The identification of cell types in complex tissues is an important step in research into cellular heterogeneity in disease. We present a linear fast semi-supervised clustering (LFSC) algorithm that utilizes reference samples generated from bulk RNA sequencing data to identify cell types from single-cell transcriptomes. An anchor graph is constructed to depict the relationship between reference samples and cells. By applying a connectivity constraint to the learned graph, LFSC enables the preservation of the underlying cluster structure. Moreover, the overall complexity of LFSC is linear to the size of the data, which greatly improves effectiveness and efficiency. By applying LFSC to real single-cell RNA sequencing datasets, we discovered that it has superior performance over existing baseline methods in clustering accuracy and robustness. An application using infiltrating T cells in liver cancer demonstrates that LFSC can successfully find new cell types, discover differently expressed genes, and explore new cancer-associated biomarkers. Bulk RNA sequencing (RNA-seq) technologies have been widely used to investigate gene expression patterns at the tissue level in recent decades . HoweverAmong these applications, cell type identification is the most fundamental and essential. Traditional cell type identification methods consist of two steps: clustering cells using unsupervised learning algorithms and labeling cells based on specifically expressed marker genes in each cluster . While pCompared with scRNA-seq datasets, many bulk RNA-seq datasets have been archived in recent decades. Hence, some cell type identification methods integrating bulk RNA-seq datasets with known cell types have also been proposed recently. These methods attempt to use information from bulk RNA-seq data to annotate single-cell data. Specifically, they often identify cell types by correlating single-cell transcriptomes with reference datasets of pure cell types sequenced by RNA-seq, then iteratively improve the label inferences. SingleR  and RCA m reference samples from bulk RNA-seq data or labeled scRNA-seq datasets by averaging gene expression profiles in the same cell type. Then, LFSC learns the relationship between cells in scRNA-seq data and the reference samples, generating an anchor graph with k-connected components, where k denotes the number of clusters.• Unlike SingleR and RCA, LFSC generates a dictionary matrix with • The advantages of LFSC are that 1) its affinity matrix, based on an anchor graph, preserves the underlying cluster structure of the data, which also reduces memory costs, and 2) its overall complexity is linear to the size of the data, which greatly improves effectiveness and efficiency.• Through benchmark evaluations with 21 real scRNA-seq datasets and application to infiltrating T cells in liver cancer, we demonstrate that LFSC is superior to existing baseline methods.To address these issues, we present a linear fast semi-supervised clustering (LFSC) algorithm that integrates reference-bulk and single-cell transcriptome data using an anchor graph to improve the effectiveness and efficiency of clustering. The overview of LFSC is shown in We consider LFSC to be different from supervised learning, in which the goal is to minimize one specific loss function, given the labels of samples. LFSC is also different from unsupervised learning because it is designed under weak supervision: a small set of bulk RNA-seq data, called reference samples, can represent the neighborhood structure of cells in scRNA-seq data. LFSC is regarded as a semi-supervised method since prior knowledge of referenced cell types, generated from bulk RNA-seq data, is combined in the unsupervised clustering process. The details of related studies and the LFSC method are provided in the following paragraphs.n and d denote the number of samples and the number of features, respectively, subspace clustering assumes that data samples can be represented by a linear combination of samples underlying the same subspace. This means that n3), which is costly in terms of running time and storage for large-scale data.Given a set of data Anchor points, a small set of data samples, were selected to represent the landmarks of the data and preserve the underlying neighbor structure see . To reduustering  as the a dataset , and theM is transformed as follows:In LFSC, the data preprocessing procedure includes two steps: quality control and normalization. First, data quality control is utilized to filter the low-expressed genes. If a gene has less than 5% or more than 95% of non-zero elements across all cells, it is filtered out. For data normalization, we utilize log-transform normalization, in which each element , accuracy (ACC), normalized mutual information (NMI), purity, and silhouette coefficient as our evaluation metrics  settings on clustering performance, we implemented LFSC with different combinations of hyperparameters on highly confident scRNA-seq datasets. Alpha (α) was selected as 0.1, 1, 10, 50, and 100. Beta (β) was selected as 0.0001, 0.001, 0.01, 0.1, 1, 10, 50, and 100. α and β. We found that the performance of LFSC is stable for a large range of α and β values. In practice, we recommend optimizing α and β by fixing α and tuning β.To investigate the effects of generated reference samples on clustering performance, we introduced the downsampling strategy to generate reference samples with different sampling ratios . In the experiment, we first chose four real gold standard scRNA-seq datasets  Without HVG selection, all overlap genes between the scRNA-seq data and the reference transcriptomics data were selected. 2) Without reference transcriptomics data, we generated the reference sample by directly implementing the K-mean algorithm on the scRNA-seq data. clustree  containing 5,063 single T cells isolated from peripheral blood, tumor, and adjacent normal tissues from six hepatocellular carcinoma patients . We firsclustree  to exploclustree , when thclustree  as the rclustree . Clusterp-value of F test <0.05. There were 48 DEGs  and cluster 14 . Some genes are associated with immunological diseases. For example, CCR2 and CCR8 are protein-coding genes associated with diseases including human immunodeficiency virus type 1 and molluscum contagiosum. GZMA and GZMK are well-known marker genes regarded as T-cell- and natural killer cell-specific serine proteases. Some studies have demonstrated IL2RA and IL18RAP to be associated with the same cytokine signaling pathway in the immune system.To determine the biological differences between cluster 5 and cluster 14, we applied Seurat to identify the differentially expressed genes (DEGs) of cluster 5 and cluster 14. The DEG genes were selected under the criteria 1) absolute log2-fold change larger than 1.5, and 2) adjusted er 5 see  and 28 Der 5 see  for clusMetascape , liver hepatocellular carcinoma (LIHC) samples from The Cancer Genome Atlas Program (TCGA) dataset  were useAlgorithm 1Input: scRNA-seq dataset:  Reference dataset:  Hyperparameters: BeginStep 1: Implement quality control and Normalize data 1. Step 2: Identify highly variable overlap genes with the package Seurat on 2. Step 3: Estimate the cluster number, k, using the package clustree on 3. Step 4: Generate the reference samples 4. Step 5: Construct the structured anchor graph 5. Step 5.1: Initialize the matrix 6.  While convergence condition does not meet do7.  Step 5.2: Update 8.  Step 5.3: Update 9.  end while10.  Step 6: Run K-means on with the cluster number k;11. EndOutput: Clustering result Framework of LFSCK-connectivity constraint is added to the cell-reference anchor graph to preserve the underlying clustering structure of the data. In general, the proposed mechanisms not only improve the clustering accuracy of the model but also make its overall complexity linearly related to data size, and they reduce the memory overhead of the model.We presented a linear fast semi-supervised clustering method, based on bulk and single-cell transcriptomes, that has the following characteristics: 1) LFSC generates reference samples with bulk-RNA-seq or labeled single-cell RNA-seq data, which implicitly provides the label information to the graph construction process; 2) LFSC introduces anchor graph theory to measure the similarities between unlabeled cells and a small number of reference samples, which significantly reduces the size of the graph; and 3) the The experiments on several scRNA-seq datasets demonstrate the following conclusions: 1) LFSC is superior to state-of-the-art methods in clustering accuracy and robustness; 2) the visualization analysis proves that the anchor graph in LFSC can retain the correct clustering structure of the data, and the learning embedding space has good separation, which has a better visualization effect compared with the benchmark methods; and 3) the results of ablation analysis show that all components of LFSC are effective and reasonable. In addition, the case study of infiltrating T cells in liver cancer demonstrated that LFSC shows promising application potential in discovering new cell types, identifying differentially expressed genes, and exploring new cancer-related biomarkers.


In recent years, single-cell RNA sequencing technology (scRNA-seq) has developed rapidly and has been widely used in biological and medical research, such as in expression heterogeneity and transcriptome dynamics of single cells. The investigation of RNA velocity is a new topic in the study of cellular dynamics using single-cell RNA sequencing data. It can recover directional dynamic information from single-cell transcriptomics by linking measurements to the underlying dynamics of gene expression. Predicting the RNA velocity vector of each cell based on its gene expression data and formulating RNA velocity prediction as a classification problem is a new research direction. In this paper, we develop a cascade forest model to predict RNA velocity. Compared with other popular ensemble classifiers, such as XGBoost, RandomForest, LightGBM, NGBoost, and TabNet, it performs better in predicting RNA velocity. This paper provides guidance for researchers in selecting and applying appropriate classification tools in their analytical work and suggests some possible directions for future improvement of classification tools. With the rapid development and innovation of single-cell RNA sequencing (scRNA-seq) technology and related bioinformatics methods ,5,6,7,8,La Manno et al.  introducWang et al.  take a bThe paper is organized as followed. The second section introduces the concept and theory of RNA velocity estimation. The cascade forest structure model and the evaluation indicators to be used in subsequent experiments are introduced in this chapter. Finally, the information of the relevant data set is briefly described. In the third section, experimental results are analyzed, such as preprocessing the data set, evaluating the experimental results of the data set, using accuracy, the kappa coefficient, and evaluating the benchmark performance of the classifier. Finally, the stability of the performance of the cascade forest model is further analyzed by parameter comparison. In the fourth and fifth parts, we review the classification problem of speed prediction and suggest the future direction of classification tools. We believe that the research on RNA velocity prediction will guide the classification of cell velocity prediction and classification tools for scRNA-seq datasets in various use cases.A comprehensive and systematic evaluation of the RNA velocity prediction classification base classifier requires scRNA-seq datasets with well-annotated cell labels, as most of the evaluation metrics rely on the underlying factual label set for their calculation. Therefore, only scRNA-seq datasets with highly plausible cell-type labels are used in this paper. In the numerical experiments in this paper, datasets with different feature dimensions and different numbers of classes were carefully selected to better characterize the performance of the integrated algorithm in the RNA velocity prediction problem.Gastrulation_e75: A subset of mouse gastrulation is E7.5, in embryonic day 7.5 (E7.5) mutants, revealing a molecular map of mouse gastrulation and early organogenesis, including 7202 from mouse embryos, and a transcriptional profile of 53,801 single cells .Bonemarrow: A human bone marrow cell dataset which consists of hematopoietic cells, bone marrow adipose tissue, and supporting stromal cells, and includes transcript levels of 14,319 genes in 5780 cells .Pancreas: A dataset from the embryonic pancreas of NVF homozygous mice, with transcript levels of 27,998 genes from 3696 pancreatic epithelial and Ngn3-Venus fusion cells .Dentategyrus: A mouse hippocampal dentate gyrus neurogenesis dataset. Comprising RNA-seq data of 13,913 genes and 2930 cells from multiple lineages, the dominant structure is the granulosa cell lineage in which neuroblasts develop into granulosa cells. The remaining populations form distinct cell types that are fully differentiated  or form sub-lineages .As shown in As with traditional scRNA-seq analysis, measurements require preprocessing. First, genes were filtered by expression level or their occurrence in cells, retaining genes with sufficient counts, selecting the top 2000 highly variable genes for datasets with less than 3000 cells and then for data with less than 6000 cells and greater than 3000 cells. The top 2500 highly variable genes were selected for the set and, finally, the top 3000 highly variable genes were selected for cells with more than 6000 cells, as shown in For highly variable genes, the expression levels of these genes vary greatly between different cells (highly expressed in some cells and low in others). Screening out highly variable genes can reduce the noise of the dataset to a certain extent. After the first filter, normalization was performed to handle differences in sequencing depth between individual cells, followed by a log transformation, and highly variable genes were identified and extracted, while all remaining genes were discarded. Finally, according to the nearest neighbor graph, the first and second moments were calculated. There are three methods for velocity estimation in scVelo: the steady-state model, stochastic model, and dynamic model. In this article, we evaluated the classification under the steady-state model and the dynamic model, respectively. From the velocity estimates, we could obtain a multidimensional RNA velocity vector For classification performance evaluation in the steady-state mode first, we trained and tested models on four single-cell RNA-seq datasets, dividing the dataset into training and test datasets in an 8:2 ratio, and then matched the training set to these classifier models to extract and learn hidden patterns. Subsequently, the learning of the test dataset was evaluated against accuracy, F1_scores, and kappa scores, and the prediction results were retrieved. To address the data imbalance problem in this paper, an oversampling method SMOTETomek  was invoWe then ran the dynamics model to learn the full transcriptional dynamics of the splicing dynamics, which was solved in a likelihood-based expectation maximization framework by iteratively estimating the parameters of the response rate and latent cell-specific variables , and it can be seen in We compared the stacking model classifier proposed by Wang et al. . We furtWith the previous experimental results, we set k to 20, although we can increase k for better performance. This paper introduces a novel machine-learning algorithm cascade forest model for RNA velocity prediction and classification tasks. The cascade forest model is a decision tree ensemble approach that has fewer hyperparameters than deep neural networks and preserves the tree model’s interpretability. Its model complexity can be determined automatically in a data-dependent manner, making cascade forest models work well even on small-scale data. This paper aims to effectively predict RNA velocity using cascade forest models to prove that machine learning (ML) algorithms based on ensemble strategies are effective in predicting RNA velocities. In this paper, experiments were performed on four scRNA-seq datasets with different complexities and splicing ratios. The cascade forest model was comprehensively evaluated with five base classifiers: XGBoost, RandomForest, LightGBM, NGBoost, and TabNet. The experimental results show that the kappa coefficient, accuracy, and F1_score performance of the cascade forest model are significantly better than XGBoost, RandomForest, LightGBM, NGBoost, and TabNet, which proves that the model substantially improves RNA velocity prediction and classification.In addition, this paper compares the cascade forest model with the stacking model proposed by Wang et al. for RNA velocity prediction and classification. Through parametric analysis, it is found that cascade forests have better stability and stronger robustness. Especially for the change of parameter d, the cascade forest model prediction accuracy will not fluctuate as much as the stacked model, and even the performance will show a significant downward trend. As parameter k increases, the number of features increases, and the cascade forest model can predict RNA velocity more accurately, showing better performance than the stacking model.In this study, we extensively analyze RNA velocity prediction classification problems. Although the first application of existing RNA velocity models has shown promising results , the selMost classification tools accurately predict the results in RNA velocity prediction on four datasets with different splicing ratios. However, this result is based on an ensemble learning framework to balance different sample feature ratios to arrive at different baseline models, but it is still an empirical approach. When the data distribution is incomplete and unbalanced, the prediction results still have a more significant impact. In experimental tests on the Bonemarrow dataset, we found that the accuracy of cascade forest models decreased by more than 20% when the data were unbalanced. Therefore, the interpretability of the model will be a problem that needs to be solved in the future.In conclusion, cascade forest models provide a new prediction-based method for studying the mechanisms of cell differentiation that can be applied to help attribute state spaces not yet covered by scRNA-seq data. In future work, we can use this interpolated direction information to conduct more in-depth research on trajectory inference. For example, differential geometry is used to extract potential adjustments for estimating the curvature of the differentiation landscape in metabolic labeling experiments . TherefoThe goal is to predict the RNA velocity vector for each cell based on its gene expression data, shown in 2D space, and to formulate this as a classification problem. For this problem, we first need to obtain a count matrix of unspliced and spliced mRNAs, which can be obtained using methods such as Velocyto , loompy/The steady-state model is one of the main models of RNA velocity. This model has two fundamental assumptions: (i) at the gene level, all full splicing dynamics with transcriptional induction, repression, and steady-state mRNA levels are captured; (ii) at the cellular level, all genes have a common splicing rate and gene expression follows steady state. At that time, the steady-state ratio is obtained, i velocity is estimated as the deviation of the ratio of spliced to unspliced molecules fitted to γ, which is:At this time, the cell In contrast, dynamic models directly solve for the complete transcriptional kinetics of each gene, rather than making transcriptome-wide assumptions. Instead of trying to fit the data into a regression model, it estimates the parameters using an Expectation Maximization algorithm (EM)  that useTP (true positive) is the number of positive samples correctly identified. FP  is the number of negative samples identified as positive. TN (true negative) is the number of negative samples correctly identified. FN  is the number of positive samples missed. In this paper, three predefined metrics are used to evaluate the performance of the five integrated classifiers: accuracy , macro_FIn this study, we use several popular integrated enhancement algorithms, such as LightGBM , XGBoostAfter evaluating the five popular methods, we used four of the classifiers, as applied to the cascade forest structure, to predict with good robustness and accuracy. As shown in https://scvelo.org (accessed on 21 June 2022) direct interview. The hippocampal dentate gyrus neurogenesis dataset at P12 and P35 is available from the Gene Expression Omnibus (GEO) with accession number GSE95753. Atlas of mouse gastrulation is available under accession number GSE87038. Mouse pancreas data is also available from NCBI GEO, accession ID GSE132188. Human bone marrow data is available through the Human Cell Atlas data portal.scRNA-seq datasets are all public datasets and can be accessed through In summary, the supervised learning problem of RNA velocity prediction problem as classification is an entirely new study, and researchers still face many challenges. This study’s comprehensive evaluation was made using accuracy, F1_score, and kappa coefficients. We have demonstrated that the cascade forest model can work well in RNA velocity prediction classification problems, and its performance is better than XGBoost, RandomForest, LightGBM, NGBoost, TabNet, and stacking models, which are currently popular classification algorithms. Compared with the above classification algorithms, the cascade forest model is more stable and robust. Therefore, the cascade forest model can be better applied to any scRNA-seq data that can estimate RNA velocity. It guides researchers in selecting and applying appropriate classification tools in their analytical work and provides some possible directions for future improvements to classification tools.Although the problem of modeling dynamics in scRNA-seq using RNA velocity is tricky, the test results in this paper suggest that it is feasible to incorporate classification into single-cell velocity predictive analysis workflows. Cascade forest models allow us to predict and infer the future expression of individual cells more accurately. In current applications, we can use it to analyze influencing genes in trajectory branching events. There are many other applications of this analysis that are worth exploring. We demonstrate that the cascade forest model substantially improves over previously proposed RNA velocity prediction methods on relevant real-world datasets from human and mouse developmental brains.


Using single-cell RNA sequencing (scRNA-seq) data to diagnose disease is an effective technique in medical research. Several statistical methods have been developed for the classification of RNA sequencing (RNA-seq) data, including, for example, Poisson linear discriminant analysis (PLDA), negative binomial linear discriminant analysis (NBLDA), and zero-inflated Poisson logistic discriminant analysis (ZIPLDA). Nevertheless, few existing methods perform well for large sample scRNA-seq data, in particular when the distribution assumption is also violated.We propose a deep learning classifier (scDLC) for large sample scRNA-seq data, based on the long short-term memory recurrent neural networks (LSTMs). Our new scDLC does not require a prior knowledge on the data distribution, but instead, it takes into account the dependency of the most outstanding feature genes in the LSTMs model. LSTMs is a special recurrent neural network, which can learn long-term dependencies of a sequence.https://github.com/scDLC-code/code.Simulation studies show that our new scDLC performs consistently better than the existing methods in a wide range of settings with large sample sizes. Four real scRNA-seq datasets are also analyzed, and they coincide with the simulation results that our new scDLC always performs the best. The code named “scDLC” is publicly available at The online version contains supplementary material available at (10.1186/s12864-022-08715-1). The development of RNA sequencing (RNA-seq) has enabled unprecedented insight into the dynamics of gene expression –7. In coFor the classification of RNA-seq data, several statistical methods have been developed , 21, in Nowadays, scRNA-seq data have been increasingly used to identify cell types and disease states for new patients. Yet to the best of our knowledge, there are still relatively few methods in the literature to classify scRNA-seq data despite the enormous potential of scRNA-seq data. Generally, low sequencing depths cause high noise levels and a large fraction of so-called “dropout” events in scRNA-seq data; and moreover, classification methods for bulk RNA-seq data may cause unacceptably large misclassification rates for scRNA-seq data. Especially for scRNA-seq data with relative large sample sizes, they may follow a more complex mixed distribution. Most existing classification methods for RNA-seq data require a certain distribution assumption, and they may fail in improving the classification accuracy for scRNA-seq data with large sample sizes. Alquicira-Hernandez et al.  developeIn this paper, we consider a deep learning classifier (scDLC) to identify cell types for large sample scRNA-seq data, which is based on the two-layer long short-term memory recurrent neural networks (LSTMs). The deep learning classifier can learn scRNA-seq data without the need of a distribution assumption. What’s more, the scDLC method considers the dependency between the feature genes in the process of classification. LSTMs  is a speOur scDLC framework for identifying cell types in scRNA-seq data can be summarized as four steps. For the first fully connected layer, the gene sequences of a sample are mapped to a larger dimension. The first step aims to enlarge the information of gene sequence and make the class difference more obvious. Second, the output of the first fully connected layer is taken as the input of the two-layer long short-term memory network layer, and the weights of all gates are estimated by network calculation in each class. Third, we reduce the output dimensions to the number of classes in the second fully connected layer. Lastly, the outputs of the second fully connected layer are transformed to a probability distribution with a softmax function. In the process of training, we compare the probability of each class to the observation and estimate the optimization parameters under the cross-entropy loss function.To summarize the main advantages of the scDLC framework for classifying scRNA-seq data with large sample sizes, we note that scDLC is applicable to all scRNA-seq data no matter what the underlying distribution is. Moreover, scDLC has the capacity to capture the difference information of gene sequence from different classes, which is another key reason why it can perform the best compared to the existing competitors. In https://github.com/scDLC-code/scDLC.We propose a deep learning framework (scDLC) based on the LSTMs model to classify scRNA-seq data. The details of the scDLC model have been shown in In this section, we evaluate the performance of the proposed scDLC method via simulation studies. To generate scRNA-seq read count data, we apply the Splatter Bioconductor package  that is n samples for the training set and another n samples for the test set. We first consider the binary classification with K=2. Study 1 investigates the effect of different sample sizes for the binary classification. We fix the proportions of differentially expressed genes DE=0.5, the probability of excess zeros pzero=0.2, and consider the gene number g=100, 200, 300 and 400. We then compute the misclassification rates of all methods with different sample sizes ranging from 100 to 900. In Study 2, we evaluate the performance of all methods when the proportions of differentially expressed genes are 0.2, 0.3, 0.4, 0.5, 0.6 and 0.7 with fixed sample size n=200, 300, 400 and 500. In addition, we set the probability of excess zeros pzero=0.2 and the gene number g=100. In Study 3, we test the performance of all methods with the different probability of excess zeros, including pzero= 0.1, 0.2, 0.3, 0.4, 0.5 and 0.6. For other settings, we let the gene number g=100, the sample size n=200, 300, 400 and 500, and 40% of genes be differentially expressed.In each experiment, we generate K=3, we also conduct three studies to evaluate the performance of the different methods. In Study 4, we evaluate the effect of different sample sizes with three classes. All other parameters are kept the same as those in the binary classification except for the sample sizes. We set n= 300, 400, 500 and 600 for three classes in Studies 5 and 6, respectively.For the multiple classification with With 1000 simulations for each experiment, we report the average misclassification rates for the binary classification in Figs. SupplementaryK=3. They coincide with the conclusions made for the binary comparison, and in particular, scDLC always performs the best. Moreover, we note that SINC does not perform well when the number of selected feature genes is small, and so it can only be recommended for large number of selected feature genes.https://www.ncbi.nlm.nih.gov/). The six datasets are summarized in Table https://singlecell.broadinstitute.org/single_cell/study/SCP424/single-cell-comparison-pbmc-data [To further evaluate the performance of the different classifiers, we also analyze six scRNA-seq datasets which are from National Center for Biotechnology Information Search database  to that within groups (WSS) as follows: We assess the performance of our proposed scDLC method with seven baseline methods, including three traditional classifiers based on the Bayesian, scPred, scClassify, SVM and SINC methods. We apply the AUC score, which is the area surrounded by the coordinate axis under the ROC curve , to meask, and K is the number of classes. Moreover, without loss of generality, we retain the top p=100 feature genes from each simulation as the inputs of the first layer of scDLC. We further repeat all the experiments 100 times and calculate the average AUC scores. We also present their respective boxplots in Fig. where Next, we compare the performance of all classifiers with different sizes of training samples. Figure Finally, we consider the performance of each classifier under different selected feature genes. Specifically, we use 70% of the dataset as the training set and the rest as the test set. According to the degree of differential expression, the top 20 to 100 genes are selected to test the performance of each classification method. Figure Supplementary Figs.The single-cell RNA sequencing (scRNA-seq) technology has been increasingly used in molecular diagnosis of clinical diseases. In this paper, we proposed a deep learning framework with two layers of LSTMs, namely scDLC, to classify large sample scRNA-seq data. The innovation of scDLC is mainly manifested in two aspects. Firstly, compared to the existing discriminant rules, our new method does not require a distribution assumption so that it can be widely applied in practice. Secondly, our scDLC also amplifies the features of the selected genes through the first fully connected layer. It is thus beneficial to improve the classification accuracy and stability of the model, and meanwhile our scDLC can be trained with less computer resource using only the top selected feature genes.To evaluate the performance of our new classifier, we considered both the binary classification and the multiple classification. Simulation results show that our deep learning method can sufficiently capture the difference information of classes in gene sequences, and that it performs much better than, or at least as well as, the existing competitors in a wide range of settings with large sample sizes. We also analyzed six real scRNA-seq datasets, including both small and large sample sizes, and they all support that our new scDLC always performs the best.As a future work, we will study from the network structure level why scDLC can efficiently capture class differences from gene sequences, and we expect that understanding the mechanism can bring deep insights to gene expression and regulation. Moreover, it can also be interesting to extend deep learning techniques to conduct in-depth research in precision medicine such as neonatal genetic disease-related gene screening.We first review the framework of long short-term memory recurrent neural networks (LSTMs), and then introduce a new workflow of the deep learning classifier (scDLC) for large sample size scRNA-seq data.xt,ht and Ct denote the input value, the output value and the cell state at time t, respectively. Let b denote the bias term, and W denote the weight matrix. Let also f, i and o denote the forget gate, the input gate and the output gate, respectively. The recurrent process of LSTMs can be expressed as follows: Hochreiter and Schmidhuber  proposedwhere The scDLC framework is shown in Fig. Fully connected layers: Each node of the fully connected layer is connected to all nodes of the previous layer. It can synthesize the extracted features through the rectified linear unit (ReLU) activation function. The function of the first fully connected layer in scDLC is to amplify the information of the gene sequence and make the class difference more obvious. This layer can greatly improve the accuracy of discrimination. The ReLU activation function is x is the input vector, W is the weight matrix, b is the bias vector, and a is the activation vector which is the output of the fully connected layer. Using the ReLU activation function in the network can make the classifier perform better. At the end of the model, we map the output of the second fully connected layer to the probability distribution of the class through a softmax function as where M is the number of classes.where LSTMs layer: In the LSTMs layer, we take two LSTMs sublayers to learn data. The horizontal connection between sublayers means that the output h of the first sublayer is entered into the second sublayer as input. The vertical connection means that the cell state C of the previous time is transferred to the next time in the same sublayer. The output of this layer will be used as the input to the second fully connected layer. The forward recursions of this layer refer to the formulas in  in this deep model are denoted as lgorithm . We furtN is the sample size, M is the number of classes, yic is an indication variable which is 1 if class c is the same as the class of the sample or otherwise 0, and pic represents the prediction probability that sample i belongs to class c.where θ. According to the MBGD algorithm, the rule for updating is as follows: The gradient descent method is a widely used optimization algorithm in machine learning. We use a mini-batch gradient descent algorithm (MBGD)  to trainη is the learning rate. In order to avoid fluctuation in the later stage of training, we further set the learning rate decay exponentially during the training. That is where γ is the decay rate, and s is the global step. The exponential-decay learning rate means that the learning rate is correlated with the number of training times, and it will decline exponentially with the increase of training times. Here, r is the decay rate, s is the global step, the maximum learning rate is set to max_lr=0.005, the minimum learning rate is set to min_lr=0.001, epoch is the training times, x is the sample size in the total training set, batch_size represents the sample size in a batch, then decay rate is computed with r=log(max_lr/min_lr)/(epoch∗x/batch_size). Then the learning rate after decay can be obtained according to the calculated decay_rate.where hidden size =64: The parameter represents the size of the hidden state of LSTMs and we set it as 64.batch size =11: For the number of samples in a batch, we randomly choose 11 samples throughout the simulations.grad clip =5: To stabilize the network in the process of training, we set the threshold as 5 for the gradient to control the weight update within a certain range. train keep prob =0.3: To prevent overfitting, we let the train keep probability equal to 0.3, which means that only 30% of the information will be used in the next time. initial learning rate =0.005: For the appropriate learning rate that can make the objective function converge to a local minimum at a suitable time, we set the initial learning rate as 0.005. Since the learning rate will decline with training, we further set the minimum learning rate as 0.001.To implement the proposed scDLC, it is further needed to determine the hyperparameters in the model. Note that the hyperparameters are the configuration outside the model, and their values cannot be estimated from the data. Appropriate hyperparameters can greatly improve the performance of the model. According to the test of different hyperparameter combinations, we set the following parameters that can yield a good performance for the classification.Additional file 1 Supplementary figures and tables. This file contains related figures and tables for simulated and real datasets.


Single-cell RNA-sequencing (scRNA-seq) technologies allow for the study of gene expression in individual cells. Often, it is of interest to understand how transcriptional activity is associated with cell-specific covariates, such as cell type, genotype, or measures of cell health. Traditional approaches for this type of association mapping assume independence between the outcome variables (or genes), and perform a separate regression for each. However, these methods are computationally costly and ignore the substantial correlation structure of gene expression. Furthermore, count-based scRNA-seq data pose challenges for traditional models based on Gaussian assumptions.We aim to resolve these issues by developing a reduced-rank regression model that identifies low-dimensional linear associations between a large number of cell-specific covariates and high-dimensional gene expression readouts. Our probabilistic model uses a Poisson likelihood in order to account for the unique structure of scRNA-seq counts. We demonstrate the performance of our model using simulations, and we apply our model to a scRNA-seq dataset, a spatial gene expression dataset, and a bulk RNA-seq dataset to show its behavior in three distinct analyses.We show that our statistical modeling approach, which is based on reduced-rank regression, captures associations between gene expression and cell- and sample-specific covariates by leveraging low-dimensional representations of transcriptional states.The online version contains supplementary material available at 10.1186/s12859-022-05054-6. Recent advances in high-throughput genomic assays have allowed for the creation of expansive data sets that are useful for exploring biological variation across cells. In particular, single-cell RNA-sequencing (scRNA-seq) technologies provide gene expression measurements at the individual cell level, allowing for the analysis of variation in transcriptional activity across cells within a single sample –4. WhileWhile methods for association studies have been widely developed for bulk RNA-sequencing (RNA-seq) data , 6, methIn this paper, we propose a statistical modeling approach based on reduced-rank regression that captures associations between gene expression and cell- and sample-specific covariates by leveraging low-dimensional representations of transcription. Within this framework, we propose two specific models: Poisson reduced-rank regression (PRRR), which adapts a generalized linear model to the reduced rank setting, and nonnegative Poisson reduced-rank regression (nn-PRRR), which provides interpretable nonnegative regression components. In what follows, we first review several related threads of research and describe our modeling approach. Then, using simulated data and single-cell RNA-seq data, spatial gene expression data, and bulk RNA-seq data, we show that our models are useful for a wide range of association study types, including studying the transcriptional hallmarks of cell types, genes correlated with disease status, and expression QTLs.Since the completion of the Human Genome Project in 2003  and the In a similar vein, quantitative trait loci (QTL) studies identify associations between genetic variants and quantitative phenotypes , 14. A cP SNPs for N individuals or tissue samples, and let Q genes in these individuals or tissues  [pth column of qth column of p and gene q for In this context, the statistical eQTL problem is to estimate the pairwise association between a set of genetic variants (the covariates or explanatory variables) and the expression level of each gene (the outcome variables). This is typically performed using a linear regression model. In particular, let tissues  . Genericciations –22. Withficients –25. Undeype data , 27.The advent of scRNA-seq technologies has opened the door for narrowing the investigation of genotype-phenotype relationships from the level of whole tissues to the level of individual cells. However, existing computational tools are insufficient for this purpose: they typically do not accommodate count-based data, and they are seldom robust to high-dimensional outcome variables. It is difficult to control the hypothesis testing error rate in many eQTL analyses, which run millions to trillions of univariate association hypothesis tests (one for each SNP-gene pair) , 28, 29.A further drawback of existing association testing frameworks is their assumption of Gaussian-distributed data. Most canonical regression models assume an independent normally-distributed response variable, with mentclass2pt{minimAn alternative to this approach is to model the gene expression data with a discrete distribution. A common choice is the Poisson distribution, whose support is restricted to the nonnegative integers and has been shown to improve the representation and interpretation of scRNA-seq data when fitting statistical models , 35. A rLatent variable modeling approaches have also been proposed for modeling multi-view data. The most popular approach has been canonical correlation analysis  and itsen shown , where tRecently, a latent variable model based on latent Dirichlet allocation , 45 for The transcriptional states of cells tend to exhibit strong correlations between genes . Thus, iP is the number of covariates, and Q is the number of genes. In most gene expression studies, Q (and sometimes P) is large, and R different programs encoded in subsets of covariates; then R programs.Consider again the linear regression model in Eq. . Here, \low rank . In partR left singular vectors of Several estimation approaches have been proposed for RRR under the assumption of Gaussian noise. A common method is to find the parameter values that minimize the squared reconstruction error , 49:\docpth row of R is specified by the modeler, and L steps or until convergence.Sparse approaches to RRR have been proposed as well. Sparsity in the decomposition leads to greater interpretability by including nonzero weights only on a subset of the covariates and genes for any component. One model  imposes k to be estimated from the data. BERRRI then uses a variational Bayes approximation to the posterior for inference of the model parameters. However, BERRRI does not explicitly model count-based data, and its inference procedure is not computationally tractable for genome-scale analyses.Another approach developed a Bayesian RRR framework for association mapping in the GWAS setting . The modThe linear RRR model has been generalized to nonlinear functions as well. The most popular nonlinear approaches have used neural networks with multiple inputs and multiple outputs . The linIn this manuscript, we propose a statistical model and associated computational framework that addresses the problems that arise with modeling genotype-phenotype associations for high-dimensional phenotypes captured with count data. We propose a reduced-rank regression model that finds low-dimensional associations between genotypes  and RNA-seq data . Relying on low-dimensional associations alleviates the problem of estimating millions of pairwise associations. Furthermore, our model uses count-based likelihoods that allow both single-cell RNA-sequencing data and bulk RNA-sequencing data. We show that our approach appropriately models gene expression data with count-based likelihoods, leads to interpretable subsets of genes and genetic variants or other covariates in each dimension, and uses flexible, computationally tractable inference methods that allow for uncertainty quantification.We propose a probabilistic reduced-rank regression model with a Poisson data likelihood—which we call Poisson reduced-rank regression (PRRR)—for association mapping in count-based sequencing data. Our approach takes the form of a reduced-rank regression model with intermediate factors that explicitly model count-based data using a Poisson likelihood. These factors are interpretable and can be used to to identify and analyze the global structure of associations between cell covariates and cell phenotypes, such as gene expression levels. We ensure that inference is tractable and efficient in these models by using stochastic variational inference.Q genes in N cells, where PRRR is designed to identify associations between cell-specific covariates and high-dimensional gene expression profiles. The response matrix PRRR uses a Poisson likelihood to model the transcript counts for each cell as the response variables, conditional on observed cell-specific covariates. The Poisson rate is parameterized by a low-rank linear mapping from the cell covariates.p in cell n, denoted by n, denoted as pth row of Specifically, the transcript count of gene i. We fix In some cases, the covariates mentclass2pt{minimWhile the PRRR and nn-PRRR models are designed for the same goal — performing reduced-rank regression with high-dimensional, count-based outcomes—some care is required when choosing which model to apply for a particular application. The choice largely depends on the goal of the analysis. If a primary goal is to examine the low-dimensional latent factors in a dataset, then nn-PRRR is often preferable because its nonnegative factors encourage a parts-based representation, which may be easier to interpret. nn-PRRR also requires that the covariates are nonnegative. On the other hand, when the primary goal is prediction, PRRR may be preferable because its real-valued factors will be less constrained due to the removal of the nonnegativity constraint. However, these are only guidelines and not hard restrictions, and often it may be preferable to fit both PRRR and nn-PRRR to a dataset, when possible, and study both sets of results to select the one with the more appropriate behavior.a posteriori (MAP) methods and 2) full Bayesian posterior inference for the regression coefficients using an approximate inference procedure.We propose two approaches to fit our model to data: 1) computing a point estimate for the coefficients using maximum Z is a normalizing constant that does not depend on Z, and leveraging the i.i.d. assumption, we arrive at our final objective for the MAP estimate of the model parameters:The MAP solution in our model is the coefficient matrices A fully Bayesian approach to inference, given a set of samples with paired cell covariates and transcript counts, nference  as implenference . For allnference  with a lWe first demonstrate the use cases of PRRR and test the robustness and accuracy of our model using simulated data.We first sought to confirm that PRRR identifies the low-dimensional relationships between covariates and outcomes.To start in a setting that can be visualized, we generated a synthetic dataset in which the covariates and outcomes are both two-dimensional. Specifically, we sampled data from the generative model Eqs. , 9, settmentclass2pt{minimWe next extended this simulation study and visualization to a small-scale synthetic eQTL study. We generated entclass1pt{minimaR of the coefficient matrix. A common approach is to evaluate the goodness-of-fit of the model at varying values of R, and select the one with the best fit to the data. To test whether this is feasible with PRRR, we use synthetic data that was generated from PRRR’s generative model with true rank R.PRRR, like other reduced-rank regression approaches, requires selecting the rank We find that the PRRR ELBO peaked at the true value of  studies , and sugWe next sought to validate the robustness of PRRR in the presence of higher-dimensional data. To do so, we generated three datasets from the PRRR model, each with a different number of response features (genes), e glmnet . We repeQ . Given their functional relatedness, these cell types are expected to show similar gene expression patterns compared to patterns found in other cell types. The competing methods, BERRRI and a neural network, were unable to separate islet and non-islet cell types in their latent spaces  Consortium . For thir, we do this by taking the outer product of the corresponding columns of interferon gamma response and inflammatory response  and nonnegative Poisson RRR (nn-PRRR)—to jointly model associations within two high-dimensional paired sets of features where the response variables are counts. In simulations, PRRR and nn-PRRR are able to effectively capture associations between paired high-dimensional data. Moreover, we show that these models can identify the optimal rank for the parameter matrix. In the context of sequencing data, we find that PRRR and nn-PRRR may be used for robust identification of cell types, quantifying the relationships between cell types, and performing association mapping of genetic variants to correlated genes.There are several limitations of our proposed model. First, PRRR and nn-PRRR only model linear associations between inputs and outputs and are unable to account nonlinear relationships. Second, we observe that the time complexity for fitting PRRR and nn-PRRR is somewhat slower than competing models  model, along with a nonnegative counterpart called nn-PRRR, for association mapping in count-based sequencing data. PRRR is able to detect associations between a high-dimensional response matrix and a high-dimensional set of predictors by leveraging low-dimensional representations of the data. Using principled Bayesian modeling, PRRR is able to properly account for the count-based nature of RNA sequencing data using a Poisson likelihood. We ensure that inference is tractable and efficient in these models by applying a fast variational inference approach.Additional file 1. Fig. S1 Graphical model for PRRR and nn-PRRR.Additional file 2. Fig. S2 BERRRI and a neural network approach fail to identify expression patterns in islet celltypes. Shown here is the latent encoding of each cell type for each pair of latent variables. Eachpoint in each subplot represents a cell type, and cell types are colored by whether they areclassified as islet cells or not. The densities on the diagonal show the distribution of latent variablevalues for islet and non-islet cell types in each latent dimension. The left panel shows the latentvariables for BERRRI and the right plot shows the latent variables from a neural network.Additional file 3. Fig. S3 nn-PRRR coefficients for pancreatic cell types. Heatmaps showing the full coefficientmatrix UV⊤ for nn-PRRR . Cell types are shown onthe rows and genes on the columns. In the left panel, white cells indicate values near zero,implying that this coefficient matrix is highly sparse.Additional file 4. Fig. S4 Marker genes identified by PRRR for pancreatic cell types. For each cell type, the tengenes with the highest coefficients in the matrix UV⊤ were extracted for each cell type. Somecell types share the same ten marker genes, which corresponds with our observation that the celltypes are largely overlapping in a PCA plot of the gene expression data .Additional file 5. Fig. S5 PCA plot of pancreas scRNA-seq data. The first two principal components (PCs) areplotted. Each point corresponds to a single cell and is colored by its annotated cell type.Additional file 6. Fig. S6 nn-PRRR coefficients for GTEx eQTL mapping. Left: U matrix showing SNPs on therows and latent factors on the columns. Right: V matrix showing genes on the rows and latentfactors on the columns.Additional file 7. Fig. S7 Time complexity. Left: Time to fit each of the four models with varying sample sizes n.Right Left: Time to fit each of the four models with varying outcome dimensions q.Additional file 8. Fig. S8 The optimization problem for reduced-rank regression (RRR) and description of GTEx experiments.


The prediction of response to drugs before initiating therapy based on transcriptome data is a major challenge. However, identifying effective drug response label data costs time and resources. Methods available often predict poorly and fail to identify robust biomarkers due to the curse of dimensionality: high dimensionality and low sample size. Therefore, this necessitates the development of predictive models to effectively predict the response to drugs using limited labeled data while being interpretable. In this study, we report a novel Hierarchical Graph Random Neural Networks (HiRAND) framework to predict the drug response using transcriptome data of few labeled data and additional unlabeled data. HiRAND completes the information integration of the gene graph and sample graph by graph convolutional network (GCN). The innovation of our model is leveraging data augmentation strategy to solve the dilemma of limited labeled data and using consistency regularization to optimize the prediction consistency of unlabeled data across different data augmentations. The results showed that HiRAND achieved better performance than competitive methods in various prediction scenarios, including both simulation data and multiple drug response data. We found that the prediction ability of HiRAND in the drug vorinostat showed the best results across all 62 drugs. In addition, HiRAND was interpreted to identify the key genes most important to vorinostat response, highlighting critical roles for ribosomal protein-related genes in the response to histone deacetylase inhibition. Our HiRAND could be utilized as an efficient framework for improving the drug response prediction performance using few labeled data. Precision medicine seeks to customize medical treatments based on the genetic characteristics of each patient. Essentially, this is the process of tailoring proactive and preventive care in order to maximize medical efficacy and cost-effectiveness . A persoIndeed, labeled data inadequacy is a common problem for both precision medicine and clinical trial. Developing a novel method that can predict the therapeutic response and identify the biomarkers based on a minimal amount of sample is a task of top priority. Semi-supervised learning has proven to be a powerful paradigm for leveraging unlabeled data to mitigate the reliance on large labeled datasets. It is necessary to fully exploit the available class label information, especially in cases where few labeled data are available. Currently, semi-supervised learning is widely used in image identification. Songpa et al. proposed a simple and efficient method of semi-supervised learning for deep neural networks: Pseudo-Label . Timo etWe introduce Hierarchical Graph Random Neural Networks (HiRAND), a graph convolutional network (GCN)-based deep learning semi-supervised model, to predict drug response using transcriptomic data. HiRAND completes the information integration of the gene graph and the sample graph by GCN in order. In the gene spatial, the neighbor information is aggregated to generate new convolutional features based on the gene weight matrix and gene adjacency matrix. In the sample spatial, by dropping out a certain proportion of sample expression data several times, the sample’s information can pass to its neighbor along the pre-built sample adjacency matrix and generate a novel perturbation matrix based on GCN. The perturbation matrix is the augmentation version of the original expression data. By doing so, we achieve data augmentation for molecular expression data and improve the model generalization. An overview of HiRAND is illustrated in Xinput in a gene sample [sample means the nodes of the sample similarity graph G(n) throughout the text] format and the gene adjacency matrix gA. For clarity, we simply described the procedure of integrating the information using GCN in the graph data as shown in Equation 1. Consider a graph G=, where Vdenoted the vertices and E denoted the edges. The aggregation process of GCN was defined as:The proposed method HiRAND mainly consisted of four parts, including gene selection, data augmentation, multilayer perception (MLP) for prediction, and consistency regularization  and sample similarity graph G(n), and convolution of those two graphs performed the gene selection and data augmentation, respectively. The consistency regularization was used to optimize the prediction consistency among S augmentation data. The pseudocode of HiRAND was provided in where Algorithm 1Input:geneAdj= g × g, adjacent matrix for g genessampleAdj = n × n, adjacent matrix for n samples X = n × g, feature matrix for n samples and g genesS: time of augmentationδ = DropNote/dropout probabilityη = learning ratemlpf: the modelFunction HiRAND : SetVariablesNull  // augment the data for s in 1 : S do   // sparse the inputX1 = SparseGCN    (X*weightV*geneAdj)   // perturb the data X2 ~ DropNote    // propagate the data   // spredict the label Z = mlpf(X3) end  // totalloss function L = labelL + unlabelL // Importance score of genes ImportanceScore = sum (abs(weightV * geneAdj)) return Z, ImportanceScoreOutput:Z: the label distribution predictionImprotenceScore: the importance score of genesThe main task of this layer was to aggregate the gene information along the gene adjacency matrix and achieve the gene selection. As Equation 2 showed:Xinput was n*g matrix, where each row represented a sample and each column denoted a gene. The gene adjacency matrix gA was g*g one-hot matrix, where i and gene j could be found in the HINT database, which was a database of high-quality protein–protein interactomes for humans (σ(·) denoted the Tanh activation function here. W(0) was a g*g trainable matrix, which contributed to the gene selection by assigning a higher weight value r humans . σ(·) degA and W(0) separately.H(1) of the gene selection layer was still n*g matrix.This output H(1) matrix by performing the random propagation strategy. The sample adjacency matrix nA indicating the relationship of samples was used to store information about the sample graph structure. For constructing the nA, the similarity between sample p and sample q as evaluated by Equation 4:The purpose of this process was to complete data augmentation for the output px and qx denoted the g-dimensional vectors of gene expression profiles of sample p and sample q, respectively. ρ was a function of calculating the distance between two different samples. ρ was the cosine distance here. µ was the hyperparameter, which was set to 0.5 in this case. pqϵ is a scale parameter and computed through Equation 5:where pN represented the neighbor’s expression vector of sample p, and similarly qN denoted the neighbor’s expression vector of sample q. Then, neighbors of a given sample were defined as the top 10 most similar samples based on the Simpq according to the mild assumption that local similarities are more reliable than remote ones  for each sample p, where δ was the drop rate. To effectively augment graph data, each sample’s expression data can be randomly dropped (referred to as Dropout) (p in H(1). Then, we adopt the GCN to propagate the neighbors’ information to each sample along the sample adjacency matrix nA as Equation 6:Next, we randomly generated the binary mask Dropout)  by multiH(2) was a sample augmentation data. nA was the sample adjacent matrix, and W(1) was the weight matrix. As shown in S sample data augmentations based on the S mask matrix, and here, S was set to 4.where m-hop neighbor, we consider using the nA to receive the information of both near and distant neighbors in the sample graph data (Equation 7):It is well known that GCN only makes the convolution for the nodes that were directly connected in the graph data. In order to explore the role of the m-hop neighbor. nA from order 0 to order m.S times, we obtained S augmented data matrices s< S). Then, these S augmentation datasets were fed into the MLP classifier separately as Equation 8:After performing the data augmentation g neurons (g means the number of columns of the input data), the hidden layer with 128 neurons, and the output layer with Cneurons (Cwas the number of classes and was set to 2 here). For each sample, the probability of being assigned to each class denoted by Where Θ denoted the model parameters. MLP consisted of three layers: the input layer with S prediction probability matrices from the previous layer, we proposed to optimize the prediction consistency among S outcomes. We first calculated the label distribution center Having generated p in the s data augmentation.p in the wth class is calculated by:Next, inspired by the sharpening algorithm , the shaT∈, and ℒlab  was a cross-entropy term representing the classification error (Equation 12):q denoted labeled nodes among n nodes, and Y was the true label of the labeled sample. ℒunlab  was a penalty term for the regularization loss that denoted the distance between the artificial label and the predicted label averaged over all augmentations (Equation 13):where K value setting, we primarily considered two aspects. On one side is exploring the model performance in the case of few labeled data, and K is set to range 2–20. On the other side, we would like to see the performance comparison with the baseline model when more samples are given, so we set the labeled sample size as {30,60,90,120,150,180,210}. We conducted 5-fold cross-validation to evaluate the predictive power of HiRAND and ran this process five times to show the robustness. Full details of data preparation and the comparison of available methods are given in the In the HiRAND training phase, the analysis strategy was shown in ij by transforming the distances matrix D between nodes according to Equation 14:To assess the performance of HiRAND, we simulated an expression matrix of 500 samples with 1,000 variables. Firstly, a protein–protein interaction (PPI) network-like adjacency matrix representing the connection strength among variables was constructed. Specifically, we employed the preferential attachment algorithm proposed by Albert  to generij, 500 multivariate Gaussian samples were obtained as input matrix X=T followed by Equation 15:Based on the covariance matrix Σβ=T and an intercept β0 were sampled in range . We also made some of the parameters negative so that both positive and negative coefficients can be accommodated, which was more consistent with the situation in practical applications. Ultimately, the outcome variable y was calculated as in Equations 16 and 17:To generate the outcome variable, we defined 20 features as the true predictors randomly. A set of parameters η−1(x)=(0.7ϕ(tan h(x))+0.3ϕ(x2))*(1+ex)2 , in which η-1(x) was the link function and m was the median of y. Thus, we generated the outcome variable y, which was the binary variable.where We applied HiRAND to the simulation data following the analysis strategy described before. We found that the area under the curve (AUC) of HiRAND is higher than all of that of compared methods in the presence of very few labeled samples, such as less than 20. The AUC of the compared methods has been improving rapidly by adding the labeled sample, especially in SVM, which roughly gets the same AUC with HiRAND trained with more than 20 labeled samples , promotes cell cycle arrest . In the Ranging from drug research and development (R&D) to precision medicine, obtaining the prognosis and treatment response labels of patients is often difficult and expensive. In this paper, we developed HiRAND, the GCN-based deep learning method for drug response prediction that enabled semi-supervised classification and feature selection using very few labeled data. One of the highlights of HiRAND is aggregating the information from both gene graph spatial and sample graph spatial simultaneously. Another major contribution is achieving data augmentation in the expression profile and overcoming the dilemma of the limited labeled sample size. Overall, our method performs significantly better than other competitive methods on the 5-fold cross-validation experiments, whether in multiple drug response predictions and translation scenarios. Notably, the advantage of HiRAND becomes more pronounced, especially in models trained using few labeled samples.This paper provided a new idea for the exploration of predicting drug response using very few labeled data. Along this line of thinking, future research could focus on designing updated model versions to speed up the clinical application process . Ideas like the HiRAND method might be expected to work well in the clinical scenario. Traditional randomized drug-centered clinical trials are cumbersome, costly, and require large numbers of patients to demonstrate a clinical benefit . ComputeAt present, studies have shown that HDACs can influence a multitude of physiological pathways in different cells. HDACs regulate non-histone proteins [adhesion proteins , transcrFrom the results of the ablation experiments, the multiple graph data augmentation strategy alleviated the low-sample size problem to some extent, based on which we utilized consistency regularization to improve the model’s generalization on unlabeled data. As expected, data augmentation made the performance better compared to standard networks trained without data augmentation. Extensive data augmentation was performed to overcome the limitation of our training data . Data auTo sum up, we introduced the HiRAND semi-supervised deep learning framework that can serve as an application for drug response prediction using few labeled samples. Meanwhile, the model could be used in the future to stratify patients based on the learned classification features, providing an important analysis tool for future applications in precision oncology and beyond.We proposed a novel semi-supervised framework HiRAND to predict the responders of treatment in precision medicine. By integrating information from both feature graphs and sample graphs, HiRAND clearly outperformed existing methods and demonstrated its capability in personal treatment decision-making. Not only this, this model is helpful for discovering outcome-oriented biomarkers by incorporating a trainable weight matrix. In addition, we introduced a data augmentation strategy into molecular biology to augment the biodata and overcome the small labeled sample size limitation. Our future effort will focus on considering more omics data into model building and increasing the performance toward biomarker discovery.The original contributions presented in the study are included in the article/Conceptualization: YH and KL; Methodology: YH, ZR, LZ, ZX, JJ, JH, WL; Supervision: KL, YH; Writing: YH; Review & editing: all; Code writing: YH, ZR, and LZ; Validation: YH, ZR, LZ, ZX. All authors contributed to the article and approved the submitted version.


This study deals with the identification of signature genes through a model using four machine learning algorithms for two cohorts of bulk and single cell RNA seq to predict immune checkpoint blockade (ICB) response in gastric cancer. Through LASSO feature selection, we identified VCAN as a marker gene signature that distinguishes responders from non-responders.VCAN, a candidate characteristic gene selected by all four machine learning algorithms, had a significantly high prevalence in non-responders (p = 0.0019) and showed a poor prognosis (p = 0.0014) at high expression values. This is the first study to discover a signature gene for predicting ICB response in gastric cancer by molecular subtype and provides broad insights into the treatment of stem-like immuno-oncology through precision medicine.Predicting responses to immune checkpoint blockade (ICB) lacks official standards despite the discovery of several markers. Expensive drugs and different reactivities for each patient are the main disadvantages of immunotherapy. Gastric cancer is refractory and stem-like in nature and does not respond to immunotherapy. In this study, we aimed to identify a characteristic gene that predicts ICB response in gastric cancer and discover a drug target for non-responders. We built and evaluated a model using four machine learning algorithms for two cohorts of bulk and single-cell RNA seq to predict ICB response in gastric cancer patients. Through the LASSO feature selection, we discovered a marker gene signature that distinguishes responders from non-responders.  Immunotherapy is a revolutionary method that uses the immune system to suppress tumors , and it Recently, using machine learning, multi-omics data were used to predict drug responses , and gasThe disadvantage of machine learning studies is that they are limited to bulk omics data; therefore, identifying the cell type as the key to predicting ICB response at the single-cell level is not possible. In this study, we attempted to predict the ICB response using a basic machine learning algorithm and used the approach of a global big data analysis to determine which cell type and ICB response predictions are related at the single-cell level. Our results suggest an effective treatment method by predicting the immune-cancer drug response of patients with gastric cancer through precision medicine.We used four machine learning algorithms to build a model for predicting ICB response. We used R version 4.0.5 with the R package. The labels of tumors of the responder and non-responder groups were assigned 1 and 0, respectively, to classify the tumors according to their ICB response in stomach adenocarcinoma (STAD). For the random forest model , glmnet n = 5927) used in previously published protocols was maintained, and imputation was performed using Markov Affinity-based Graph Imputation of Cells (MAGIC) [We used Seurat version 4.0 for meta-analysis of single-cell data and classified cell types using marker genes from previous studies . The num (MAGIC) .We predicted ICB response using bulk expression data sets and Tumor Immune Dysfunction and Exclusion (TIDE). METASCAPE  was usedPredicting the ICB response in gastric cancer is critical. We used bulk expression and single-cell data from two cohorts of gastric cancer and one validation set and the TIDE algorithm  for ICB HBB, SHOC2, HBA2), gland mucous cells , metaplastic stem-like cells , proliferative cells , and pit mucous cells   . In addill types E. We selll types F. The call types G.These results confirmed the common mechanism of ICB response in various cell types.GOLM1, IGFBP4, and VCAN   H. After = 0.011) I,J. For = 0.011) L–N. Inte= 0.011) K. In sumhttp://gepia2.cancer-pku.cn/#index) (accessed on 29 March 2022), and 8 genes were excluded. Therefore, we analyzed 77 signature genes found through machine learning and the hub genes through the PPI network of 20 clinically targeted ICB genes  (VCAN was significantly high in the non-responder group (p = 0.0019) (VCAN [We confirmed the positive correlation (R = 0.58) between  dataset B. The ge dataset C. To detset  H. The ac 0.0019) I. VCAN [9) (VCAN  is chondThese results verify that our machine learning model had good performance and worked well in the validation set.VCAN significantly interacted with them. VCAN acts as a mesenchymal stem cell marker, the expression of which was significantly higher in the non-responder group than in the responder group. In summary, our study selected a signature that can predict ICB response with a basic machine learning algorithm using gastric cancer bulk and single-cell expression data. This will enable efficient treatment of patients with precision medicine.Studies have been conducted to identify potential therapeutic targets of cancer using omics data in machine learning algorithms. We used a basic machine learning algorithm to perform feature selection and predict the ICB response in gastric cancer. The signature genes  have theHowever, there are some limitations to machine learning studies. One of these is deterministic problems. For example, a neural network can find links between inputs and outputs, but it cannot tell you why they are connected. Another issue is the amount of data. Neural networks are complicated designs that necessitate a large quantity of training data to provide useful results. As the design of a neural network grows larger, so too does the amount of data that it requires. Thus, an immunotherapy system’s biology, as well as its description, are beyond the comprehension and scope of neural networks.Predicting the immunotherapy response in patients with gastric cancer is an important issue, particularly in stem-like molecular types, which show drug resistance and several non-responders. Our results can be used in clinical practice for predictive responses to ICB in patients with gastric cancer. Moreover, by suggesting drug targets, combination therapy can be performed according to ICB response, which contributes to drug development and precision medicine.


Recent studies have indicated that a special class of long non-coding RNAs (lncRNAs), namely Transcribed-Ultraconservative Regions are transcribed from specific DNA regions (T-UCRs), 100The aim of this work is to develop a methodology, based on machine learning techniques, for the selection of a predictive signature panel for bladder cancer onset. To this end, we analyzed the expression profiles of T-UCRs from surgically removed normal and bladder cancer tissues, by using custom expression microarray. Bladder tissue samples from 24 bladder cancer patients (12 Low Grade and 12 High Grade), with complete clinical data, and 17 control samples from normal bladder epithelium were analysed. After the selection of preferentially expressed and statistically significant T-UCRs, we adopted an ensemble of statistical and machine learning based approaches  for ranking the most important diagnostic molecules. We identified a signature panel of 13 selected T-UCRs with altered expression profiles in cancer, able to efficiently discriminate between normal and bladder cancer patient samples. Also, using this signature panel, we classified bladder cancer patients in four groups, each characterized by a different survival extent. As expected, the group including only Low Grade bladder cancer patients had greater overall survival than patients with the majority of High Grade bladder cancer. However, a specific signature of deregulated T-UCRs identifies sub-types of bladder cancer patients with different prognosis regardless of the bladder cancer Grade.Here we present the results for the classification of bladder cancer (Low and High Grade) patient samples and normal bladder epithelium controls by using a machine learning application. The T-UCR’s panel can be used for learning an eXplainable Artificial Intelligent model and develop a robust decision support system for bladder cancer early diagnosis providing urinary T-UCRs data of new patients. The use of this system instead of the current methodology will result in a non-invasive approach, reducing uncomfortable procedures (such as cystoscopy) for the patients. Overall, these results raise the possibility of new automatic systems, which could help the RNA-based prognosis and/or the cancer therapy in bladder cancer patients, and demonstrate the successful application of Artificial Intelligence to the definition of an independent prognostic biomarker panel.The online version contains supplementary material available at 10.1186/s12859-023-05167-6. Additio genomes . The conh cancer . Therefoh cancer . The reliscovery , Random mentclasspt{minimaiscovery , penaliziscovery , and Graiscovery . Despitementclass2pt{minimmentclass2pt{minimThe analyses performed by the ensemble models permitted to rank the T-UCRs with respect to the relevance of their altered expression in BlCa patients. In order to merge the results from the different methodologies, we assigned a score at each T-UCRs depending on the rank they obtained in each of the ensemble of feature importance models. We associated higher rank coinciding with higher score and we considered that the models of the ensemble have comparable significance. Formally, the sum of the scores obtained by a T-UCR for each methodology, was used to define a new ranking of significance for the T-UCRs which takes into account the results of all the used methodologies, meaning that we don’t operate penalties or normalization. A further cut-off was applied to the ranking generated from the estimation of the four methodologies, in order to shrink the number of significant T-UCRs . This estimate allows us to define a number of selected T-UCRs with altered expression profiles in cancer as a possible signature panel able to describe the difference between NBE and LG or HG BlCa patients.p values were determined assuming a null hypothesis that there are no differences at all among the groups. Python scripts based on “lifelines” software [p value of the patients survival using Kaplan-Meier analysis.The survival analysis of BlCa patients based on the T-UCRs differential expression signature panel was assessed using Kaplan-Meier survival analysis. Survival data, in months, of the LG and HG patients have been used. The log-rank software  were useIn this section we describe the results obtained for selecting the representative T-UCRs from real data.p value of 0.001 and 0.005 for each comparison and a FC threshold of 2 and 3  using the We created two lists of genes to have different degrees of pre-selection of T-UCRs and to confirm, with more robust analysis, the ranking of the most significant T-UCRs.Applying the ensemble of feature importance methodologies described in section, we ranked the 70 and 24 T-UCRs obtained varying the FC from 2 to 3, respectively. The ranking produced by each methodology returns a similar result only for very few T-UCRs, like uc.8+, making necessary another step of scoring (section) for the definition of the best discriminating panel of T-UCRs. In Table mentclass2pt{minimmentclass2pt{minimUsing the two panels of the newly identified T-UCRs, we reported in a Heatmap plot Fig. a their dp value (0.001), has made the signature panel able to better discriminate between patients BlCa Grades. These observations are in agreement with the lower log-rank p values calculated for the groups of patients predicted by the 13 T-UCRs signature panel  are used for ranking, by scoring methodology, to identify the relevant markers to be taken into account during the clinical practices. Among all the gene expressions obtained from the feature ranking, the uc.8+ stands out for its importance. This results aims for focusing on new automatic systems, which could support the prognosis and/or RNA-based BlCa therapy. Furthermore, our methodology could be applied to other forms of cancer which are characterized for abnormal expression of T-UCRs, such as in hematopoietic tissues (leukemia) , dependiIn  the authp value less than 0.01. Normalized and raw T-UCRs data files were uploaded to the Gene Expression Omnibus (http://www.ncbi.nlm.nih.gov/geo) under GEO accession number GSE68594.Trying to identify/build a diagnostic signature for BlCa early diagnosis, 962 sense and antisense transcripts of 481 known UCRs have been evaluated using a custom microarray (OSU-CCC 4.0), which included sense and antisense probes. The first one corresponding to the sense genomics sequence (named “+”) and the other one to the complementary sequence (named “+A”) for all the 481 human ultraconserved sequences reported by Bejerano et al. . Each prt test are the two main parameters for measuring differential expressions [t test is applied for differential expression with a standard two-tailed test on every sequence in BlCa and NBE data obtaining a p value for each sequence. Using the FC and the p values, we determined the most differentially expressed T-UCRs, comparing the BlCa and the NBE samples. We adopt a cut-off criteria A large amount of T-UCRs expression data from microarray experiments was analysed in order to obtain a differential expression profiling. Fold-Change (FC) and ressions . In partAny ML method depends in part on the learning and generalization capacity of the implemented technique and in large part, on the characteristics of each observation. This definition is only partially true because providing a high number of features does not always lead to good learning. This is because the quality of the data, i.e., the expressive capacity of a feature against the data itself is often more important than the number of features. Including irrelevant elements increases the computational complexity and the problems of learning, therefore leading to problems of underfitting and overfitting. This type of behavior is recognizable in any type of task, whether it is a problem inherent in the data classification, data regression, or generation of new data. To deal with this kind of problem it is common to use feature importance techniques . Therefore feature importance aims to assign a score to input features of a model based on how significant they are at predicting a target variable  through Logistic regression (LR) is a statistical model that in its basic form uses a logistic function to model the probability of a certain class or event [or event . FeatureLeast Absolute Shrinkage and Selection Operator (LASSO) [ (LASSO)  consistsRandom Forest (RF) are an ensemble learning method for classification and regression operating by constructing a multitude of decision trees at training time [ing time . Each treXtreme Gradient Boosting (XGBoost) is the most efficient decision-tree-based ensemble ML algorithm that implements gradient boosting [boosting . A benefThe feature importance models that we consider are:Additional file 1. A new biomarker panel of ultraconserved long non-coding RNA for bladder cancerprognosis by a machine learning based methodology, supplementary materials.


The model's robustness was verified using a 10-fold cross-validation (CV). Survival was analyzed by the Kaplan-Meier method. Univariate and multivariate Cox regression was used to estimate hazard risk. The model was validated in three independent cohorts with different endpoints.  Patients  with stomach adenocarcinoma from The Cancer Genome Atlas (TCGA) cohort were included. An autoencoder was constructed to integrate the RNA sequencing, miRNA sequencing, and methylation data. The features of the bottleneck layer were used to perform the k-means clustering algorithm. The high-risk group had a significantly higher risk of poor survival , a concordance index (C-index) of 0.714, and a Brier score of 0.184. The model performed well both in the 10-fold CV procedure and three independent cohorts from the Gene Expression Omnibus (GEO) repository.  The patients were divided into low-risk and high-risk groups according to the  A robust and generalizable model based on the autoencoder was proposed to integrate multiomics data and predict the prognosis of patients with stomach adenocarcinoma. The model demonstrates better performance than two alternative approaches on prognosis prediction. The results might provide the grounds for further exploring the potential biomarkers to predict the prognosis of patients with stomach adenocarcinoma. Stomach cancer is responsible for approximately 769,000 deaths in 2020 and is the fifth most common cancer and the fourth cause of global cancer-related mortality . StomachAs the result of technological advancement and decreasing costs, high-throughput sequencing technology generated a large amount of multiomics data, which contains a wide spectrum of omics such as genome, transcriptome, and epigenome, and provides an opportunity to identify the risk of stomach adenocarcinoma at different molecular levels. Since single-omics data could only provide limited information, multiomics data could provide a holistic view of the biological system through identifying important biomarkers and providing biological information at multiple levels –7.TherefDeep learning, also called deep neural network (DNN), is a new category of machine learning methods and widely used in many fields –11. Deepk-means clustering algorithm was performed to obtain the subgroup of patients with stomach adenocarcinoma. A Kaplan-Meier curve was drawn for survival analysis, and the log-rank method was used for statistical testing. The obtained subgroup was compared with two alternative approaches: principal component analysis (PCA) and similarity network fusion (SNF). A 10-fold cross-validation- (CV-) like was performed to assess the robustness, and three independent cohorts from the Gene Expression Omnibus (GEO) repository were used to validate the performance of the prognosis model.In this study, an autoencoder was constructed to integrate multiomics data of patients from The Cancer Genome Atlas (TCGA) cohort with stomach adenocarcinoma to identify the risk and predict the prognosis, including mRNA expression, miRNA expression, and CpG methylation. The bottleneck layer was thought to represent the information of multiomics data, and then, the univariate Cox proportional hazard (Cox-PH) model was used to select the nodes in the bottleneck layer related to survival. The Since more information could be provided by multiomics data compared to single-omics data, many algorithms were proposed to integrate different types of omics data, such as similarity network fusion (SNF)  and iCluTo compare the performance of different deep learning autoencoders for cancer subtype identification using multiomics data, Franco et al.  performeBesides, some deep learning frameworks were proposed to integrate multiomics data of patients with cancer to identify the subgroup and predict the prognosis. A framework to integrate multiomics data by a denoising autoencoder for accurate cancer prognosis prediction (DCAP) was proposed by Chai et al. . The fraPoirion et al.  proposedYang et al.  proposedSome of the frameworks involve other types of information beside multiomics data to obtain the subgroup and predict the prognosis. Liu et al.  proposedZhao et al.  proposedHowever, only few studies constructed a deep learning-based model for detecting the subgroups of patients with stomach adenocarcinoma to predict the prognosis and identify the prognostic biomarkers.β-value of all CpG within the gene promoter region, which is defined as 1500 base pairs (bp) upstream of transcription start sites (TSS) of genes, was calculated as the promoter methylation values. Promoter features which have missing value in more than 20% samples were excluded, and samples which have missing value in more than 20% promoter features were excluded. And then, the missing values were imputed by the impute package (https://bioconductor.org/packages/release/bioc/html/impute.html) in R. All the features obtained above were unit scaled by samples as follows:v is a vector of samples and ‖v‖22 is the l2 norm of v.In this study, TCGA-Assembler package  in R wasTo validate the performance, three independent cohorts obtained from the GEO dataset were used. The first cohort was obtained from GSE15459 –39, whicP value and the highest concordance index (C-index), the model was not chosen because of its bad performance in the 10-fold CV procedure  = (x − x′)2. However, to avoid overfitting, a batch normalization layer was appended after the hidden layer. Moreover, an adaptive momentum (Adam) algorithm was used with 32 epochs.Autoencoder is an unsupervised feedforward neural network. According to the previous study , more hiP value greater than 0.10 were screened out. The k-means clustering algorithm was applied to the remaining features. Silhouette index [P value, C-index, and Brier score were calculated.For each representation feature obtained from the bottleneck layer, a univariate Cox proportional hazards (Cox-PH) model was built using survival package in R, and the features with te index  and Calite index  were calk-means algorithm, internal and an external validations were performed.To verify the robustness of the subgroup obtained from the k-means clustering was performed to obtain the subgroup labels. Then, the top 50 mRNA, 30 miRNA, and 50 methylation features were selected based on the P value of analysis of variance (ANOVA) to build a support vector machine (SVM) model. Three single-omics data and the multiomics data were used to build a SVM model, respectively. Subgroup labels of samples from the test sets were predicted by the SVM classifier. Then, log-rank P value, C-index, and Brier score were calculated to evaluate the robustness of the prognosis model.In order to ensure sufficient sample size of the test set, a 10-fold CV-like procedure , 15, 21 P value of ANOVA, of the whole TCGA cohort. The subgroup labels of three independent cohorts were predicted, and the log-rank P value, C-index, and Brier score were calculated.In the external validation, the mRNA features within both the TCGA cohort and the independent cohort were firstly selected. Then, like in the internal validation, a SVM classifier was built using the top 50 mRNA features, which were selected by the x =  is a vector of feature and mad(x) = median({|xi − median(x)|, xi ∈ x}).However, two scaling steps were applied before constructing a SVM classifier whether in training sets, test sets, or the independent cohort. For the mRNA and methylation features, median scale normalization and robust scale normalization were performed. And for miRNA features, median scale normalization and unit scale normalization were performed. Unit scale normalization was shown in the aforementioned procedure, and the median and robust scale normalization were performed as follows:https://CRAN.R-project.org/package=e1071) in R, and 5-fold CV was used to perform a grid search of the best hyperparameters. C-index and Brier score were calculated using the survcomp package [All SVM classifiers were constructed using the e1071 package  [Two alternative approaches were used to compare with the autoencoder. In the first approach, principal component analysis (PCA) was performed and the number of principal components was set to the same as the bottleneck layer. Then, a univariate Cox-PH model was built for each principal component, and the on (SNF)  was usedM value using the lumi package [M value difference| > 1 and FDR < 0.05 using moderate t-test with the limma package [Differential expression analysis was performed between different subgroups of the TCGA cohort. For mRNA and miRNA data, the DESeq2 package in R was used to identify the differentially expressed genes (DEGs) and miRNA expression. The features of the mRNA or miRNA which satisfy the criteria of |log2FC| > 1 and false discovery rate (FDR) < 0.05 were considered to be significant. For methylation data, beta value was transformed into  package  in R, an package  in R.Kyoto Encyclopedia of Genes and Genomes (KEGG) enriched analysis was performed for the significant DEGs, which were obtained from the differential expression analysis, with the threshold of FDR < 0.05, using the clusterProfiler package , 49 in RThe workflow of overall study is shown in P value was set to 0.10. Then, 104 features were thought to be related to survival and used to implement the k-means clustering. According to the silhouette index and the Calinski-Harabasz criterion, K = 2 could be considered as the optimal number of clusters , age , pathologic tumor (T) stage , pathologic node (N) stage , and stage  were identified as risk factors related to OS time. The multivariate Cox regression model also found the same result  after the adjustment of age, pathologic T stage, pathologic N stage, and stage.As the univariate Cox-PH models  showed, k-means clustering, a 10-fold CV-like procedure was performed to assess the robustness. In each fold, ANOVA was performed to select the top 50 mRNA, 30 miRNA, and 50 DNA methylation gene features associated with the obtained subgroup , differentially expressed miRNAs , and DMGs  are shown in Differential analysis was performed to detect the differentially expressed genes (DEGs), differentially expressed miRNAs, and differentially methylated genes (DMGs). 1839 upregulated and 56 downregulated genes were obtained with a criterion of |log2FC| < 1 and FDR < 0.05. 27 differentially expressed miRNA were obtained with the same criterion as DEGs. 1323 DMGs were obtained with a criterion of |As the result of implementation of KEGG pathway enrichment analysis, the upregulated and downregulated DEGs were significantly involved in 30 and 8 signaling pathways, respectively .Wide popularity and poor prognosis of stomach adenocarcinoma make it an urgent request for risk identification. In previous studies, deep learning-based unsupervised methods were implemented using multiomics data and obtained better prognosis performances –16. The P value. Regretfully, GSE26253 and GSE84437, with an endpoint of DFS and response of fourfold increasement of tumor size, respectively, produced a high Brier score, indicating high error of the model fitting on survival data. This suggests that the endpoint of OS would be more suitable in prognosis prediction using autoencoder-integrating multiomics data.According to the 10-fold CV-like validation, the robustness of the model identifying the subgroups has been verified. In addition, the subgroup could be considered as a risk factor according to the univariate and multivariate Cox-PH model. Moreover, the model was validated in three independent cohorts with different endpoints, and each cohort produced a significant log-rank P value  and C-index . This may indicate that complex architecture could not provide a better performance. Information from miRNA expression may also play an important role in the model based on the autoencoder to show its robustness. Both studies provide guidance for personalization of medical services.In fact, Xu et al.  have alrDEGs, differentially expressed miRNAs, and DMGs between two subgroups were obtained and provided an opportunity to be used as potential prognostic biomarkers or candidate therapeutic targets in future clinical practice. Differential analysis and enrichment analysis were practiced to understand the difference between two subgroups at the molecular level. Some studies have revealed the relationship between the top 10 DEGs, DMGs, and stomach adenocarcinoma. Expression of CLDN6 indicates poor prognosis of gastric cancer –52. RBFOHowever, only RNA-Seq, miRNA-Seq, and DNA methylation data were used in this study. This might not provide sufficient information of the biological process, and more omics data could be included in the further study. Regretfully, no independent cohort with miRNA-Seq and DNA methylation data has been found to use in the external validation. Moreover, the poor interpretability of deep learning may prevent the prognosis model from being widely used in clinical practice, and a more theoretic approach is required to explain how the model works.P value of 2.80e − 06, a C-index of 0.714, and a Brier score of 0.184. The robustness of the prognosis model was successfully validated using a 10-fold CV-like procedure, and the performance was verified in three independent cohorts. The model based on the autoencoder has a better performance than PCA  and SNF  on prognosis prediction. DEGs, differentially expressed miRNAs, and DMGs between two subgroups were uncovered. The results might provide the foundation for further exploring the potential biomarkers to predict the prognosis of patients with stomach adenocarcinoma.Prognosis-related risk was evaluated based on the architecture of the autoencoder, and the patients were divided into low-risk and high-risk groups. The high-risk group had a significantly higher risk of poor survival with an adjusted HR of 2.386, a log-rank