundance tool on each dataset within this study. As input the script took a tab-delimited ASV abundance table, a rarefied version of that same table, and a metadata file that contained a column that split the samples into two groups for testing. This script also accepted a prevalence cut-off filter to remove ASVs below a minimum cut-off, which was set to 10%  for the filtered data analyses we present. Note that in a minority of cases a genus abundance table was input instead, in which case all options were kept the same. When the prevalence filter option was set, the script also generated new filtered rarefied tables based on an input rarefaction depth.72. The workflow used to run each differential abundance tool  is described below. The first step in each of these workflows was to read the dataset tables into R (version 3.6.3) with a custom script and then ensure that samples within the metadata and feature abundance tables were in the same order. An alpha-value of 0.05 was chosen as our significance cutoff and FDR adjusted p-values (using Benjamini-Hochberg adjustment) were used for methods that output p-values 73.Following these steps, each individual differential abundance method was run on the input data using either the rarefied or non-rarefied table, depending on which is recommended for that tool. Rarefaction was performed using GUniFrac (version 1.1)aldex function from the ALDEx2 R package (version 1.18.0)15 which generated Monte Carlo samples of Dirichlet distributions for each sample, using a uniform prior, performed CLR transformation of each realization, and then performed Wilcoxon tests on the transformed realizations. The function then returned the expected Benjamini-Hochberg (BH) FDR-corrected p-value for each feature based on the results the different across Monte Carlo samples.We passed the non-rarefied feature table and the corresponding sample metadata to the 74 (https://github.com/FrederickHuangLin/ANCOM) (version 2.1) function feature_table_pre_process, which first examined the abundance table to identify outlier zeros and structural zeros74. The following packages were imported by ANCOM-II: exactRankTests (version 0.8.31), nlme (version 3.1.149), dplyr (version 0.8.5), ggplot2 (version 3.3.0) and compositions (version 1.40.2). Outlier zeros, identified by finding outliers in the distribution of taxon counts within each sample grouping, were ignored during differential abundance analysis, and replaced with NA. Structural zeros, taxa that were absent in one grouping but present in the other, were ignored during data analysis and automatically called as differentially abundant. A pseudo count of 1 was then applied across the dataset to allow for log transformation. Using the main function ANCOM, all additive log-ratios for each taxon were then tested for significance using Wilcoxon rank-sum tests, and p-values were FDR-corrected using the BH method. ANCOM-II then applied a detection threshold as described in the original paper16, whereby a taxon was called as DA if the number of corrected p-values reaching nominal significance for that taxon was greater than 90% of the maximum possible number of significant comparisons.We ran the non-rarefied feature table through the R ANCOM-II75, which we input to corncob’s differentialTest function (version 0.1.0)10. This function fits each taxon count abundance to a beta-binomial model, using logit link functions for both the mean and overdispersion. Because corncob models each of these simultaneously and performs both differential abundance and differential variability testing10, we set the null overdispersion model to be the same as the non-null model so that only taxa having differential abundances were identified. Finally, the function performed significance testing, for which we chose Wald tests (with the default non-bootstrap setting), and we obtained BH FDR-corrected p-values as output.We converted the metadata and non-rarefied feature tables into a phyloseq object (version 1.29.0)8 with default settings, except that instead of the default relative log expression  the estimation of size factors was set to use ‘poscounts’, which calculates a modified relative log expression that helps account for features missing in at least one sample. The function performed three steps: (1) estimation of size factors, which are used to normalize library sizes in a model-based fashion; (2) estimation of dispersions from the negative binomial likelihood for each feature, and subsequent shrinkage of each dispersion estimate towards the parametric (default) trendline by empirical Bayes; (3) fitting each feature to the specified class groupings with negative binomial generalized linear models and performing hypothesis testing, for which we chose the default Wald test. Finally, using the results function, we obtained the resulting BH FDR-corrected p-values.We first passed the non-rarefied feature tables to the DESeq function (version 1.26.0)https://joey711.github.io/phyloseq-extensions/edgeR.html), we added a pseudocount of 1 to the non-rarefied feature table and used the function calcNormFactors from the edgeR R package (version 3.28.1)9 to compute relative log expression normalization factors. Negative binomial dispersion parameters were then estimated using the functions estimateCommonDisp followed by estimateTagwiseDisp to shrink feature-wise dispersion estimates through an empirical Bayes approach. We then used the exactTest for negative binomial data9 to identify features that differ between the specified groups. The resulting p-values were then corrected for multiple testing with the BH method with the function topTags.Using the phyloseq_to_edgeR function  hypothesis test to identify potential differentially abundant features, followed by linear discriminant analysis (LDA) of class labels on abundances to estimate the effect sizes for significant features. From these, only those features with scaled LDA analysis scores above the threshold score of 2.0 (default) were called as differentially abundant. This key step is what distinguished LEfSe from the Wilcoxon test approach based on relative abundances that we also ran. In addition, no multiple-test correction was performed on the raw LEfSe output as only the p-values of significant features above-threshold LDA scores are returned by this tool.The rarefied feature table was first converted into LEfSe format using the LEfSe script format_input.py21 function voom to convert normalized counts to log2-counts-per-million and assign precision weights to each observation based on the mean-variance trend. We then used the functions lmFit, eBayes, and topTable in the limma R package to fit weighted linear regression models, perform tests based on an empirical Bayes moderated t-statistic76 and obtain BH FDR-corrected p-values.We first normalized the non-rarefied feature table using the edgeR calcNormFactors function, with either the trimmed mean of M-values (TMM) or TMM with singleton pairing (TMMwsp) option. We choose to run this tool with two different normalization functions as we found the standard TMM normalization technique to struggle with highly spare datasets despite it previously being shown to perform preferentially in DA testing. Furthermore, the TMMwsp method is highlighted within the edgeR package as an alternative for highly sparse data. During either of these normalization steps a single sample was chosen to be a reference sample using upper-quartile normalization. This step failed in some highly sparse abundance tables; in these cases, we instead chose the sample with the largest sum of square-root transformed feature abundances to be the reference sample. After normalization, we used the limma R package (version 3.42.2)22. We specified arcsine square-root transformation as in the package vignette (instead of the default log) and total sum scaling normalization. For consistency with other tools, we specified no random effects and turned off default standardization. The function fit a linear model to each feature’s transformed abundance on the specified sample grouping, tested significance using a Wald test, and output BH FDR-corrected p-values.We entered either a rarefied or non-rarefied feature table into the main Maaslin2 function within the MaAsLin2 R package (version 0.99.12)11. Next, we used cumNormStat and cumNorm to apply cumulative sum-scaling normalization, which attempts to normalize sequence counts based on the lower-quartile abundance of features. We then used fitFeatureModel to fit normalized feature counts with zero-inflated log-normal models (with pseudo-counts of 1 added prior to log2 transformation) and perform empirical Bayes moderated t-tests, and MRfulltable to obtain BH FDR-corrected p-values.We first entered the counts and sample information to the function newMRexperiment from the metagenomeSeq R package (version 1.28.2)t-test for each feature to compare the specified groups. We corrected the resulting p-values for multiple testing with the BH method.We applied total sum scaling normalization to the rarefied feature table and then performed an unpaired Welch’s p-values with the BH method.Using raw feature abundances in the rarefied case, and CLR-transformed abundances (after applying a pseudocount of 1) in the non-rarefied case, we performed Wilcoxon rank-sum tests for each feature to compare the specified sample groupings. We corrected the resulting 77. Spearman correlations between the percent of significant ASVs identified by a tool and the following dataset characteristics were computed using the cor.test function in R: sample size, Aitchison’s distance effect size as computed using a PERMANOVA test 78, sparsity, mean sample ASV richness, median sample read depth, read depth range between samples and the coefficient of variation for read depth within a dataset. In addition, for the unfiltered analyses, we also computed Spearman correlations with the percent of ASVs below 10% prevalence in each dataset . Correlations were displayed using the R package corrplot (version 0.85) and gridExtra (version 2.3). Dataset manipulation for plotting and reshaping were conducting using the following R packages: doMC (version 1.3.5), doParallel (version 1.0.15), matrixStats (version 0.56.0), reshape2 (version 1.4.4), plyr (version 1.8.6) and tidyverse (version 1.3.0).We compared the number of significant ASVs each tool identified in 38 different datasets. Each tool was run as described above using default settings with some modifications suggested by the tool authors, as noted above. A heatmap representing the number of significant hits found by each tool was constructed using the pheatmap R package (version 1.0.12)We compared the consistency between different tools within all datasets by pooling all ASVs identified as being significant by at least one tool in the 38 different datasets. The number of methods that identified each ASV as differentially abundant were then tallied. A second way of examining the between method consistency without choosing a specific significance threshold was to examine the overlap between the top 20 ASVs identified by each DA method. To do this ASVs were ranked for each DA method depending on their significance value apart from ANCOM-II, where its W statistic was used for ranking. Like the above analysis, we than tallied the number of methods that identified each ASV as being in its top 20 most differentially abundant ASVs. Multi-panel figures were combined using the R package cowplot (version 1.0.0) and ggplotify (version 0.0.5). To get another view of the data principal coordinate analysis plots were constructed using the mean inter-tool Jaccard distance across the 38 main datasets. Distances were computed by averaging over the inter-tool distance matrices for all individual datasets to weight each dataset equally using the R packages vegan (version 2.5.6) and parallelDist (version 0.2.4). Labels were displayed using the R package ggrepel (version 0.8.1).To evaluate the false positive rates of each DA method, eight datasets were selected for analysis based on having the largest sample sizes, while also being from diverse environment types. In each dataset, only the most frequent sample group was chosen for analysis to help ensure similar composition among samples tested. Within this grouping, random labels of either case or control were assigned to samples and the various differential abundance methods were tested on them. This was replicated 100 times for each dataset and tool combination aside from ALDEx2, ANCOM-II, and Corncob. These were run using 100 replicates in only 3 of the 8 datasets ) with 100 ALDEx2 replications also being run in the Human - HIV (3) dataset. This was due to the long computational time required to run these tools on all datasets. The remaining datasets were replicated 10 times for each of these three tools. After this analysis was completed, the number of differentially abundant ASVs identified by each tool was assessed at an alpha value of 0.05. Boxplots for this data was constructed using the R packages ggplot2 (version 3.3.0), ggbeeswarm (version 0.6.0), and scales (version 1.1.0).79 and the dia_schneider55, datasets , to bring the number of diarrhea-related datasets to five. These three pre-existing datasets all related to enteric infections that had all been previously demonstrated to show a distinct signal of microbial differences driven by diarrhea in patient samples23.For this analysis we acquired two additional pre-processed datasets that were not used for other analyses, which are the GEMS164. We also included an additional obesity dataset, ob_zupancic80, that we acquired from the microbiomeHD database.For the obesity cross-study analysis we leveraged four datasets that were part of the core 38 datasets: Human – OB (1–4)The ASVs in each of these datasets were previously taxonomically classified and so we used these classifications to collapse all feature abundances to the genus level. Note that taxonomic classification was performed using several different methods, which represents another source of technical variation. We excluded unclassified and sensu stricto-labeled genus levels. We then ran all differential abundance tools on these datasets at the genus level. These comparisons were between the diarrhea and non-diarrhea sample groups. The same processing workflow was used for the supplementary obesity dataset comparison as well.For each tool and study combination, we determined which genera were significantly different at an alpha of 0.05 (where relevant). For each tool we then tallied the number of times each genus was significant, i.e., how many datasets each genus was significant in based on a given tool. The null expectation distributions of these counts per tool were generated by randomly sampling genera from each dataset. The probability of sampling a genus  was set to be equal to the proportion of actual significant genera. This procedure was repeated 1000 times, with genus replicates equal to the actual number of tested genera . For each replicate we tallied the number of times the genus was sampled across datasets. Note that to simplify this analysis we ignored the directionality of the significance . We also excluded genera never found to be significant. We computed the mean of these 1000 distributions to generate an empirical distribution of the expected mean number of studies where a genus would be called as significant, given random sampling. We determined where the observed mean values lay on each corresponding distribution to calculate statistical significance.81. Multiple different optimal abundance cut-offs were then used to classify samples based on the input ASVs abundance. Classifications were then compared to the true sample groupings to generate ROCs for each ASV within the 38 tested datasets. For each tool the mean AUC of all ASVs identified as being differentially abundant in each dataset was computed, based on both relative and CLR abundances separately. We then calculated the precision, recall and F1 scores of each tool for the tested datasets when AUC cut-offs of 0.7 or 0.9 were used. In each case the ‘true positives’ were treated as features that were above the specified AUC threshold.We calculated the discriminatory value of each ASV  based on the area under the curve (AUC) of the receiver operator curve (ROC) for that ASV. This was performed independently for both non-rarefied relative and CLR abundances. For each ASV in a dataset the abundance of that ASV along with metadata groupings was used as input into the prediction function in the ROCR R packageFurther information on research design is available in the Supplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Data 1Reporting Summary


Multi-omics molecules regulate complex biological processes (CBPs), which reflect the activities of various molecules in living organisms. Meanwhile, the applications to represent disease subtypes and cell types have created an urgent need for sample grouping and associated CBP-inferring tools. In this paper, we present CBP-JMF, a practical tool primarily for discovering CBPs, which underlie sample groups as disease subtypes in applications. Differently from existing methods, CBP-JMF is based on a joint non-negative matrix tri-factorization framework and is implemented in Python. As a pragmatic application, we apply CBP-JMF to identify CBPs for four subtypes of breast cancer. The result shows significant overlapping between genes extracted from CBPs and known subtype pathways. We verify the effectiveness of our tool in detecting CBPs that interpret subtypes of disease. Complex biological processes (CBPs) are the coordinated effect of multiple molecules, which result in some functional pathways and the vital processes occurring in living organisms. In addition, the vast amounts of multi-omics data, such as genomics, epigenomics, transcriptomics, proteomics, and metabolomics, can be integrated to understand systems biology accurately . For example, Brunet et al. (etc. (more details are in Non-negative matrix factorization (NMF)  data. The natural representation of these diverse MG data is a series of matrices with measured values in rows and individual samples in columns. Recently, there are integrative analysis tools based on NMF technique that reveal low-dimensional structure patterns. The low-dimensional structure patterns reflect CBPs and sample groups while preserving as much information as possible from high-dimensional MG data  to identify the underlying CBPs which characterize the specific functional properties of each group. CBP-JMF can be used to mark unlabeled samples with groups of known labels. For ease of use, CBP-JMF can recommend reasonable parameter settings for users. CBPs found by CBP-JMF are connected network markers, and they are distinguished between sample groups. These markers usually have specific biological functions and play important roles in phenotypes. As an example, CBPs for subtypes of breast cancer are obtained by CBP-JMF, but they may not have been collected in any reference database yet.In general, most particular matrix factorization techniques are being developed to enhance their applicability to specific biological problems. Meanwhile, the applications to represent disease subtypes , X(2), ..., XP) is a matrix of gene expression data, i-th row on the j-th sample. Basically, each non-negative matrix Xp)( ≈ Up)(Sp) Up)( ∈ Rm×k and sample basis matrix (SBM) V ∈ Rk×n are the pattern indicator matrices of k CBPs and k sample groups, respectively. Scale absorbing matrix (SAM) Sp), SBM indicates the structure pattern between samples, and SAM absorbs the difference of scales between MCM and SBM , X(2), ..., XP)( can be jointly factorized into specific U(1), U(2), ..., UP), S(2), ..., SP), X(2), ..., XP), π(2), ..., πP). CBP-JMF differentiates the importance of datasets by the weight constraint ||Π||2, and πp)( will get a weight to represent the contribution of data Xp)( to objective function after optimization. If Xp) and Wp  are the weighted adjacency matrices (see La (Laffinity) and Lp  are the Laplacian matrix of Wa and Wp, respectively, where La=Da − Wa, Lp=Dp − Wp, Da=where ices see  in SM coCombining weighted joint tri-NMF and the constraints of correlation between labeled samples mentioned above, we give the formulation of the optimization objective function of CBP-JMF as follows :2. In total, each Xp); we incorporate this prior information with graph Laplacian. We can also learn the weights of different input data to conclude the roles that different data matrices play in CBP-JMF.Parameters β and ω represent the importance of the graph Laplacian regularization and weight constraint ||Π||X ≈ USV, we firstly randomly initialize the solution of U, S, and V and then apply iterative multiplicative updates as the optimization approach similar to EM algorithms  with U is:The partial derivatives of ijUij = 0, we can get the following update rules:Based on the KKT conditions ΨW, VL, and VUL:Similarly, we can get the update rules for U,V, and S are fixed, minimization of O(π) is a convex optimization, and we use convex optimization toolbox to update π.As for updating of π, when Up)( as j-th column of Up). CBP-JMF calculates a z-score for each value in z-score >2 in our tests). Then, they are mapped to a built-in molecule interaction network (see “Section ‘Results”') to extract their connected components as the final CBP.To select features associated with each module, CBP-JMF calculates the z-scores of each molecule for each column vector of We applied CBP-JMF to BRCA with multi-omics data. The reason we chose BRCA as example is that breast cancer is a heterogeneous complex disease, and it is the most commonly occurring cancer. BRCA is also a type of cancer that can be divided into smaller groups based on certain characteristics of the cancer cells. Distinct complex biological processes represent different subtypes. Characterizing the processes can provide us comprehensive insights into the mechanisms of how multiple levels of molecules interact with each other and the heterogeneity of breast cancers.P-value < 0.01 and |log(fold change)|> 0.5 to filter out genes which are not associated with breast cancer. Fifthly, we imputed missing miRNA data using knnimpute package in MATLAB. About the CNV data, the GISTIC2  ∈ R2913×725 and ME data X(2) ∈ R516×725. Among 725 samples, 179 samples are marked with subtype labels  and shared between GE, ME, and CNV datasets. Furthermore, we calculated the Pearson correlation of 179 labeled samples using CNV data to construct Wa ∈ R179×179, Wp ∈ R179×179, and their Laplacian matrices to form the graph Laplacian regularization Firstly, we downloaded the Gene Expression (GE) data, miRNA expression (ME) data, and copy number variation (CNV) data across the same set of 738 breast cancer samples from UCSC Xena  ∈ R2913×4, U(2) ∈ R516×4, S(1) ∈ R4×4, and S(2) ∈ R4×4 and a common matrix V ∈ R4 ×725.In our example, we set parameters Up)(, p = 1, 2 onto an integrated gene regulation network from Reactome (Croft et al., To get heterogeneous CBPs , directeTo explore whether the genes in the CBPs of luminal B and basal-like subtype have significant biological importance or not, we performed an enrichment analysis with all 124 genes from p-value 0.031 and similar survival curves like the labeled samples. This proves that the CBP-JMF framework is useful for cancer subtyping, as the framework incorporates integration of multi-omics data and samples' prior information.Meanwhile, to classify unlabeled samples into subtypes, CBP-JMF returned predicted labels for unlabeled samples . Figure Understanding CBPs is vital to help us further understand the development of disease and intervene in the disease. NMF is an effective tool for dimension reduction and data mining in high-throughput genomic data. In this paper, we proposed CBP-JMF, an improved method of multi-view data analysis. It is designed for heterogeneous biological data based on NMF. Moreover, we created an easy-to-use package in Python. CBP-JMF analyzes multi-dimensional genomic data across the same samples integrally. Our method can discover CBPs that underlie sample groups and classify unlabeled samples through learning the relationship between labeled samples.We tested this framework on the gene expression data and miRNA expression data of BRCA. CBP-JMF discovered subtype-specific biological processes and classified unlabeled samples into four subtypes. We did survival analysis and function analysis, and the results showed that CBP-JMF has great performance. Furthermore, CBP-JMF is a weighted joint tri-NMF framework in essence. We expect that it can be applied to vast fields including disease subtypes, cell types, and population stratification. Meanwhile, we expect that CBP-JMF can be used to identify hub genes or predict the association between genes or non-coding mRNA and diseases by integrating a variety of data. Though CBP-JMF is efficient to uncover CBPs by integrating multi-omics data, CBP-JMF must integrate different multi-omics data that have the same samples. This weakness limits the use of more types of data and integrates more information to obtain more significant results.In this article, we develop CBP-JMF, a matrix tri-factorization and weighted joint integration tool, for detecting CBPs, which characterize prior disease subtypes and cell groups in Python. We improve its usability by estimating the parameters, such as determining the number of features through consensus clustering. CBP-JMF always gives reference values of all parameters. In applications, CBP-JMF characterizes the CBPs of four subtypes of BRCA based on gene and miRNA expression data from TCGA, and we find the significantly different functional pathways that characterized luminal B and basal-like subtypes.https://github.com/wangbingbo2019/CBP-JMF.The datasets presented in this study are publicly available and the addresses for finding them are listed within the article. Prediction results and a reference implementation of CBP-JMF in Python are available at: BW, YWu, and XM conceived and designed the experiments. YWu and MX performed the experiments. XM, RD, CZ, LY, XG, and LG analyzed the data. BW, YWu, XM, and YWa proofread the paper. All authors contributed to the article and approved the submitted version.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Many analyses require “mosaic integration”, including both features shared across datasets and features exclusive to a single experiment. Previous computational integration approaches require that the input matrices share the same number of either genes or cells, and thus can use only shared features. To address this limitation, we derive a nonnegative matrix factorization algorithm for integrating single-cell datasets containing both shared and unshared features. The key advance is incorporating an additional metagene matrix that allows unshared features to inform the factorization. We demonstrate that incorporating unshared features significantly improves integration of single-cell RNA-seq, spatial transcriptomic, SNARE-seq, and cross-species datasets. We have incorporated the UINMF algorithm into the open-source LIGER R package ( Single-cell genomic technologies present unique data integration challenges. Here the authors introduce an integrative nonnegative matrix factorization algorithm that incorporates features unshared between datasets when performing dataset integrations, improving integration results for spatial transcriptomic, cross-modality, and cross-species data. Each cell type or state within an organism is distinguished by its gene expression, epigenetic regulation, and spatial location within a tissue. Single-cell sequencing technologies measure each of these features in individual cells, allowing researchers to classify cells in a data-driven manner. Determining what features are common, or different, between each cell type provides researchers insight into the function of the cell. Comparing the profiles of diseased cells with those of healthy cells also reveals disease-related aberrant features. An ideal characterization of a cell type goes beyond analyzing features such as epigenetic and gene expression individually, instead examining their relationships. Jointly examining cellular features holds promise for understanding gene regulatory mechanisms that control cell fates.1. In particular, emerging techniques such as the Multiome assay from 10X Genomics can measure gene expression and chromatin accessibility from the same cell7, but do not generally capture methylation or spatial features. Spatial transcriptomics, named Method of the Year 2020 by Nature Methods8, encompasses a rapidly growing suite of techniques12 that interrogate gene expression patterns within intact tissue. However, protocols for spatial measurements of epigenomic state are not widely available.Current single-cell sequencing technologies cannot simultaneously measure all relevant aspects of cell state. Recently developed multi-omics technologies are limited to capturing only a couple of the modality measures that encompass cell identity13, are designed for datasets containing multiple modalities measured within the same cells, while other approaches focus on integrating modalities from different single cells into a shared latent space. Most existing computational approaches for multi-omic data integration are designed for either vertical or horizontal integration scenarios15. Vertical integration approaches are useful for datasets measured across a common set of samples or cells. Well-established methods for multi-omic integration of bulk data, such as similarity network fusion and iCluster17, fall into this category, as well as recent methods for single-cell datasets with multiple modalities per cell such as MOFA+, totalVI, and the Seurat v4 weighted nearest neighbors algorithm20. Conversely, horizontal integration uses a set of common variables or features to integrate over multiple experiments, typically using shared genes as the anchors for integration. Batch effect correction approaches originally designed for bulk sequencing data  solve a horizontal integration problem. Similarly, dataset alignment algorithms developed for single-cell data, such as Seurat v3, Harmony, and our previous method LIGER26 also rely on shared features and can thus be considered horizontal integration techniques.The different types of features measured by different single-cell technologies create unique computational data integration challenges. Some more recent methods, such as Seurat v4’s Weighted Nearest Neighbor (WNN) algorithm15. In this review, Argelauget et al. also identified a type of problem that they call mosaic integration–in which only some features or cells are shared across datasets–and for which they did not identify any existing approaches. Our work here aims to address some of the challenges of mosaic integration.A recent review of single-cell computational integration approaches identified a third category of approaches as those for diagonal integration, in which neither features nor cells are assumed to be shared across datasets27. However, these three approaches are all constrained to integrate across features shared between datasets, and require that the input matrices all contain a common set of genes or features that are measured in all datasets. Thus, these methods cannot incorporate features unique to one or more datasets, such as intergenic epigenomic information.LIGER, Seurat v3, and Harmony are effective tools for a number of single-cell integration tasks, and were chosen as the best methods in a recent systematic comparison of 14 computational methods5 or 10X Multiome with single-cell or spatial transcriptomic datasets. Such integration analyses do not fit neatly into either the horizontal or vertical integration paradigm, requiring the development of different methods.Restricting single-cell integration analyses to features shared across all datasets is problematic because it often necessitates discarding pertinent information. For instance, scRNA-seq measures transcriptome-wide gene expression within individual cells, but spatial transcriptomic protocols often measure only a chosen subset of all genes. Yet for many applications, we want to integrate scRNA-seq and spatial transcriptomic datasets, which have neither the same number of features (genes) nor the same number of observations (cells). By integrating the datasets using only shared features, we fail to capitalize on the higher resolution provided by the scRNA-seq modality. When integrating cross-species datasets, the integration is restricted to orthologous genes, disregarding all genes without unambiguous one-to-one relationships between species. Likewise, when integrating single-cell epigenomic data with single-cell transcriptomic data, horizontal integration approaches do not take into account the important epigenomic features from intergenic regulatory elements. As a final example, existing methods do not provide a way to leverage paired epigenomic information when integrating data types such as SNARE-seqThe critical need to include unshared features in single-cell integration analyses motivated us to extend our previous approach. We developed UINMF, a nonnegative matrix factorization algorithm that allows the inclusion of both shared and unshared features. UINMF can integrate data matrices with neither the same number of features  nor the same number of observations (cells). Furthermore, UINMF does not require any information about the correspondence between shared and unshared features, such as links between genes and intergenic peaks. By incorporating unshared features, UINMF fully utilizes the available data when estimating metagenes and matrix factors, significantly improving sensitivity for resolving cellular distinctions. Note that UINMF is not designed to jointly leverage multiple modalities from the same cell as in Seurat v4 or MOFA; rather, the approach solves a problem more like the Seurat v3 anchors approach.U to the iNMF objective function, incorporating features that belong to only one, or a subset, of the datasets when estimating metagenes and cell factor loadings. Previously, dataset integration using the iNMF algorithm operated on features common to all datasets25. Each dataset (Ei) was decomposed into dataset-specific metagenes (Vi), shared metagenes (W), and cell factor loadings (Hi), and the optimization problem was solved iteratively. By including an unshared metagene matrix (Ui), we provide the capability to include unshared features during each iteration of the optimization algorithm . Furthermore, the addition of the unshared features in each iteration of the matrix decomposition does not impose a prohibitive increase in time or memory usage in practice. Rather, UINMF demonstrates a moderate increase in time and memory usage due to the unshared features while providing significant benefits compared to algorithms incapable of incorporating unshared features , we progressively decreased the number of shared genes from 500 to 100. We then performed two UINMF integrations, one using the SMART-seq data as the source for the unshared features, and the other using the 10X dataset as the source for the unshared features. We calculated the ARI and purity scores for each resulting integration al genes 500, we pOur results indicate that using unshared genes from the SMART-seq data, known to be higher quality than the 10X data, consistently increases the quality of dataset integration, even with a continued reduction in the number of shared genes. The 10X data, while initially improving dataset integration, is more dramatically impacted by the reduction of shared features. Nevertheless, the benefit of using UINMF to include additional features in dataset integrations is clear, with the amount of benefit derived correlated with the quality of the dataset from which the unshared features are being chosen.13. In contrast, UINMF uses the unshared feature matrix to incorporate the ATAC reads present between genes–intergenic peaks–when estimating the metagenes 25, which uses only gene-centric features. Over multiple random initializations, iNMF obtained an average FOSCTTM score of 0.2977 and an average alignment score of 0.756 , as well as a significantly higher average alignment score of 0.812 . These findings indicate that incorporating unshared features from the chromatin accessibility data improves the integration of scRNA and snATAC datasets.In contrast, UINMF achieved a significantly lower average FOSCTTM score of 0.251  and FOSCTTM score . Compared to Seurat v3, UINMF had a significantly improved alignment score , however, Seurat v3 did have a significantly better FOSCTTM score than UINMF .We also compared UINMF with Seurat v3 and Harmony. UINMF significantly outperforms Harmony in both alignment , taking the best of 5 initializations over 10 seeds, and calculating the alignment and FOSCTTM scores. We then added the 1,000 most variable intergenic bins, and repeated the analysis and metric calculations. Iteratively, we added the next 1000 top variable intergenic bins until we reached 7000 unshared features. As the number of variable intergenic bins used increases, the alignment Fig.  and FOSCWe expect the UINMF algorithm to be especially effective for integrating targeted spatial transcriptomic datasets, as the number of genes measured in such datasets is often limited. Integrating such datasets with scRNA-seq provides the opportunity to pair transcriptome-wide profiles from dissociated cells with spatial transcriptomic data. This mitigates the loss of sensitivity for distinguishing cell types, while mapping cell types to their spatial positions within a tissue.10 and scRNA-seq data29. We used a STARmap dataset that contains spatial position and transcription level for 28 genes across 31,294 cells within a 3D block of tissue from the mouse frontal cortex. To our knowledge, this dataset is unique in that it is the only dataset of spatially resolved gene expression for multiple genes within a 3D tissue block.To explore the utility of the UINMF algorithm for integrating targeted spatial transcriptomics and scRNA-seq datasets, we analyzed STARmap data29 and perform Louvain community detection. We annotate the scRNA-seq cells using their previously published cellular annotations29. We observe improved cluster resolution using iNMF with only shared genes to integrate the STARmap dataset with the scRNA-seq dataset , paired one-sided Wilcoxon test) higher ARI and cluster purity compared to the iNMF algorithm. UINMF also significantly outperforms both Seurat v3 and Harmony in both ARI and purity metrics . In short, the addition of the unshared genes significantly improves the integration of STARmap and single-cell RNA-seq data.To quantify the advantage of the UINMF method, we calculated Adjusted Rand Index (ARI) and purity metrics for multiple initializations of the UINMF and iNMF algorithms across a range of different Louvain resolution parameters Fig. . The UINW, V1, V2, and U) for each factor (methods). Both U and V are regularized in the UINMF objective to encourage the reconstruction to come primarily from the shared factors. Consistent with this regularization, we found that W, the shared metagenes, contributed the most to the matrix reconstruction, and the dataset-specific V1 and V2 contributed the least 33, which are known to comprise vascular structures. Using KNN imputation, we are able to visualize the imputed gene expression within the 3D volume . Using iNMF to integrate the osmFISH and DROPviz datasets utilizes the 33 genes measured in the osmFISH protocol as the shared features res Fig. . The iNMres Fig. . Using Ures Fig. . A disti34. The white matter region, located inferior to layer 6 and known to be composed of oligodendrocytes and polydendrocytes36, is likewise observable. Lastly, the presence of the caudoputamen and internal capsula region can be identified by the small grouping of inhibitory neurons lateral to the white matter12.As with the STARmap data, we then plotted the derived UINMF labels within their corresponding spatial context Fig. . The exc−16, paired one-sided Wilcoxon test) and purity  metrics across the whole range of clustering resolutions. A similar improvement was observed when comparing the UINMF performance to Seurat v3 and Harmony. Note that only a single value is shown for Seurat v3 and Harmony at each resolution because these algorithms are deterministic. UINMF performed significantly better than Seurat v3 and Harmony in both ARI  and purity  metrics.To quantify the advantage of using UINMF, we measured the ARI and purity scores for both UINMF and iNMF over multiple initializations and multiple clustering resolutions Fig. . UINMF pSingle-cell multimodal technologies measure epigenomic and transcriptomic profiles from the same cell, providing an exciting opportunity to define cell types from multiple molecular modalities. However, many applications require integrating such multimodal measurements with single-modality datasets. In such applications, the ability of UINMF to incorporate unshared features allows us to capitalize on the multimodal information, rather than using only shared features.To demonstrate the advantages of such an approach, we used UINMF to integrate STARmap and SNARE-seq data. The STARmap dataset provides gene expression data for 2522 cells across 1020 genes while preserving the 2D spatial coordinates for each cell. The SNARE-seq dataset  provides simultaneous chromatin accessibility and gene expression levels from the same barcoded cells.U matrix  and purity . The iNMF algorithm has an ARI competitive with that of UINMF at only a single louvain resolution (0.7). At this resolution, UINMF still has a superior purity score, substantiating the benefit of including additional features using the UINMF algorithm.To quantify the derived benefit of including the additional features into the analysis, we then calculated the purity and ARI scores for ten initializations Fig. . UINMF sP = 0.0004184). Additionally, UINMF also has superior purity over Seurat v3 across all tested resolutions . Similarly, UINMF has a significantly higher purity score (P = 2.2 × 10−16) at all Louvain resolution in comparison to Harmony. UINMF also has a significantly higher average ARI score than Harmony at all Louvain resolutions (P = 0.002927). While Harmony does achieve higher ARI scores at the higher Louvain resolutions, it is critical to note that these are clearly not optimal values for this dataset. Taken together, these results show that the use of UINMF to incorporate added features to the data integration significantly improves the integration of single-cell multimodal data and spatial transcriptomic data.Next, we benchmarked the UINMF method against Seurat v3 and Harmony. In comparison to Seurat v3, UINMF has a significantly better ARI score across resolutions  as unshared features. We also integrated the SNARE-seq and STARmap datasets using UINMF, and only the unshared peaks (1431 peaks) as unshared features  from the pallium of the bearded dragon lizard (Pogona vitticeps)37 with scRNA data from the mouse frontal cortex 29. We first selected 1979 variable genes that were annotated as one-to-one orthologs between the two species. Then we selected an additional 166 non-orthologous variable genes from the lizard dataset. We integrated the datasets using UINMF, with the one-to-one orthologs as shared features, and the non-orthologous genes from the lizard as unshared features  and the purity  of the mouse dataset  of the lizard data set  of the lizard dataset, UINMF is able to achieve a higher maximum purity score at most resolutions  and lizard  labels. When comparing ARI scores, there is not a significant difference between Seurat v3 and UINMF using the lizard labels ; however, the mouse labels show a significant improvement . Therefore, UINMF significantly outperforms Seurat v3 on three out of the four measures assessed. When examining the difference in performance between UINMF and Harmony, Harmony shows significantly improved ARI  and purity  scores using the mouse labels. However, UINMF has superior performance when comparing the ARI  and purity  scores using the lizard labels. Harmony’s increased performance using the mouse labels, but decreased performance when using the lizard labels, leads us to believe that Harmony has learned principal components driven primarily by the mouse dataset, neglecting to learn factors that likewise distinguish the lizard cells. The large difference in dataset size between the mouse  and lizard (4187 cells) supports this hypothesis. UINMF innovatively learns joint metagene factors, resulting in a final integration that respects biological factors in both datasets.We also compared the Purity and ARI scores of UINMF to those achieved by Seurat v3 and Harmony. UINMF shows a significant improvement in purity scores over Seurat v3 using both mouse , mouse (8242 cells), and the marmoset (8166 cells)Using 2757 orthologous genes shared between all three species as shared features, we then selected 353 non-orthologous mouse genes, 290 non-orthologous marmoset genes, and 671 non-orthologous human genes as unshared features. UINMF successfully aligned the three datasets , with those L5 ET mouse cells that were unaligning (Cluster 13). We observed that the ion channel subunits previously annotated25 by adding an unshared feature matrix. This addition accommodates features that are not present in all datasets and increases the amount of information that is used to define the metagenes. We showed that the inclusion of unshared features provides clear advantages across four different types of integration analyses. First, UINMF can be used to incorporate intergenic information when integrating transcriptomic and epigenomic datasets. Second, UINMF can incorporate genes not measured in targeted spatial transcriptomic datasets, allowing better resolution of fine cellular subtypes within a spatial coordinate frame. Third, UINMF can utilize all of the information present in single-cell multimodal datasets when integrating with single-modality datasets. Additionally, UINMF can accommodate non-orthologous genes in cross-species integration analyses.We have extended our previous integrative nonnegative matrix factorization algorithm39. Therefore, the resulting reduced dimensions are not biologically interpretable. In contrast, UINMF learns factor loadings that represent metagenes, groups of genes that often reflect an underlying biological process or technical artifact. Second, MultiMAP makes a key assumption that the data is uniformly distributed on the latent manifold. While this assumption may hold at times when the datasets to be integrated are sampled from the same tissue, several common integration scenarios violate this assumption. For example, nuclear isolation protocols and whole-cell dissociation protocols each have different cell-type-specific biases, leading to different cell type distributions. Similarly, cross-species integrations may present a challenge if the proportions of homologous cell types are different. In contrast, UINMF does not rely on the uniform distribution assumption.A recent preprint described MultiMAP, another single-cell data integration approach that can incorporate unshared features. Our approach differs from MultiMap in several key ways. First, MultiMAP uses singular value decomposition followed by nonlinear dimensionality reductionU matrix can incorporate any type of cellular features, with no assumptions about their relationship to gene-centric features, the algorithm is inherently flexible to accommodate a variety of data types and modalities. Future applications could examine the incorporation of data types such as Hi-C40 measurements, as well as the potential to use UINMF on a diverse collection of in situ hybridization and immunohistochemistry datasets with limited numbers of genes. We expect that, as additional experimental methods for single-cell measurement are developed, our approach will prove increasingly useful for a broad variety of single-cell integration tasks.With the rapid development of multimodal and spatial transcriptomic technologies, we anticipate that the UINMF algorithm will prove useful for a wide variety of analyses. As the additional 25 so that we can now incorporate unshared features when integrating across datasets. The unshared feature matrix can accommodate any type of unshared feature, whether gene-centric or otherwise. In this paper, we incorporated intergenic peaks from snATAC-seq data and additional genes not measured in all datasets, although many other applications are possible.We extend our previously published ANLS algorithm for solving the iNMF problemE1, E2, ....En, we normalize the data, and select m variable genes , and zi variable features , such that after scaling i = 1,....,N). For a given K, the user-defined number of metagenes, and λi, the UINMF optimization problem is:Pi is the unshared feature matrix, Hi are the cell factor loadings, W is the shared metagenes, Vi are the dataset-specific, shared metagenes, and Ui are the dataset-specific, unshared metagenes.For each data set 41 for solving the UINMF optimization problem. The BCD approach divides the parameters into blocks, and then finds the optimal parameters by updating each block while holding the others fixed. Because each block-wise optimization sub-problem is convex, iterating these updates is guaranteed to converge to a local minimum41. To solve the UINMF optimization problem, we use matrix blocks, one block for each of We then derive a coordinate block descent (BCD) algorithm42. To update Hi, we solveε = 1.0 × 10−10 and set the maximum number of iterations to 30 for each analysis, unless otherwise noted.Each sub-problem is a nonnegative least squares optimization, which we solve numerically using an efficient C++ implementation of the block principal pivoting algorithmλ for all datasets. When implementing UINMF, however, we introduced a separate λi parameter for each dataset, such that the penalty applied to E is weighted by λ1, E2 has a regularization weight of λ2, etc. The inclusion of λi allows for the tuning of dataset penalization at the user’s discretion. We found that in some cases, using a different penalty value for different datasets could improve results. However, we simply used λi = 5  for all analyses except the STARmap and DROPviz integration. The STARmap and DROPviz integration does achieve the best results with different λ values for each dataset.Note that iNMF uses a constant penalty term g shared features, and let g = m + z, where m is the number of shared features and z is the number of unshared features of the UINMF dataset. Let K be the user-defined number of metagenes. For each iteration, UINMF solves for Uz × K and Vim × K separately, but iNMF performs the same number of calculations to solve for g = m + z. When solving for the shared metagene matrix, W, iNMF solves the optimization problem for a g × K matrix, whereas UINMF must only solve a m × K matrix. Because the shared metagene matrix has less features in UINMF (g > m), each iteration of the algorithm actually constitutes less computational complexity than iNMF given the same total number of features.The difference in computational complexity between UINMF and iNMF increases with the number of unshared features used in UINMF, but the difference between the runtime of the two algorithms is not prohibitive in practice  as well as the IntegrateData (Seurat 4.0.0) functions. The number of principal components within RunPCA (Seurat 4.0.0) was also set to 27 for Harmony as well as Seurat v3 , is a measure that captures how well two samples align uniformly within a latent space. A score closer to zero indicates a poor alignment, or mixing of the two samples, whereas a score closer to one is indicative of datasets that share underlying cell types.3. We calculate the FOSCTTM score by finding the distance between the scRNA-seq cell and the snATAC-seq label for each barcode. We then divide by the total number of barcoded cells to derive the average FOSCTTM score.Fraction of Samples Closer Than the True Match (FOSCTTM) scores measures how closely two measurements of the same cell are placed within the latent spaceCluster purity is calculated based on a reference clustering. Each cluster is assigned a type based on the predominant label for that cluster. The cells that correspond correctly to this label are counted. We calculate purity by summing the correct number of labels across all clusters, and dividing by the total number of labeled cells present. Consequently, a score closer to 0 indicates that the cells are not being accurately grouped into clusters by cell types, and a score of 1 indicates perfect grouping by cell type.To calculate the Adjusted Rand Index (ARI), we measured the similarity between two clusterings by whether we observe matching or non-matching clustering between pairs of samples. The ARI score can range from 0 (no matches) to 1 (perfect matching).2 with iNMF, using the top 2589 variable genes and their associated snATAC peaks. We took the best optimization of 5 random initializations, each performed with K = 30 and λ = 5, across ten random seeds. We performed quantile normalization with parameter knn_k = 20. We then calculated the average FOSCTTM and alignment scores for each of the 10 random seeds. To assess the additive properties of including the intergenic peaks into the integration, we used the U-matrix to hold 1000, 2000, 3000, 4000, 5000, 6000, and 7000 of the top variable intergenic bins. To select these bins, we binned the genome into sections of 100,000 bp. We counted the number of peaks within each bin, where a peak was considered to be inside a bin if over 50% of the peak’s base pairs overlapped the bin. We then filtered the bins, removing bins that were empty, or overlapping with ENCODE Blacklisted regions43, genes or promoters. After normalization, we then used the FindVariableFeatures function (Seurat 4.0.0) to select the top variable bins. We saw the greatest improvement in performance using 7000 intergenic bins, as this allowed the capture of a large amount of the data variance, without oversaturating the factor loadings with noise. We performed UINMF with K = 30, λ = 5, and knn_k = 20. Using a paired, one-sided Wilcoxon test, we compared the FOSCTTM and alignment scores of UINMF and iNMF.For a baseline, we integrated the scRNA and snATAC datasets that resulted from the original SNARE-seq publicationTo compare UINMF performance to that of Seurat v3 and Harmony, we integrated the two datasets using the 2589 shared features. For Seurat v3, we used a PCA dimension of 30. To compare UINMF and Seurat v3 performance, we performed a paired, one-sided Wilcoxon test on the alignment and FOSCTTM scores of UINMF and Seurat v3.RunPCA (Seurat 4.0.0). We also used 30 neighbors for the FindNeighbors function. We calculated the alignment and FOSCTTM, and then performed a paired, one-sided Wilcoxon test to assess the difference between UINMF and Harmony performance. To cluster just the RNA and ATAC cells, we similarly used K = 30, λ = 5, knn_k = 100, and a Louvain resolution of 1. To derive ground truth cell type labels, we clustered and annotated the RNA-seq cell barcodes using marker genes. We use these consistent labels as ground truth labels for each UMAP presented in Fig. Similarly, to run Harmony, we used the 2589 shared features and 30 principal components for K = 27 dimensions for both iNMF and Seurat v3. For iNMF we also used λ = 5, and a quantile normalization with K-nearest neighbors of 20. Using UINMF, we included an additional 2775 of the most variable genes. The parameters for the UINMF integration were K = 40 and λ = 10 for the STARmap data and λ = 1 for the scRNA-seq data; knn_k = 20 for the quantile normalization; and Louvain resolution of 1. For both iNMF and UINMF, we perform 5 initializations with the same random seed and pick the best one. We calculate the cluster purity for both algorithms using the scRNA-seq labels, and use the highest number of cells present to annotate the clusters by cell type. These annotations were then applied within the context of 3D space using the originally provided STARmap coordinates. For five different random seeds, we measured the difference between the cluster purity and ARI of iNMF and UINMF using a paired, one-sided Wilcoxon test.We integrated the STARmap spatial transcriptomic dataset  and a scRNA-seq dataset ) using iNMF. For this iNMF analysis, we were limited to the 28 genes measured in the STARmap dataset. Both iNMF and CCA/PCA (used by Seurat v3) are limited to no more components than the number of genes, while UINMF can estimate more dimensions because it also incorporates unshared genes. We thus used For Seurat v3, we similarly used the 28 shared genes and a PCA dimension of 27. We then calculated the Purity and ARI scores at each Louvain resolution from 0.1 to 1, in increments of 0.1. We performed a paired, one-sided Wilcoxon test to assess the difference between UINMF and Seurat v3 performance quantified by purity and ARI scores.RunPCA (Seurat 4.0.0). We also used 27 as the number of dimensions used for the FindNeighbors function. For each Louvain resolution from 0.1 to 1, in increments of 0.1, we calculated the purity and ARI scores. We then performed a paired, one-sided Wilcoxon test to assess the difference between UINMF and Harmony performance quantified by purity and ARI scores.Similarly, to run Harmony, we used the 28 shared genes and 27 principal components for λ = 5 and K = 27 for all time and memory analyses.To analyze the effect of the additional features on the memory usage and run time of the algorithm, we performed five initializations for 0, 1000, 2000, 3000, and 4000 extra features  to the matrix reconstruction, we develop the calcNormLoadings function. Since l in K, we measure the contribution to reconstruction asTo examine the individual contribution of each factor , n_neighbors = 150 for the runUMAP function (rliger 1.0.0), and a resolution of 0.5 for Louvain community detection (rliger 1.0.0).Using the osmFISH dataset  we excluded hippocampal and cells from the top left of the tissue slice originally labeled “excluded” in the original osmFISH publication, as well as cells with zero detected genes. A total of 5185 cells passed these filtering criteria. The scRNA-seq dataset, originally 71,639 cells, was reduced to 70,020 . We ran the  iNMF algorithm using the 33 shared genes, For the Seurat v3 integration, we also used the 33 shared genes and a PCA dimension of 32. Using louvain resolutions from 0.1 to 1.0 in 0.1 increments, we assessed the performance of Seurat v3 using purity and ARI scores. We compared Seurat v3 and UINMF using a paired, one-sided Wilcoxon test.RunPCA and FindNeighbors functions (Seurat 4.0.0). We quantified Harmony performance by calculating purity and ARI scores for louvain resolutions from 0.1 to 1.0 in 0.1 increments, and compared the results against UINMF using a paired, one-sided Wilcoxon test.Using Harmony, we integrated the two datasets using the 33 shared genes and 32 as the number of principal components and dimensions for the 37 originally had 4202 cells, but we limited the cells used to the 4187 cells deemed high quality in the original publication. We integrated this dataset with the scRNA-seq dataset from the mouse brain29 . We used the original publication’s 1-to-1 ortholog labels to select orthologs common to both the mouse and lizard dataset. Using these as our shared features, we normalized and scaled the data. We then selected 1979 shared genes, using a variance threshold of 0.3. For UINMF, we used the same variance threshold to select 166 non-orthologous genes from the lizard. We optimized UINMF and iNMF with K = 30, λ = 5, and took the best of 5 random initializations for 10 random seeds. We performed quantile normalization for each optimized object using the mouse dataset as a reference. To ensure that any differences in purity and ARI score were not driven by a single species, we calculated the ARI and Purity scores using both the lizard and the mouse cell labels separately as ground truth. We performed these calculations for each of the ten seeds at louvain resolutions from 0.1 to 1.0 in increments of 0.1. To examine the difference between UINMF and iNMF performance, we performed a paired, one-sided Wilcoxon test between the ARI and Purity values, for the mouse and lizard labels, respectively. When generating the UMAPs shown, we used the default louvain resolution of 0.25, and the default nearest neighbors of 10.The Lizard Pallium datasetFor Seurat v3 integration, we used the 1979 highly variable, orthologous genes identified between the datasets, and a PCA dimension of 30. Using louvain resolutions from 0.1 to 1.0 in 0.1 increments, we assessed the performance of Seurat v3 using purity and ARI scores with both the lizard and mouse annotations. To compare the performance of Seurat v3 and UINMF, we used a paired, one-sided Wilcoxon test.RunPCA and FindNeighbors functions (Seurat 4.0.0). We quantified Harmony performance by calculating purity and ARI scores for louvain resolutions from 0.1 to 1.0 in 0.1 increments, and compared the results against UINMF using a paired, one-sided Wilcoxon test.Similarly, when evaluating the performance of Harmony in integrating the two datasets, we use the same 1979 orthogolous genes. We use 30 as the number of principal components and dimensions for the K = 30, λ = 5, and took the best of 5 random initializations for 10 random seeds. We performed quantile normalization for each optimized object using the SNARE-seq dataset as a reference. Using the SNARE-seq cell labels as ground truth, we calculated the ARI and Purity scores for each of the ten seeds at louvain resolutions from 0.1 to 1.0 in increments of 0.1. We set nearest neighbors to 100 when generating the UMAPs shown, and the louvain resolution to 1. To assess the difference between UINMF and iNMF functioning, we performed a paired, one-sided Wilcoxon test between the ARI and purity values. The UMAPs shown have a louvain resolution of 1.0, and are labeled by jointly examining the original STARmap and SNARE-seq cell labels.To integrate the multi-omic SNARE-seq dataset  with the spatial transcriptomic STARmap dataset (2522 cells), we used the number of shared genes (944 genes), as well as 4,119 unshared features. To generate the unshared features, we selected genes with a variance threshold higher than that of 0.1, and then removed genes shared between datasets, for a total number of 2688 unshared genes. We selected the chromatin accessibility peaks with a variance greater than 0.01 (1431 peaks). For iNMF benchmarking, we used only the 944 shared genes. We optimized UINMF and iNMF with K = 30, λ = 5, and took the best of 5 random initializations for 10 random seeds. We performed quantile normalization for each optimized object using the SNARE-seq dataset as a reference. Using the SNARE-seq cell labels as ground truth, we calculated the ARI and purity scores for each of the ten seeds at louvain resolutions from 0.1 to 1.0 in increments of 0.1 . Similarly, we used the default (30) for the number of dimensions in the FindNeighbors function (Seurat 4.0.0). Using louvain resolutions from 0.1 to 1.0 in 0.1 increments, we assessed the performance of Harmony using purity and ARI scores. We compared Harmony and UINMF using a paired, one-sided Wilcoxon test on both the purity and ARI scores.Using Harmony to perform the integration, we used the 944 shared genes and the default 30 principal components for λ = 5 and K = 30 for all time and memory analyses.We assessed the impact of the additional features on runtime and memory usage by performing UINMF using 0, 1000, 2000, 3000, and 4000 extra features . We then defined the 2500 most variable genes between datasets.In order to better quantify how the number of shared and unshared features used within an analysis interact to produce the observable differences in the quality of integration, we perform a stepwise analysis. We select two single-cell transcriptomic datasets taken from the mouse Primary Motor Area (MOp)K = 30, and λ = 5, selecting the best optimization score from three random initializations. After performing matrix decomposition, we performed quantile normalization using the SMART-seq dataset as our reference, and performed Louvain community detection with a resolution of 0.1. Using the SMART-seq labels as ground truth, we calculated the resulting purity and ARI scores. We then decreased the number of shared genes by 100, and repeated the integration, and metric calculations. We continued this process for 500, 400, 300, 200, and 100 shared genes. We repeated this process for ten different sets of randomly selected held-out genes.From these 2500 most variable genes, we randomly sampled a set of 500 genes. Using these as shared features, we integrated the datasets using iNMF, letting K = 30, λ = 5 as the parameters for UINMF optimization, selecting the optimal optimization of three initializations. Similarly, we perform quantile-normalization with SMART-seq as the reference dataset, and calculate the Louvain community detection with a resolution of 0.1. After calculating the purity and ARI scores, we repeat the UINMF analysis for the same 400, 300, 200, and 100 shared genes, adding the unshared genes to the unshared features, such that the number of total features for the SMART-seq dataset always totals to the 2500 top variable genes. We repeat this process for the ten sets of randomly selected held-out genes used for the iNMF analysis.To assess how including the unshared features benefits the dataset integration, we integrate the datasets using UINMF. The same 500 shared genes are used as shared features, and the remaining 2000 variable genes not selected are used as unshared features for the SMART-seq dataset. For consistency, we use n_neighbors = 20, we plotted the resulting UMAPS from each analysis using 500 shared features and only 100 shared features  and STARmap (28 genes), iNMF required the selected K to be less than the number of genes. Since one of the advantages of our algorithm is that it does not have this constraint, we selected a value of K = 40 for both spatial transcriptomics integrations, the largest K we could select without severely impacting the alignment scores  for the STARmap integration with the scRNA-seq data. The higher penalty is assigned to the STARmap data, and the use of the vectorized lambda showed improved alignment scores over five initializations . Further information on research design is available in the Supplementary InformationReporting Summary