As an important approach to cancer classification, cancer sample clustering is of particular importance for cancer research. For high dimensional gene expression data, examining approaches to selecting characteristic genes with high identification for cancer sample clustering is an important research area in the bioinformatics field. In this paper, we propose a novel integrated framework for cancer clustering known as the non-negative symmetric low-rank representation with graph regularization based on score function (NSLRG-S). First, a lowest rank matrix is obtained after NSLRG decomposition. The lowest rank matrix preserves the local data manifold information and the global data structure information of the gene expression data. Second, we construct the Score function based on the lowest rank matrix to weight all of the features of the gene expression data and calculate the score of each feature. Third, we rank the features according to their scores and select the feature genes for cancer sample clustering. Finally, based on selected feature genes, we use the K-means method to cluster the cancer samples. The experiments are conducted on The Cancer Genome Atlas (TCGA) data. Comparative experiments demonstrate that the NSLRG-S framework can significantly improve the clustering performance. High-throughput DNA microarray technology has long been used to collect biomedical cancer gene expression data . In geneFeature selection is an important data processing method that can select the most important feature subset from a set of features and reduce the dimension of the feature space. The existing feature selection methods can be divided into two groups: “wrapper” methods and “filter” methods . WrapperAs we know, the global structure plays an important role in clustering when the data contain multiple subspaces . The LS Motivated by the above insights, we propose a novel framework that integrates the advantages of the LRR and LS methods. Based on the multi-cancer gene expression dataset, the proposed framework is used to select the feature gene for cancer sample clustering.First, we incorporate the constraints of the non-negative symmetric low-rank matrix and graph regularization in the LRR method and propose a non-negative symmetric low-rank representation graph regularized method, or NSLRG method for short. The NSLRG method considers the property and structure of the gene expression data. The NSLRG method obtains the lowest rank matrix, which preserves the local data manifold information and the global data structure information of the raw data.Second, according to the lowest rank matrix, we construct a Score function to evaluate each gene for selection of the feature genes. The importance level of a gene depends on its significance for the global and local structures of the raw data. We integrate the NSLRG method with the Score function to achieve the aim of evaluating and selecting feature genes, and we refer to it as the NSLRG-S framework.Finally, we apply the K-means method to cluster cancer samples based on the selected feature genes. Based on the different multi-cancer gene expression data, the experimental results suggest that the performance of the NSLRG-S framework is better than that of other methods.In summary, the contributions of this paper include the following main aspects:We propose a novel data mining method known as the NSLRG method. The NSLRG method operates under graph regularization and non-negative symmetric low-rank matrix constraints. The NSLRG method can learn the lowest rank matrix to satisfactorily represent the gene expression data and can capture the global structures and local geometric structures of the raw data. Non-negativity is more consistent with biological modelling. The symmetric constraint improves the interpretability of the lowest rank matrix. The constraints of non-negativity and symmetry facilitate the lowest rank matrix to learn the structure of the gene expression data.Based on the lowest rank matrix, we propose a Score function to select the feature genes for cancer sample clustering. The selected feature genes have important significance to the raw data. In the clustering of cancer samples, the selected genes have strong discriminability to realize the classification of different samples.We present a novel feature selection framework, known as NSLRG-S, that is designed to evaluate and select the feature genes for cancer sample clustering. Based on this framework, the selected result of the gene expression dataset has lower dimensionality. In multi-cancer sample clustering, this method has a high recognition rate to find subsets using the selected result as experimental data. We conduct extensive experiments to demonstrate that the feature gene subset selected by NSLRG-S has good performance in cancer sample clustering.Related Work, we briefly review the original LRR and several related variants as well as the LS method. In section Method, we first present the NSLRG method and its optimal solution, and based on the Score function, the NSLRG-S framework is clearly given for modelling of multi-cancer gene expression data. Section Experiments analyses and discusses the NSLRG method based on multiple evaluation indicators and convergence analysis. The performance of the NSLRG-S framework is validated by experiments based on synthetic data and multi-cancer gene expression data. Section Conclusions Work presents the conclusion of our work.The remainder of this paper is organized as follows. In section In this section, we briefly introduce the original Low-Rank Representation (LRR) , the relX = ∈ℝm×n represents the observed data, of which each column is a data sample. Therefore, the matrix X contains n data samples drawn from independent subspaces. The matrix D = ∈ℝm×k represents the dictionary data and is overcomplete. The general model of the LRR method is formulated as follows.The Low-Rank Representation (LRR) method is an efficient method for exploring observed data and subspace clustering. The main idea is that each data sample can be represented as a linear combination of the dictionary data. In general, the matrix Z∈ℝk×n is the coefficient matrix. The aim of this model is to learn a lowest rank matrix Z* to represent the observed data X. In the actual application, the matrix X always replaces D as the dictionary data  and l2,1- norm   , and λ >Many researchers have attempted and proposed variants based on the original LRR method. The main idea is to introduce constraint items to optimize or improve existing methods. For example, the original LRR method is improved by considering the geometric structures within the data, including the graph regularization method  and k-neUnder certain conditions, the geometric structure within the data is crucial for the result that we desire. To address this issue, researchers introduced graph regularization into the LRR method to create the graph-regularized low-rank representation (GLRR) method . The equl2,1-norm and tr(⋅) is the trace of the matrix, L is the graph Laplacian, and λ1 and λ2 are two parameters used to balance the graph-regularized item and the error item. Based on manifold learning, the graph-regularized item achieves the aim that representative data points zi and zj can hold the property of the data points ix and jx of X, which are closed in the intrinsic manifold. Therefore, the inherent geometric structure in the raw data is preserved in the low-rank matrix Z.where the error item uses the The non-negativity constraint ensures that every data point is in the convex hull of its neighbours. The sparse constraint ensures that each sample is associated with only a few samples. The non-negative and sparse low-rank matrix supplies a well discriminated weight for the subspace and information group.Inspired by the above insights, Zhuang et al. proposed the non-negative low rank and sparse graph (NNLRS) method . The forZ∥1 is the l1-norm to guarantee the sparsity of coefficient matrix. In real-world applications, the sparsity and non-negativity matrix Z obtained by the NNLRS method can offer a basis for semi-supervised learning by constructing the discriminative and informative graph  is the estimated variance of the r-th feature in all data points, and the larger the Var, the more information held by the r-th feature. The r-th feature between all samples. For larger values of Sij and the smaller values of LS(r) tends to be smaller, meaning that the importance level of the feature is higher. Therefore, the important features are selected according to LS(r).where the heat kernel function NSLRG Method presents the NSLRG method and its optimization algorithm. In subsection NSLRG With Score Function, we introduce the NSLRG method with the Score function. The last subsection Framework of NSLRG-S is devoted to clustering of cancer samples based on NSLRG-S modelling of gene expression data.In this section, we propose a novel feature selection framework to select the feature genes for cancer clustering. This framework is set up based on the NSLRG method and the Score function. We refer to this approach as the NSLRG-S Subsection Because graph regularization can preserve the intrinsic local geometric structure in the original data, it has received much attention from researchers. The theory of graph regularization is based on the principle that the representation of the intrinsic local geometric structure that is distributed in the original data is inherited by a graph under the new basis mapping. In the graph, the vertices correspond to the data points, and the edge weights represent the relationships between the data points . Thus faix and jx are “close”, an edge exists between ix and jx. In this work, we use the K-nearest neighbour method to find the connection of ix and jx. In other words, if ix or jx is among the K-nearest neighbours of each other, the data points ix and jx are located on the same edge. This construction strategy is simpler for determination of connected edges, which tends to lead to a connected graph. In the next step, the edge weights are defined to represent the affinity between the data points. In current study, we define a symmetric weighting matrix W by the heat kernel weighting function  method, and its objective function is written as follows.We introduce graph regularization and sparse items into the original LRR. Furthermore, we impose the non-negative and symmetric constraints on the low-rank matrix Z. The low-rank matrix should be sparse to improve the recognition ability. Therefore, the matrix Z with a sparse constraint could make the result of the representation more discriminative. However, the ∥Z∥0 item of problem (10) is NP-hard. Thus, as suggested by matrix completion methods  to O(rn3), where r is the rank of low-rank matrix Z. This algorithm makes it possible for LRR to be applied on large-scale dataset, such as video surveillance, digital images, and gene expression data. Therefore, the LADMAP algorithm has been recognized as the most efficient algorithm for solving the problem of convex relaxation of low-rank and sparse matrices. Similarly, we also adopt LADMAP to solve (11).As we know, many algorithms are based on convex relaxation to solve the high-dimension optimization problem, such as Singular Value Thresholding (SVT) , AccelerZ, we use an auxiliary variable Q to separate the variables, i.e., nuclear norm (∥Z∥*) and l1-norm (∥Z∥1). The objective function can be rewritten as equation (12) using the Augmented Lagrange Multiplier method  is the Euclidean inner product between the matrices A and B; and ∥⋅∥F is the Frobenius-norm. Mathematically, equation (12) is equivalent to equation (13) after applying a small transformation. Equation (13) facilitates processing of the next step.where Hence, We divide equation (13) into three subproblems and solve it in three steps. The three subproblems are written as follows.Finally, we solve the above subproblems to find the optimal solution. The specific steps are given as follows.Step 1. Update Z: The matrix Z can be obtained by solving subproblem ℓ1 while keeping E and Q fixed. First, we define the following formula (17) based on ℓ1.Zk, we can obtain the following formula (18).By setting the first derivative of ℓ1 can be replaced by solving the following problem (19).According to LADMAP, subproblem where Equation (19) can be transformed into the following formula (20).Z, we adopt Lemma 1 of , its closed solution is equation (22).Ur, ∑r and Vr are the members of the skinny singular value decomposition (SVD) of the matrix r = diag; rδ is the singular value for which the positive singular values are greater than Ir is an identity matrix with size r × r.In this work, Lemma 1, we make Zk+1 using the singular value thresholding operator Sϵ = sgn(x)max. The iterative formula is written as follows.Based on Zk+1 by equation (23), the non-negative constraint is imposed on matrix Zk+1 through a non-negative operator. The non-negative operator is defined as follows.where Finally, the non-negative symmetric low-rank matrix Step 2. Update E: The matrix E can be obtained by solving subproblem ℓ2 while keeping Z and Q fixed. Analogously, following equation (18), the first derivative of ℓ2 is set with respect to Ek, i.e., E is given as follows.According to the NSHLRR method , the iteStep 3. Update Q: The matrix Q can be obtained by solving subproblem ℓ3 while keeping Z and E fixed. Similar to Step 2, we set the first derivative of ℓ3 with respect to Qk, i.e.,Q is written as follows.According to the NSHLRR method , the iteAlgorithm 1 clearly summarizes the above solution steps. The initialization parameter values are set based on experimental experience and the existing relevant research recommendations , which occurs before the first inflection point of the score curve. Thus, we cluster the cancer samples based on the selected feature genes.Based on the result of the Score function, all features are arranged in ascending order to form a score curve. The number of selected features is We refer to the NSLRG method with the Score function as the NSLRG-S framework for short. In a nutshell, the NSLRG-S framework can be divided into four steps. In the first step, the lowest rank matrix is obtained by the NSLRG method. In the second step, the Score function is used to evaluate and rank features based on the lowest-rank matrix of the first steps. In the third step, the feature genes are selected according to the results of the Score function. In the fourth step, cancer sample clustering is processed based on the selected feature genes. This novel framework delivers better reliability in selection of the most important feature for cancer sample clustering according to the global and local structure of the raw data.Based on the proposed NSLRG-S framework, our goal is to model the gene expression data and cluster the cancer samples according to the selected feature genes.Xm×n represents the gene expression data with size m × n, and one row represents the expression level of a same gene in different samples. The totals of genes and samples are m and n, respectively. Usually, m is notably large and n is rather small. The matrix τ (τ <m) feature genes are selected based on the first inflection point of the score curve. Finally, we cluster the cancer samples based on the selected feature genes to demonstrate the selected genes with efficient discrimination. The result is compared with those of different methods, including the K-means, Graph Regularized Nonnegative Matrix Factorization (GNMF) (Experiments on Gene Expression Data. Algorithm 2 is the framework of the NSLRG-S for clustering of gene expression data.The modelling process is shown in n (GNMF) , Robust n (GNMF) , Sparse n (GNMF) , Graph-Ln (GNMF) , LS (He n (GNMF) , and LLRn (GNMF)  methods.Evaluation and Quantitative Benchmarks, we select three quantitative benchmarks to evaluate the experimental results. In subsection Experiments on Synthetic Data and subsection Experiments on Gene Expression Data, comparative experiments are conducted on synthetic data and cancer gene expression data, respectively.To evaluate the performance of the NSLRG-S framework, we compare the NSLRG-S framework with multiple typical methods, including the K-means, GNMF , RPCA C, SPCA J, GLPCA , LS He , and LLRTo evaluate the performance of the clustering results based on comparison methods, we select three quantitative benchmarks: the clustering accuracy rate (Acc) , F1 measThe Acc is defined as follows.N is the total number of samples, and Ξ) is used to identify whether iξ and ir are matched. The iξ and ir are the actual label and clustering label of the i-th sample, respectively, and if they are matched, the value of Ξ) is equal to one; otherwise, its value is equal to zero. The map(ir) is the mapping function based on the Kuhn-Munkres method  is the item that records the number of positive samples that are clustered into their own positive class, fp  is the item that records the number of negative samples that are clustered into the positive class, and fn  is the item that records the number of positive samples that are clustered into negative class. tp, fp and fn. The F-Measure can balance the contribution of fn by weighting Recall through the parameter ϕ > 0. When the parameter ϕ = 1, F-Measure becomes the most common form, i.e., F1 measurement, and equation (31) is rewritten as follows.where Precision rate and Recall rate to the F1 measurement are equal.F1 measurement reaches its best value at 1 and its worst score at 0. The relative contributions of the Algorithm 2). The Rand Index (RI) is used to compute how similar the result of clustering is to the actual classification. The RI is defined as follows.The given data have two partitions: one is the actual classification, and the other is the clustered result  and (2). These synthetic data contain ten independent subspaces.Oi+1 = TOi, 1 ≤ i ≤ 9. The value of the database ranges from 0 to 1, T is the transform random rotation matrix, and O1 is a random orthogonal matrix of 1000×100. The rank of each original database is 100.Construction of 10 original databases by Xi = OiQi,1 ≤ i ≤ 10, where the matrix N, and its size is 100×10. All extracted data vectors are combined in synthetic data We extract 10 data vectors from each original database by FE-V(k) based on the loss function value to calculate the convergence rate. In the same iterations, the smaller the value of the Error-Values, the faster the convergence rate. The formula is given as follows.We define an Error-Values function FE-V(k) is equal to zero. To clearly characterize the convergence rate, where the minimum value of In this subsection, we conduct experiments on gene expression datasets. The experimental datasets are downloaded from the famous gene expression database The Cancer Genome Atlas (TCGA). We cluster the cancer samples based on the feature genes obtained by the NSLRG-S framework. The experimental results demonstrate that we can improve the performance in cancer samples clustering by applying the selected feature genes.The TCGA database is a source of experimental data and is an important project for accelerating and comprehensively understanding cancer genetics using innovative genome analysis technologies . This daWe downloaded five cancer gene expression datasets, namely, esophageal carcinoma (ESCA), head and neck squamous cell carcinoma (HNSC), cholangiocarcinoma (CHOL), colon adenocarcinoma (COAD) and pancreatic adenocarcinoma (PAAD). Each type of gene expression dataset contains cancer tissue samples and normal tissue samples. There are 20,502 genes in each tissue sample. The distribution of each gene expression dataset is listed in In addition, to find the feature gene with a high recognition rate between different cancers for cancer sample clustering, we construct seven mixed datasets. The mixed datasets are HN-PA, ES-PA, CO-ES and HN-CH; HN-PA-CH, ES-PA-CH, and CO-PA-CH. The construction rule combines tumour tissue samples that come from different gene expression data, and the combined datasets contain two or three types of cancers. For example, in the HN-PA data, HN represents all of the cancer tissue samples of the HNSC data, and PA represents the total of the cancer tissue samples of the PAAD data. The cancer tissue samples of HN and PA are combined to construct the new mixed data, i.e., HN-PA, which contain two types of cancers and have 574 cancer tissue samples. For the other mixed datasets, the distributions are listed in The five original datasets and seven mixed datasets are used in experiments. We classify all datasets into three categories according to the number of cancers they contain. The datasets that contain one type of cancer belong to Category I. Thus, Category I contains PAAD, HNSC, ESCA, COAD, and CHOL. Datasets that contain two types of cancers belong to Category II, and they are HN-PA, ES-PA, CO-ES, and HN-CH. The datasets that contain three types of cancers belong to Category III, and the names of these datasets are HN-PA-CH, ES-PA-CH, and CO-PA-CH. λ1, λ2, λ3) of the NSLRG method, we assume that the optimal value of each parameter exists within an estimation range of 10t. We study the influence of each parameter on feature selection and select the optimal parameters according to the different datasets. First, our main task is to determine the sensitivity of each parameter to the different datasets. We change one parameter within the candidate interval while holding the other two parameters fixed to explore the influence degree of this parameter on the dataset. We find that the parameter λ3 is insensitive for all datasets. Therefore, the NSLRG method is robust for the parameter λ3, and we select the λ3 = 10-3 according to experimental experience. The details of selection of the other two parameters are listed in In the experiments, we need to select the optimal parameters of the different datasets. For the three parameters , the more unstable the result. Therefore, in our experiments, we improve the reasonableness of the result by running the experiment 50 times. The mean of the results is taken as the measurement of the clustering results.By comparing the clustering results of NSLRG-S and other methods, we find that the results of the NSLRG-S method are the best of all methods in most datasets. According to In addition to the numerical comparison, we also find that the NSLRG-S method has different advantages after comparing it with different comparison methods. In the next section, we conduct a more detailed comparison and analysis between NSLRG-S and the other comparison methods.In the seven comparison methods , K-means is the traditional clustering method; GNMF belongs to matrix factorization techniques, which extend the nonnegative matrix factorization with preservation of the intrinsic geometric structure ; RPCA, SFirst, we compare the NSLRG-S framework with K-means. Based on Second, we compare the NSLRG-S with the GNMF method. In GNMF, a nearest neighbour graph is constructed by encoding the geometrical information of the data space. The method seeks matrix factorization, which incorporates the graph structure . Based oThird, we compare the NSLRG-S with the RPCA, SPCA, and GLPCA methods. RPCA, SPCA, and GLPCA belong to principal component analysis methods and are suitable for processing high-dimensional gene expression data by learning a low-dimensional representation. The results of NSLRG-S are better than those of three methods, except for the CHOL dataset. We can conclude that the NSLRG-S method is better than the variant methods of principal component analysis in clustering of multiple cancer samples.Fourth, we compare the NSLRG-S with the LS method. Based on Finally, we compare the NSLRG-S with the LLRR method. Based on Furthermore, we note an interesting trend in the results of three categories of datasets for each method, as shown in In this paper, we cluster the cancer samples of multi-cancer gene expression datasets based on select feature genes obtained by the NSLRG-S framework. In addition, NSLRG-S simultaneously considers the local and global structure of the raw gene expression dataset. The selected feature genes have a high recognition rate in subspace clustering. The comparison experimental results suggest that the NSLRG-S framework can significantly improve the cancer samples clustering performance.https://cancergenome.nih.gov/. We have uploaded scripts and examples on GitHub to adhere standards for reproducibility. The URL is https://github.com/guoguoguolu/NSLRG-S-method-scripts-and-example-files.The datasets generated for this study can be found in the [The Cancer Genome Atlas (TCGA)] JW and CL conceived the original research plans and methodology. JL and XK performed synthetic data analysis. JW, CL and XK performed experiments on gene expression data. JW and CL supervised and wrote the original draft. JW, CZ, and XZ reviewed and revised the writing.This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 61872220, 61702299, and 61873117.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


R/Bioconductor package singscore (https://bioconductor.org/packages/singscore).Gene set scoring provides a useful approach for quantifying concordance between sample transcriptomes and selected molecular signatures. Most methods use information from all samples to score an individual sample, leading to unstable scores in small data sets and introducing biases from sample composition (e.g. varying numbers of samples for different cancer subtypes). To address these issues, we have developed a truly single sample scoring method, and associated singscore against widely-used methods, including GSVA, z-score, PLAGE, and ssGSEA. Our approach does not depend upon background samples and scores are thus stable regardless of the composition and number of samples being scored. In contrast, scores obtained by GSVA, z-score, PLAGE and ssGSEA can be unstable when less data are available (NS < 25). The singscore method performs as well as the best performing methods in terms of power, recall, false positive rate and computational time, and provides consistently high and balanced performance across all these criteria. To enhance the impact and utility of our method, we have also included a set of functions implementing visual analysis and diagnostics to support the exploration of molecular phenotypes in single samples and across populations of data.We use multiple cancer data sets to compare singscore method described here functions independent of sample composition in gene expression data and thus it provides stable scores, which are particularly useful for small data sets or data integration. Singscore performs well across all performance criteria, and includes a suite of powerful visualization functions to assist in the interpretation of results. This method performs as well as or better than other scoring approaches in terms of its power to distinguish samples with distinct biology and its ability to call true differential gene sets between two conditions. These scores can be used for dimensional reduction of transcriptomic data and the phenotypic landscapes obtained by scoring samples against multiple molecular signatures may provide insights for sample stratification.The The online version of this article (10.1186/s12859-018-2435-4) contains supplementary material, which is available to authorized users. It shouweb-tool  which dogene set .singscore. Using breast cancer data and several gene expression signatures we compare our approach to the methods listed above. The singscore method is simple, making the scores directly interpretable , and our comparisons show that it is not only fast, but it also produces stable and reproducible scores regardless of the composition and number of samples within the data. Finally, we include examples from breast cancer gene expression data to show visualisation options and demonstrate the application of the singscore method for molecular phenotyping in a clinical context.Here, we introduce a rank-based single sample scoring method, For a sample transcriptome which has been corrected for technical within-sample bias , genes are ranked by increasing mRNA abundance.S) and normalised score  or unidirectional signatures with known direction , genes are ranked based on their transcript abundance in increasing order for the up-set and in decreasing order for the down-set. Mean ranks are separately normalised relative to the theoretical minimum and maximum values, centered on zero and then summed to provide the score (i.e. dir is the gene set direction (i.e. expected up- or down- regulated genes);Sdir, i is the score for sample i against the directed gene set;g in the directed gene set (increasing transcript abundance for expected up-regulated genes and decreasing abundance for expected down-regulated genes);Ndir, i is the number of genes in the expected up- or down-regulated gene set that are observed within the data (i.e. signature genes not present within the RNA abundance data are excluded);i against genes in the signature, and;Smin, i and Smax, i are the theoretical minimum and maximum mean ranks which can be derived from an arithmetic sum (assuming unique ranks); for a series of n numbers starting at a1 and with a constant difference d, the sum can be calculated as a1 = 1, d = 1, n = Ndir, i and dividing through by Ndir, i to obtain the mean:Where:a1 = :Similarly, the maximum value can be obtained by setting Ntotal, i is the total number of genes in sample i.Where:For undirected gene signatures (without a known or expected direction for changes in expression), we compute the average, absolute, median-centred rank Eqs.  & 6. As Si is the score for sample i against the undirected gene-set;g in the undirected gene set; i.e.ceil represents the ceiling function;Ni is the number of genes in the undirected gene set that are observed within the data (i.e. signature genes not present in the RNA abundance data are excluded);i against the undirected gene-set, andSimin,  and Simax,  are the theoretical minimum and maximum mean ranks obtained from the arithmetic series expansion. For undirected gene-sets, the minimum  and maximum  values can be derived as:Where:As shown above, scores are normalized against theoretical minimum and maximum values, centered on zero (directed signatures) and if applicable  scores are then summed. Centering and normalization is performed in this manner to maintain independence between samples. This is similar to a Wilcoxon rank-sum test when examining an expected up- or down-regulated gene set.p-value) and abundance (high mean logCPM or logTPM), then, singscore can score individual samples with an estimate of significance. Under the null hypothesis that members of the expected up-regulated genes are not enriched within high-abundance transcripts (and/or expected down-regulated genes are not enriched within low abundance transcripts), a permutation test with random gene sets can be performed. Care should be taken when interpreting such results without a specific biological hypothesis as gene sets expressed at high levels and/or heavily influenced by the experimental protocol  may lead to spurious conclusions. As shown in Additional file If users have a gene set associated with a specific cell phenotype and these genes undergo large changes in expression, for example, the results from a differential expression analysis where genes are filtered by significance (low FDR or adjusted R (v. 3.3 and greater) and Bioconductor (v. 3.4 and greater). We have produced an R/Bioconductor package, singscore, to implement this method, and have included several visualisation functions that produce both static  and intg plotly ) plots.R/Bioconductor package GSVA (v1.26.0) was used to evaluate the performance of the GSVA, ssGSEA, z-score and PLAGE methods [!Norm, by removing the  normalisation step in the GSVA package implementation of ssGSEA, to test performance in smaller data sets with less samples. However, it should be noted that while ssGSEA scores obtained from the GSVA package and GenePattern are highly correlated, the scores are not directly comparable , and the integrated cell line TGFβ-EMT data from Foroutan et al. [In this study, we used The Cancer Genome Atlas (TCGA) breast cancer  RNA-seq n et al.  Table 1seebelowR/Bioconductor, and count level data were obtained using the featureCount function with default parameters. The edgeR package [The SRA files from Daemen et al. were obtained July 2016 (GSE48213), and converted to fastq files using the fastq-dump function in the SRA toolkit . Reads wsi, two data sets were created by sampling from both the RNA-seq and microarray data to select a sample si and n − 1 other random samples. The score for sample si was then computed using all listed methods, and this process was repeated across all 500 samples at a given sample size, such that there are 500 matched scores in total from both the microarray data and RNA-seq data. The Spearman’s rank correlation coefficient and concordance index were then calculated between sample scores from the microarray and the RNA-seq data. We note that for some methods sampling data in this manner can modify the background samples for a sample of interest, reflecting the influence of overall sample composition on the final scores. A similar analysis was performed by varying the number of genes, sub-sampling genes from the gene set of interest.Method stability was examined using 500 TCGA breast cancer samples with both RNA-seq and microarray data , and genes, NG = . All permutations were repeated 20 times to estimate error margins.We performed this analysis with both epithelial and mesenchymal gene sets (expected up-regulated gene sets) , and the7. We simulated NS = 30 samples and NG = 1000 genes, representing two biological conditions (NS = 15 in each group) with 30 differentially expressed genes (DEGs) between them. This simulation was repeated 100 times, each time creating three gene sets of size 30 to represent the three scenarios with different signal to noise ratios: (i) when 50% of the genes in the gene set were differentially expressed (15 DEGs and 15 non-DEGs), (ii) when 80% of the genes were differentially expressed (24 DEGs and 6 non-DEGs), and (iii) when none of the genes were differentially expressed (30 non-DEGs). We also varied the logFC of DEGs (effect size) across the two conditions. We then used all methods to score samples against these gene sets and applied a t-test on the scores to evaluate the performance at separating the two conditions. The statistical power and type 1 error  were estimated at α = 0.05 for each effect size with a given signal to noise ratio. The power was calculated as the proportion of the positive tests  in 100 simulations for each scenario (50% DE and 80% DE). The type 1 error was calculated as the proportion of simulations where non-DEG sets tested positive .We evaluated the power of each method to differentiate biologically distinct groups. For this, we simulated RNA-seq data using methods from Law et al. . An inveNS = 30 and NG = 10,000, representing two biological conditions (NS = 15 in each group) with 2000 DEGs (logFC or effect size = 1.1). We repeated this simulation 100 times, each time creating (i) 500 gene sets (of size 30) where 50% of genes were DE, (ii) 500 gene sets where 80% of genes were DE, and (iii) 500 gene sets where genes were randomly sampled, representing gene sets with no signal. We then scored samples against all 1500 gene sets in each simulation and performed a t-test between the group scores. Next, p-values from the 50% DEG set  and non-DEG set  were combined and adjusted for multiple hypothesis testing to produce estimated q-values [q-values were thresholded at FDR = 0.05, with gene sets that tested positive considered as DEG sets. Performance of these predictions was quantified using the F1 score which accounts for both the precision and recall of each method. This was repeated for p-values from the 80% DEG sets and non-DEG sets.Next we compared methods for their ability to produce different scores for two conditions with differentially expressed gene sets. RNA-seq data were again simulated using the method of Law et al.  with NS q-values . These qTo compare the computational time of each scoring method, we randomly selected 10,000 gene sets from MSigDB signatures , 21 and singscore method was compared to GSVA, z-score, PLAGE, ssGSEA, and ssGSEA without normalization (ssGSEA!Norm), using both microarray and RNA-seq data from the TCGA breast cancer cohort. Overlapping samples between the two platforms (NS = 500) were scored using three gene signatures: the epithelial, mesenchymal, and TGFβ-induced EMT (TGFβ-EMT) signatures [singscore and ssGSEA!Norm compared to the other methods when varying the sample number and number of genes in the data . This demonstrates that the singscore may be particularly useful in cases where sample numbers are relatively low, or where there may be a heterogeneous sample composition . We depict these effects by changing the balance/composition of samples under two settings: (1) overlaying mesenchymal scores for control and TGFβ-treated cell lines (NS = 2–4) on to the score distributions for a larger set of samples related to these groups  and a collection of breast cancer cell lines [NS = 64 RNA-seq) against mesenchymal and epithelial signatures from Tan et al. [Scoring samples against multiple molecular signatures and plotting them in 2D can be useful to stratify samples based on the associated molecular phenotypes of samples. For example, scoring TCGA breast cancer samples  of the gene set ranks to estimate relative rank dispersion. Plotting scores against dispersion for the samples in the TGFβ-EMT data shows that samples with a high total score also have lower dispersion, demonstrating more coordinated changes in the up- and/or down-sets in these samples Fig. . The lesR/Bioconductor package singscore. Our method can easily be applied on any high throughput transcriptional data from microarray or RNA-seq experiments. While our method is non-parametric, genes with low read counts should be filtered out, adjusted for gene length [We have described a rank-based single sample gene set scoring method, implemented in the e length , 25, ande length  and othee length , 28, becsingscore approach yields stable scores for individual samples because they are treated independently from other samples, in contrast to GSVA, PLAGE, z-score, and ssGSEA  also results in stable scores, the raw scores produced by the ssGSEA!Norm algorithm cannot be directly interpreted . This issue became apparent when comparing unnormalized ssGSEA scores from either the GSVA or GenePattern implementations (using the same parameters) where it was observed that while the scores are highly correlated they are not directly comparable   have notsingscore method provides a simple and easy-to-understand pipeline which is also computationally fast. This method performs as well as the comparable scoring methods in large data sets in terms of stability, while outperforming them in smaller data sets by providing more stable scores, which are also easily interpretable. We further show that, excluding PLAGE which had relatively poor performance in these tests, all methods had a similar power, type I error, and/or F1 score when the signal to noise ratio was high, however, the singscore, GSVA and z-score performed slightly better for data with a less prominent signal. Several visualisation options at both the bulk and single sample level are provided in the R/Bioconductor package singscore to enable users to explore genes, gene signatures, and samples in more depth.We also note that methods requiring a large number of samples and a balanced composition to calculate a precise and stable score for individual samples may need to be re-run several times across a large data set when new samples are added. This adds extra complexity which may not be obvious to most users running such scoring methods. Our singscore generates scores that are stable across a range of sample sizes and numbers of measured genes. This is due to it being a non-parametric, rank-based, and truly single sample method. Moreover, scores generated by our method show high level of consistency across independent data sets and can be normalised at a single sample level, resulting in easily-interpretable scores.In the context of personalised medicine there is an increasing need to examine data from an individual patient, or from a small number of samples in pre-clinical experiments. Current scoring methods are parametric and/or depend on a large number of samples to produce stable scores, while Additional file 1:This includes eight supplementary figures supporting the conclusions of the article. (DOCX 1948 kb)Additional file 2:This includes IDs for 500 of the overlapping samples between the TCGA breast cancer RNA-seq and microarray data. (TXT 8 kb)


Feature selection and classification are the main topics in microarray data analysis. Although many feature selection methods have been proposed and developed in this field, SVM-RFE (Support Vector Machine based on Recursive Feature Elimination) is proved as one of the best feature selection methods, which ranks the features (genes) by training support vector machine classification model and selects key genes combining with recursive feature elimination strategy. The principal drawback of SVM-RFE is the huge time consumption. To overcome this limitation, we introduce a more efficient implementation of linear support vector machines and improve the recursive feature elimination strategy and then combine them together to select informative genes. Besides, we propose a simple resampling method to preprocess the datasets, which makes the information distribution of different kinds of samples balanced and the classification results more credible. Moreover, the applicability of four common classifiers is also studied in this paper. Extensive experiments are conducted on six most frequently used microarray datasets in this field, and the results show that the proposed methods have not only reduced the time consumption greatly but also obtained comparable classification performance. The invention of DNA microarray technology has spawned massive gene expression microarray data, which brings a new way for the gene-related studies, mainly gene recognition and disease diagnosis . Over thSmall sample size with high dimensionality is the main challenge of microarray data analysis, and class imbalance makes this case worse. Class imbalance refers to the large gap in the number of samples belonging to different classes, which often results in an unreliable classification result. For example, if given a test set containing two classes of samples, in which the sample number of A is two times that of the other B. In this case, if we predict all the samples in test set as A, then we would get the accuracy 66.67% which is much bigger than 50%. This is very unreasonable. That is to say, class imbalance can lower the credibility of classification accuracy. In addition to this, ranked features with imbalance dataset are also problematic because the information is unevenly distributed in training set. Therefore, various resampling technologies emerge to alleviate this issue –10. AmonFeature selection methods have received significant attention in the last decades, some of which emerge as new algorithms while some others merge as variants , 2. For Classifiers are the core component of microarray data analysis. However, they are not given enough attention in the existing researches, which is not reasonable. Guyou et al. claim that the features selected matter more than the classifier used and the differences in classifiers had little effect on the results. Moreover,  just putThe remainder of this article is organized as follows: In section 2, we introduce the methods presented in this paper successively, including random value-based oversampling, recursive feature elimination with variable step size and large-scale linear support vector machine. Section 3 presents the experiments, including the description of datasets, data preprocessing, parameters estimation, performances evaluation measures, experimental results and the discussion. Section 4 is the conclusion.The values of microarray data are the results of genes expression which are biologically specific and should not be arbitrarily altered. The approach presented in this section aims to solve the class imbalance problem of microarray data while maximizing the biological significance without causing information loss and model overfitting.Random value-based oversampling (RVOS) assumes that the samples with the same category label are subject to the same distribution. Under this assumption, we construct a data matrix with the minority class and choose one value randomly from each of column as the value of the corresponding position of the new sample; and then, save the current sample and repeat for k times to make the sample numbers of two classes are equal. Thus, we finally obtain k samples which are different from the source data but subject to the same distribution. The details of RVOS are shown in The RFE strategy introduced by Guyon et al.  is concrThe main shortcoming of RFE is the problem of tremendous time consumption, especially when the input dimensionality is extremely high. Therefore, it is indispensable to increase the step size so that the number of iterations will be decreased. However, some researchers state implicitly that a large step size would have a negative effect on the result of the feature selection, especially when the process of RFE is nearly completion . Later, To reduce the time cost of RFE and minimize the adverse effect on feature selection simultaneously, we develop RFE strategy and propose an improved version called recursive feature elimination with variable step size (VSSRFE). Specifically, we firstly give the step size a large initial value, and then cut the value in half when the number of features to be eliminated has been reduced to half of its original size. Repeat the procedure until the step size is one. It can be deeply explained from two aspects: first, the step size varies from large to small and does not change every time. It depends on the update condition, update rule and the number of features to be removed. Second, the process of feature elimination is gradually refined from roughness. Generally, gene expression microarray data has a huge number of genes, and only a few of them are strongly related to the class labels. So, we have reason to believe that the relatively more genes excluded at first are very irrelevant with class labels. In other words, the later the gene is deleted the more significant it is. Therefore, in the earlier stage of feature selection, we can set a relatively large step size to reduce the number of iterations. At the later stage of the feature selection process, step size is reduced step by step and features are more carefully selected, thus ensuring the quality of selected features. This is the basis for us to improve RFE. In addition, we set the initial value of step size as a key parameter which relates to specific dataset. SVM is one of the best choices for feature selection and the most frequently employed classifier for microarray data. However, most of these SVMs are typical support vector machines, what is to say, these SVMs are all based on kernel techniques  and Lagrange dual solver (e.g. ). To accThe objective function of LLSVM is defined as:Unlike traditional SVMs which introduce Lagrange multipliers to solve a dual problem, yuan et al. in  applied To update Formula (6) is an approximate expression as One iteration is completed when all variables have been updated. After m iterations, the result tends to be stable. Readers can find the details in , 21, andThis section focuses on the experimental verification of the methods proposed in this paper. Six most frequently used datasets are applied. The description about datasets is introduced in section 3.1. After that, relevant experiment settings are described in detail including data preprocessing in section 3.2, parameter estimation in section 3.3, and performance evaluation measures in section 3.4. Finally, in section 3.5, we introduce the experimental results and corresponding analysis.http://featureselection.asu.edu/datasets.php, Prostate can be downloaded from here: http://www2.cs.siu.edu/~qcheng/featureselection/, and the others can be downloaded from here: http://csse.szu.edu.cn/staff/zhuzx/Datasets.html. These datasets are all binary and almost all of them suffer from the problem of class imbalance. We choose binary datasets rather than multiclass ones because they are typical microarray dataset and more widely used in the published literature. The details are showed in We conduct extensive experiments on six gene expression microarray datasets, and all of them are available online and most widely used in this field , 22. LeuTo solve the class imbalance issue, The RVOS algorithm proposed in section 2.1 is applied to the six datasets mentioned above separately. Specially, new samples are obtained from class 1 so that #class 1 equals to #class 2. As the result, IR of all the datasets becomes 1.0 and SDR changes accordingly.Empirically, we standardize each of the datasets  as zero mean and unit variance at first. Thus, the adverse effects caused by different genes with a huge gap in expression values are eliminated. Considering the mRMR method used in this paper is based on mutual information, it is necessary to discretize the datasets specially. When setting about to do that, we exploit the measure proposed in  as folloThus, we get two versions of datasets, discrete and continuous, which are all standardized. The discrete datasets are employed for mRMR while the continuous datasets are used for other feature selectors.Before selecting features with LLSVM, SVM, Random Forest (RF) and classifying the transformed datasets with SVM, Naïve Bayes (NB), k-Nearest Neighbors (kNN) and Logistic Regression (LR), some parameters of them (except for NB) should be settled down first. For LLSVM, SVM and LR, the key parameter is the penalty factor C. The value of C affects the result of feature selection and the complexity of the classification model for SVM, LLSVM and LR. For RF, the depth is fixed as five, thus the number of basic trees becomes the vital parameter. Here we use N to represent the number of the basic trees, the larger N is the better performance will be obtained, in theory. But for a specific dataset, the effect becomes very limited when N exceeds a certain limit while the execution time of algorithm increases linearly. Therefore, we should set specific N values for different datasets. K refers the number of nearest neighbors to be selected for kNN. This value also requires patient tuning, too big or too small is not a good choice. When these models are employed as feature selectors or classifiers, we estimate the parameters with the corresponding model separately. Moreover, step size input  is another parameter need to be confirmed before applying VSSRFE with LLSVM or SVM (denoted as LLSVM-VSSRFE and SVM-VSSRFE respectively). In the process of specifying these parameters, we utilize stratified 5-fold cross-validation and grid search to achieve the best results. From Tables We choose three common measures as the performance evaluation measure in this study: Accuracy (ACC), area under ROC curve (AUC) and Matthew’s correlation coefficient (MCC). These measures are all widely used in classification evaluation task, among which, ACC and MCC are defined as follows:TP denotes true positive, FP is false positive, TN is true negative and FN is false negative. ACC is the most common evaluation standard, and applying it alone is usually not enough. MCC is often chosen as one of the best final choice because even when the dataset is class imbalanced, MCC still can give back a good evaluation performance. MCC is essentially a correlation coefficient between the observation and predictive value, and its falls between +1 and -1. A coefficient of +1 represents a perfect prediction and -1 represents the worst. AUC takes into account both Ture Positive Rate (TPR) and False Positive Rate (FPR) whose definitions are as follows:AUC can be seen as a probability value that one sample is classified correctly, the larger the better.In this section, we perform four sets of comparative experiments and a model evaluation experiment. In the first three sets of comparative experiments, we verify the proposed RVOS, VSSRFE and LLSVM algorithms respectively. And then, in the fourth set of experiments, we evaluate four common classifiers and discuss about which is more suitable as a classifier for microarray data. Finally, we conduct appropriate amount of experiments to evaluate the generalization capability of the classification model.http://scikit-learn.org/stable/index.html.What have to be highlighted is that all the experiments are conducted with stratified 5-fold cross-validation. We opt for 5-fold cross-validation because it is a common choice in this domain, and the stratified cross-validation strategy guarantees that the proportions of instances belonging to two classes both in the training set and test set are equal. The experiments in this literature are founded on two public machine learning libraries called scikit-learn and scikit-feature , which aIn this section, we balance the datasets with RVOS and then conduct a set of experiments with SVM-VSSRFE on six raw and balanced datasets to select genes. We choose SVM-VSSRFE as the feature selector because SVM-RFE is very time-consuming, and SVM-VSSRFE can achieve the same goal more quickly. Linear SVM (C = 1) is chose as the classifier, and each dataset is executed 128 times to select 1 to 128 genes, separately.Figs And, of course, we observe that the performances of the balanced Ovarian and Prostate are unsatisfactory, but this occurs when fewer genes are selected. As the number of genes increase, the results achieved by the balanced datasets get equal to or better than the raw datasets. In addition, it is confusing that some raw datasets with higher IR value achieve better results after balanced  while the lower one gets worse . Considering the randomness of the new sample generated by the RVOS algorithm and the complexity of the gene expression data, we consider this to be the result of noise interference . Beyond This section aims to validate the effectiveness of VSSRFE. We use traditional linear SVM as the basic feature selector, and combine it with RFE and VSSRFE separately to conduct the experiments on the six balanced datasets. Two group experiments are conducted under the same conditions except the step size of recursive feature elimination: one is fixed to one, and the other is determined by the input initial value and the number of features to be eliminated. In addition to this, we choose four as the number of genes to select because four is relatively small, as some researchers doubted, which is likely to get an adverse effect on the quality of feature selection. Also, linear SVM (C = 1) is chose as the classifier.This section is intended to verify the efficiency of LLSVM. LLSVM combining VSSRFE as a feature selector is compared with SVM-VSSRFE, random forest (RF), mRMR and relief . The maiFigs In this section, we carefully validate four typical classifiers, including Naïve Bayes (NB), k-Nearest Neighbors (kNN), linear SVM (SVM) and L2 regularized Logistic Regression (LR). LLSVM-VSSRFE is employed as the feature selector to select 1 to 32 genes from the balanced datasets and then evaluate these genes with these well-tuned classifiers. In addition, we utilize LLSVM-VSSRFE as the feature selector and LR as the classifier to conduct experiments on three balanced datasets, which is aimed to get the training scores and testing scores so as to evaluate the generalization capability of the classification model.Figs Concretely, for SVM and LR, SVM has few advantages . This is quite surprising, because SVM is always regarded as the best classifier for the existing research in this field. In addition, the additional information we can observe is that the curves of LR are smoother than that of SVM. That is to say, the performance of LR is more stable. Most importantly, LR is a simple classifier and easier to implement which means much for dataset with too little sample size just like microarray data. Comprehensively, as a classifier for microarray data analysis, Logical Regression should be paid more attention for the scientific community.Although the proposed methods in this paper have achieved promising results compared with the existing methods, there are still some topics should be discussed in depth:(1) The methods proposed in this paper are implemented based on two Python libraries, but the execution efficiency of Python is not the fastest. So our approach can be further optimized, such as utilizing C or C++ to encode and implement.(2) Although experimental results show that RVOS has achieved good performance, the algorithm also has some limitations. If the number of samples belonging to the rare class is quite small and many more supplementary samples are needed, RVOS may not work well as in this paper because the number of expression values for each gene is limited. To solve this problem, much more hard research work needs to be done in the future.(3) A main shortcoming for VSSRFE strategy is to choose the best initial value of step size, which is related to dataset, update condition and rule of the step size. What’s worse, in some cases, the selection of the best initial value of step size is depended on the number of genes to select. This means that some adjustment work is necessary in order to determine this parameter. Fortunately, VSSRFE is efficient enough, so the related adjustment work is acceptable to some extent just as the k for KNN. In addition, the update conditions and rule of step size can be adjusted flexibly, which will have a direct impact on the efficiency of the feature selection process and the quality of the feature selection results. If the update conditions and rule of step size are set reasonably, the results will get better.(4) Because of the characteristics of microarray data, more advanced analytical techniques are required. In recent years, representation-based methods are of great interest both for feature selection , 33 and (5) This article does not pay attention to the relationships between genes (features). The existing studies have shown that there are some relationships or effects between genes, but the identification of gene interaction is a rather complex issue, especially for researchers who have no biomedical background. This paper focuses on the efficient screening of key genes and the classification of microarray data. The interaction recognition between genes can be further studied in the future.Complex diseases such as breast cancer remain the greatest threat to human life. The growth of microarray data and the development of statistical methods have provided new possibilities for the prediction and treatment of such diseases. Feature selection and classification are the core technologies of microarray data analysis. They both play key roles in genes recognition and diseases diagnosis. Limited to the characteristics of microarray data, many typical methods in this field still need to be paid more attentions to overcome their disadvantages.Small sample size, high dimensionality and class imbalance are the main characteristics of microarray data as well as the main challenges for researchers to conduct microarray data analysis. Among them, Class imbalance is rarely studied by researchers in this field. To preprocess the datasets, this paper firstly proposes a simple but effective resampling method called RVOS to solve this issue. By doing this, the distribution of two kinds of samples is balanced and the problem of small sample size is also alleviated to some extent.SVM-RFE is a typical method which is widely studied by researchers in this field. To reduce the time consumption of SVM-RFE Fundamentally, we firstly propose an improved version of RFE called VSSRFE. VSSRFE tries to reduce the recursion times by a large step size, and keep the step size decreasing while the number of features to be eliminated is getting smaller and by this way to ensure the quality of the meaningful genes selected. There are thousands of genes in human beings, so it means much to apply an efficient feature selection strategy. VSSRFE provides an interesting idea to speed up the procedure of gene selection. This may contribute to the microarray data analysis in the future. Moreover, we induce another efficient implementation of linear SVM called LLSVM. LLSVM is a kind of pure linear classifier based on support vector, so it inherits the advantages of SVM and reduces unnecessary computational cost for large-scale linear separable data such as microarray data. Combined with VSSRFE, LLSVM-VSSRFE becomes an efficient and effective feature selector compared with the existing methods and has potential in the gene selection field.Finally, we conduct a study on the effects of different classifiers on the classification results and observe that sometimes L2 regularized Logistic Regression is a better choice for microarray data classification. This is also a question that worth paying more attention to validate in the future.S1 FileSection 3.2 and section 3.5.1 are implemented by this code file.(PY)Click here for additional data file.S2 FileSection 3.5.2 is implemented by this code file.(PY)Click here for additional data file.S3 FileThis code file implements LLSVM-VSSRFE and is used to conduct experiments in section 3.5.3.(PY)Click here for additional data file.S4 FileThis code file implements LLSVM-VSSRFE and SVM-VSSRFE and is used to conduct experiments in section 3.5.3.(PY)Click here for additional data file.S5 FileThis code file implements mRMR and is used to conduct experiments in section 3.5.3.(PY)Click here for additional data file.S6 FileThis code file implements random forest and is used to conduct experiments in section 3.5.3.(PY)Click here for additional data file.S7 FileThis code file implements reliefF and is used to conduct experiments in section 3.5.3.(PY)Click here for additional data file.S8 FileThis code file implements SVM-RFE and is used to conduct experiments in section 3.5.2.(PY)Click here for additional data file.S9 FileSection 3.5.4 is implemented by this code file.(PY)Click here for additional data file.S10 FileSection 3.5.5 is implemented by this code file.(PY)Click here for additional data file.S11 File(ARFF)Click here for additional data file.S12 File(ARFF)Click here for additional data file.S13 File(MAT)Click here for additional data file.S14 File(ARFF)Click here for additional data file.S15 File(ARFF)Click here for additional data file.S16 File(CSV)Click here for additional data file.S17 File(CSV)Click here for additional data file.


However, the traditional experimental paradigm is costly, and previous In this paper, we modeled the prediction of drug-target interactions as a binary classification task. Using transcriptome data from the L1000 database of the LINCS project, we developed a framework based on a deep-learning algorithm to predict potential drug target interactions. Once fully trained, the model achieved over 98% training accuracy. The results of our research demonstrated that our framework could discover more reliable DTIs than found by other methods. This conclusion was validated further across platforms with a high percentage of overlapping interactions.Our model’s capacity of integrating transcriptome data from drugs and genes strongly suggests the strength of its potential for DTI prediction, thereby improving the drug discovery process. The identification of drug-target interactions (DTIs) is significant to drug research and development (R&D). The ability to predict DTIs has been applied widely for drug repositioning and for anticipating adverse reactions , 2. LargResearchers have developed a variety of computational algorithms to facilitate the prediction of DTIs. For example, Campillos et al. proposed an algorithm to predict whether two drugs share target protein based on similarities of phenotypic side-effect . Bleaklein silico prediction has been held back by the wide variety of data production platforms and scarcity of data.In principle, both data source and prediction algorithm contribute to the performance of DTI prediction. Researchers have attempted to use various aspects of drug informatics data, such as cellular response data, pharmacological data, chemical data, and side effect data, to identify novel DTIs , 10, 11.http://www.lincsproject.org/LINCS). The L1000 database of the LINCS project includes millions of genome-wide expression profiles gathered from cell lines stimulated by more than 20,000 small molecule compounds, or when more than 4000 genes were knocked out in the respective cell lines. The L1000 database provides a unified and extensive gene expression profile source for DTI prediction.To address the problem of data scarcity, the National Institute of Health (NIH) launched the pilot phase of the Library of Integrated Network-based Cellular Signatures (LINCS) project in 2010. This project aims to provide a comprehensive map of multilevel cellular responses when cells are exposed to various perturbations, including small molecule compound stimulation and gene knockdown , consists of four levels. Level 1 data represents the expression value of the 978 landmark genes. Level 2 data represents the normalized expression value of the 978 landmark genes. Level 3 data records genome-wide expressions. Level 4 data records the Z-score of genome-wide gene expressions, which is used in this research for drug perturbations and gene knockdown perturbations in the PC3 cell line.The L1000 database provides direct measurement of the expression profiles of only 978 landmark genes, and uses correlations to these genes to infer the remaining ∼20,000 gene expressions. The data structure of the LINCS project, like the TCGA project  as input. Each sample was constructed by fusing a drug datum and a gene datum. The definition details are as follows.DM is an m by n matrix that consists of all drugs, which is the drug perturbation profile in the dataset S. m is the number of drugs, and n is the number of landmark genes. Each line means one drug.Drug matrix GM is an q by n matrix that consists of all genes, which is the gene knockdown perturbation profile in the dataset S. q is the number of genes, and n is the number of landmark genes. Each line means one gene.Gene matrix DMi,j and GMi,j are both real numbers; each corresponds to the expression of the jth landmark gene for sample i.Features LM is a q by m matrix. LMi,j is the single label for the interaction between gene i and drug j. If LMi,j = 0, then the combination of gene i and drug j is either an unlabeled sample or a negative sample, depending whether gene i is one of the target proteins or not. Otherwise, gene i  is a target of drug j recorded in the DrugBank database, and the combination of gene i and drug j is a positive sample.Label matrix CM is an l by k matrix. l = mq is the number of all possible DTIs between m drugs and q targets, and k = 2 indicates the positive or negative interaction between each drug-target pairs. CMi,0 is the probability of sample i (the ith DTI) belonging to the negative class. CMi,1 is the probability of sample i belonging to the positive class.Classification matrix F is the set of joint probability distributions and conditional probability distributions. If the model f is selected as a decision function, for any input X the predicted value Y*=f(X) is obtained. The objective function L), a real-valued function of f(X) and Y, is constructed for measuring the nearness between predicted values and true values. Since the loss value becomes smaller, the fit of the model improves on the training sets.In supervised learning, hypothesis space As a result of the improved availability of data for cell biology and drug chemistry, our proposed DNN was able to serve as an powerful tool for DTI prediction. The computational power was derived in two ways: first, through a massively parallel distributed structure, and second, through the network’s ability to learn and generalize. The DNN had a built-in ability to adapt parameters according to the changes of the surrounding environment.Every neuron in the DNN was nonlinear. This property was highly significant, particularly where the underlying physical mechanism responsible for generation of the input signal was inherently nonlinear, and potentially could be affected by the global activity of all other neurons in neural network. Above all, the DNN automatically extracted more abstract features representing raw chemical and biological data. Nonetheless, the architecture remains a huge challenge when feature space is high-dimensional.K-fold cross-validation. Last, a Softmax regression, as defined in  at eachfined in . This diAs discussed earlier in this paper, we modeled the discovery of new DTIs as a binary classification task. The whole dataset contained all the expression data of drugs, target and non-target protein genes. However, there were more negative samples (combining drug data and non-target protein gene data) than the number of positivie samples (combining drug data and target protein gene data). Therefore, the input space consisted of all positive samples and uniformly sampled negative samples. As the result of some intrinsic linear and nonlinear patterns in the LINCS project , linear DNNs are multilayer systems of connected and interacting artificial neurons that perform various data transformations. They have several hidden layers of neurons, which allows for adjustment of the data abstraction level. The ability to learn at the higher abstraction level makes DNNs an effective and promising tool for working with chemical and biological data. In the LINCS project, linear features can be captured by linear methods, but classification performance reaches a plateau because such methods ignore complex nonlinear relationships between the expressions of genes.In order to learn hierarchical nonlinear features systematically, we designed a DNN that included one input layer with 1956 neurons corresponding to the dimensionality of features, two hidden layers with 200 neurons and 10 neurons respectively, and one Softmax layer as the binary classification layer. After feature extraction, each sample was represented as a 10-dimensional feature vector, and such feature learning contributed effectively to classification. However, overfitting is a serious problem for fully connected network, and a complicated network is time consuming when using forward propagation. This is why we adopted the dropout technique to simplify network architecture. The critical idea is to drop neurons randomly during training to prevent these neurons from co-adapting too much . The arcCMi,0 of all negative samples, as defined in , and Gradient Boosting Decision Tree (GBDT) using the L1000 dataset. We compared the performance of our proposed DNN with other methods by examining the F-score, validation accuracy, percentage of positive cases (PoPC), and predictive error. LR is responsible for linear analysis because it can capture effective linear features. RF and VC, as ensemble classifiers consisting of multiple weak classifiers, are adopted widely in classification tasks. GBDT showed excellent performance in recommender systems because it has the advantage of combining different features.xi, as defined in (3), was less than 0, the performance of the model was worse than the performance of the DNN. Otherwise, the other models were shown to be better than the DNN. As shown in Fig. As shown in Table After training and evaluating our model, we utilized it to predict novel DTIs. To validate whether our prediction results were in accord with current knowledge, we examined the predicted DTIs using other DTI database, including STITCH, DGIdb, and CTD. A total of 221 pairs were found in STITCH, 466 pairs in DGIdb, and 3254 pairs in CTD. After that, we used D-score to rank all predicted DTIs, and calculated pairs count that overlap between the predicted results and the interactions from the other three databases. Then we counted the number of overlapping pairs in the sliding bins of 500 consecutive interactions (as shown in Fig. The distribution of prediction results across different therapeutic property labels of drugs is illustrated in Fig. The ability of DTI prediction is essential and have improved substantially in recent years, but a paucity of data and lack of efficient algorithms leads to hardly systematic DTI prediction. Currently, two advances are poised to facilitate new strategies. First, the LINCS project, launched in 2010, is able to provide rich transcriptome data. Second, deep learning methods have been applied successfully in biomedical research. Nonetheless, even deep neural network has a strong ability of automatically extracted high-level features, the performance of the network is related with the depth and breadth of the layers, and the risk of over-fitting increases resulting from too complicated architecture. Especially after the dimensionality of genome-wide expression declines to 978, how to design an effective architecture of deep neural network for further learning features remains a challenge, and it is difficult to explain such abstract representations.In order to make the model have better potential for DTI prediction, we rebuilt the objective function for decreasing the PoPC, but validation accuracy went down as well. Because whether a new DTI was reliable depended on the distance score. In future work, we will explore a probability to find an inside property for evaluating new DTI potential.In this work, we proposed a framework for DTI prediction based on transcriptome data in the L1000 database gathered from drug perturbation and gene knockout trials. The pipeline of our framework included a combination of data from drugs and genes, as well as negative data sampling. As a result of the increasing availability of data and GPU computing, the DNN employed in our framework served as an effective tool for feature extraction and classification. Once the DNN was trained, the results demonstrated that our framework can discovery more reliable DTIs than found by other methods. Furthermore, this conclusion was validated across platforms with a high percentage of overlap interactions. These findings also demonstrated that our model can integrate transcriptome data from drugs and genes, and has wider prospects for predicting DTIs and improving the drug discovery process.


Molecular classification of tumour clonality is currently not evaluated in multiple invasive breast carcinomas, despite evidence suggesting common clonal origins. There is no consensus about which type of data  and especially which statistical method is most suitable to distinguish clonal recurrences from independent primary tumours.n = 37), DNA copy number (n = 37), DNA methylation (n = 8), gene expression microarray (n = 7), RNA sequencing (n = 3), and SNP genotyping data (n = 3). Different statistical methods, e.g. the diagnostic similarity index (SI), were used to classify the tumours as clonally related recurrences or independent primary tumours.Thirty-seven invasive breast tumour pairs were stratified according to laterality and time interval between the diagnoses of the two tumours. In a multi-omics approach, tumour clonality was analysed by integrating clinical characteristics  of patients. Notably, no association was found between the current clinical guidelines and molecular tumour features.A more accurate classification of clonal relatedness between multiple breast tumours may help to mitigate treatment failure and relapse by integrating tumour-associated molecular features, clinical parameters, and statistical methods. Guidelines need to be defined with exact thresholds to standardise clonality testing in a routine diagnostic setting.The online version of this article (10.1186/s13058-018-1022-y) contains supplementary material, which is available to authorized users. Approximately 2–15% of women previously diagnosed with breast cancer will develop a second primary carcinoma in the contralateral breast during their lifetime . HoweverIpsilateral  secondary tumours occur in 10–15% of patients undergoing breast-conserving surgery and radiation therapy . At presDifferent techniques in the field of molecular genetics have been used to elucidate tumour clonality, e.g. allelic imbalances , 12, CGHIn the present study, 74 invasive breast tumours corresponding to 37 patients were stratified by laterality  and the time interval between the diagnosis of the first and second tumour (synchronous vs. metachronous). Both tumours from the same patient were analysed using several genome-wide screening methods and statistical approaches to assess tumour clonality. The level of concordance among the different statistical techniques and molecular data might help to define clonality in multiple tumours and guide treatment decisions for clinicians.2 ratio ≥ + 0.5 and HER2- was set to log2 ratio < + 0.5 [Fresh-frozen tumour specimens for 74 invasive breast carcinomas, corresponding to 37 patients diagnosed in Western Sweden between 1988 and 1998 with multiple breast cancers, were selected from the tumour bank at the Sahlgrenska University Hospital Oncology Lab . The patients were stratified into four groups based on the anatomic location of the multiple breast cancers  and time interval between the diagnoses (synchronous or metachronous). Ipsilateral was defined as tumours occurring in the same breast while bilateral was defined as the occurrence of tumours in both breasts. Metachronicity was defined as a time interval greater than 6 months between the diagnoses of the first and second tumours, while synchronicity specified that the two tumours occurred concurrently. Clinicopathological information was obtained from Regional Cancer Centre West  and the Sympathy and Melior databases . A part of the dataset was stratified into the molecular breast cancer subtypes +, luminal subtype B/HER2-, and HER2/oestrogen receptor (ER)-) as described elsewhere , 24. Lum < + 0.5 . Routinep value and required copy number data procession with the “DNAcopy” package [aCGH and data pre-processing was performed as previously described  and summ package .Sixteen samples were randomly selected to represent each clinical group with four samples corresponding to two patients per group. Purified genomic DNA was processed at the SNP&SEQ technology platform, Uppsala, Sweden, using Illumina Infinium MethylationEPIC BeadChips . Raw data (IDAT files) were processed in R using the “RnBeads” package . The proTotal RNA samples were processed at the Science for Life Laboratory . Illumina TruSeq strand-specific RNA libraries  containing 125 bp paired-end reads were obtained for each sample on a HiSeq2000 sequencer . The computations were performed on resources provided by SNIC through Uppsala Multidisciplinary Center for Advanced Computational Science (UPPMAX) , as descGenome-wide SNP genotyping analysis was processed with Illumina Infinium HumanOmni2.5–8 v1.3 Beadchips at the SCIBLU Genomics DNA Microarray Resource Center (SCIBLU), Sweden, as described in the Additional file p value cut-off of 0.05 was applied in all statistical tests.A Tumours derived from a common precursor tumour cell should share certain features, i.e. similar CNAs, genetic variants, shared segments, DNA methylation and gene expression patterns, in addition to non-matching features that were acquired over time. We applied different statistical methods on different types of molecular data to identify similarities between the tumours that classify a tumour pair as clonal and reject the null hypothesis (different features due to independent development of primary tumours).NU), shared (NS), and opposite (NO) changes were calculated for each tumour pair to obtain the SI:The SI assesses whether two tumours identified in the same patient are clonally related or two independent entities by identifying genetic aberrations that are patient-specific and non-recurrent aberrations frequently identified in cancer . In briePSI gives the percentage of similarities between two tumours that are not due to recurrent chromosomal aberrations or randomness.The SI ranges between 0 (completely different) and 1 . The permutation-based 2 ratios were discretized using a 1.5 fold change cut-off (underexpressed (log2 ratio < − 0.58); neutral; overexpressed (log2 ratio > 0.58)).The SI remained unchanged for the gene expression microarray data. The normalised logmet) because the SI for copy number data is based on measuring the amount of alterations from the biologically neutral state . In DNA methylation, neither methylated nor unmethylated can be defined as the neutral state of a cytosine due to the dynamic of methylation. The SImet uses beta values discretized according to thresholds defined by Du et al. [met counts the number of all common states between the first and the second tumour per probe and divides it by the total number of probes, giving the percentage of shared methylation states. The main difference is that the SImet uses all probe states while the SI is based on the changes from the neutral state and therefore does not count two tumours that are normal as a shared state.Calculation of the SI was modified for the methylation data , the DNA methylation data , the microarray-derived gene expression data , and the SNP array data  and log R ratio (LRR) values). Two tumours of the same patient were defined as similar  if they clustered together in the terminal branch of the dendrogram.Unsupervised hierarchical clustering was applied using single linkage with Euclidean distance . Cluster2 ratios), the DNA methylation data , the microarray-derived gene expression data , and the SNP array data . The distance measure was calculated for true tumour pairs which derive from the same patient and for all artificial combinations of tumour pairs from different patients (permutation). Tumour pairs that are more similar on the probe level will show a shorter distance from each other. Statistical significance for clonality was defined as the distance of a tumour pair of the same patient that is in the lower fifth percentile of the distribution of distances.The distance measure was used to compute the distance matrix of the Euclidean distances between different tumour samples to evaluate the similarity between two samples. The Euclidean distance was computed using the basic “stats” package  for the 2 ratios), DNA methylation array , and SNP array . Shared segments were counted for true tumour pairs and all artificial pairs of the respective cohort. Clonality was defined as the number of shared segments above the 95th percentile.In segmented copy number data, the breakpoints and the copy number of each segment was compared between the tumours. A shared segment was defined as an overlap of the exact loci in both ends of the segment where the change in status (loss or gain) occurred with the same direction (increase or decrease in copy numbers). The segment analysis was performed on segmented copy number data derived from aCGH .The 37 breast cancer patients were stratified into four clinical groups based on tumour laterality and the time interval between the diagnoses of the first and second tumours . The clinicopathological characteristics are shown in Additional file For the clinical classification of clonality, several histopathological and molecular features were taken into consideration, including histological subtype, the status of ER and HER2, and the molecular subtype Table . While tDNA copy number analysis using aCGH was performed to identify recurrent regions of DNA copy number gain (blue) and loss (red) in at least 25% of the tumours in the patient cohort. Recurrent DNA gains were identified on chromosomes 1q, 8q, 16p, 17q, and 20q, while DNA loss was detected on 1p, 8p, 11q, 13q, and 16q Fig. . These rP = 0.007), while no further associations to other variables were found. Kruskal’s non-metric multidimensional scaling (MDS) demonstrated that most of the synchronous samples were further away from each other, while the metachronous samples formed a distinct cluster, suggesting a higher variability of beta values in synchronous samples . The clonality analyses based on gene expression microarray data showed strong concordance to the clinical groups with all four synchronous cases being similar for all analyses while 2/3 metachronous cases were classified as different entities  containing the same fusion breakpoints in the 5′- and 3′-gene partners in both tumours : PClinical groups = 0.229), highlighting the alarming reality that there is very little connection between current clinical guidelines and the biology underlying tumour clonality.Calculation of Cohen’s kappa indices was applied to detect the highest agreement between the different statistical methods used to estimate clonality. For the aCGH data, hierarchical clustering and the similarity index (SI) were identified as the most appropriate . Since the SI is easier to interpret as a measure and independent of the cohort, it presented the most reasonable definition of clonality and determined 46% (17/37) of the tumour pairs as clonal , and receptor status are currently used to choose treatment strategies for patients with multiple breast tumours. However, to fully comprehend the association between multiple tumours, routine clinical and diagnostic testing needs to be conducted in conjunction with molecular and bioinformatics methods.In the majority of the analyses, the type of molecular data analysed had a stronger impact on clonality determination than the analytical method used. This raises the question of which biological phenomenon provides the most stable evidence for clonality. DNA methylation and gene expression are more dynamic than DNA mutations and CNAs, and might therefore be more similar due to environmental factors. CNAs are acquired at early stages of tumourigenesis , 46 makiHierarchical clustering has been used, among other methods, in several studies to define clonality , 47, 49.In the DNA methylation cohort, clustering of the intensity values classified 7/8 tumour pairs as clonal and therefore did not provide a precise segregation between clonally related tumours and independent tumours. The aCGH, DNA methylation intensity and LRR data should biologically refer to the same phenomenon (CNAs) and consequently show the same tendencies for different genomic loci. Therefore, it was unexpected that the results of the clustering and shared segment analysis for those data sets did not show stronger concordance. Furthermore, it was anticipated that the results from the clustering and the distance measure were more in agreement since the first step of clustering is the Euclidean distance. In most cases, the distance measure seemed to be a stricter method than the SI and clustering.In comparison with genomic variants, mutation analyses based on exonic variants or gene panels represent a subset of the full picture. The different tendencies between the methods represent a drawback for potential applications of sequencing panels in the clinic. The fusion transcript analysis was the only method that did not show any overlaps between patients. Moreover, unspliced fusion transcripts provide the transcribed level of CNAs, which highlights the functional consequences of CNAs and makes them an important tool to assess tumour clonality. Our RNA-seq-based mutation approach had several limitations starting with the lack of matched normal samples to exclude germline mutations and normal DNA nucleotide variations. However, common genetic variants found in the human population were removed. Furthermore, our approach did not account for the frequency of mutations in breast cancer since rare mutations give much stronger evidence for clonality than common mutations . In the Whole genome sequencing (WGS) is the more appropriate method to evaluate mutations in comparison with RNA-seq, which does not give information on untranscribed DNA sequences. Hence, the lack of common mutations cannot be considered as a guarantee that tumour pairs are independent. However, intratumour heterogeneity complicates clonality analyses due to biological differences in different parts of a tumour and subclone evolution. In aCGH, contamination with normal cells could diminish the intensity of detected CNAs and small cell populations might not be detected. However, by using only samples that showed a tumour cell content of at least 70%, we ruled out that a lack of clonal relatedness could be due to a lack of tumour cells.Few studies based on molecular approaches have been conducted to define clonality in multiple breast tumours and there is no consensus on which type of data and analysis method provides the most stable definition of clonality. A direct comparison of these studies to the findings presented here might, however, not be justified due to differences in the study set-up, methods and statistics. In a study on a contralateral cohort using low-coverage WGS, Alkner et al. demonstrated clonal relatedness in 10% (1/10) of the patients , which wThere are many studies published on tumour clonality using different types of data and statistical methods. Most studies defined their own methods and cohort-specific cut-offs. Currently, there is no consensus about which type of data and especially which statistical analysis is the most suitable and there are surprisingly few studies that compare and evaluate the feasibility of these different approaches. Nonetheless, extremely similar or different tumour pairs  showed consistent results regardless of the statistical analysis or biological data used, but clinic guidelines need to be defined with exact thresholds in order to standardise clonality testing in a routine diagnostic setting. In metachronous cancer, clonality between the first and second tumour may indicate an insufficient effect of the treatment for the first tumour and the patient could benefit from a change in treatment. An independent new primary tumour would indicate a more favourable prognosis than a recurrence. Hence, the discrimination between a clonal and independent origin of the second tumour is of high importance for the patient. In our study, the distance measure proved to be the most conservative method for defining clonality and the shared segment analysis the most liberal. Gene expression data classified all ipsilateral-synchronous cases as clonal, demonstrating that gene expression strongly depends on the nearby tumour microenvironment. The SI using aCGH data was found to be the most suitable method to classify tumour clonality, as it had the highest concordance with all results and can be easily integrated into clinic routine using FFPE samples to obtain copy number data. But most importantly, the definition of tumour clonality based on the current clinicopathological markers needs to be revised due to the limited intersects between current clinical guidelines and the underlying biology of tumour clonality.Additional file 1:. Description of nucleic acid isolation and purification, aCGH gene expression microarray, RNA-seq and SNP array analysis. (DOCX 37 kb)Supplementary MethodsAdditional file 2:Table S1. Overview of clinical characteristics of the patient and tumour information stratified by the clinical groups . (XLSX 16 kb)Additional file 3:Table S2. Variabilities of the studied sample groups with the variability spanning between 5th and 95th percentile of the beta values. (XLSX 10 kb)Additional file 4:Table S3. Summary of clonality tests for the gene expression microarray cohort (n = 7). (XLSX 14 kb)Additional file 5:Figure S1. Non-metric multidimensional scaling (MDS) plot of (A) normalised log2 ratios from gene expression data, and (B) LRR values from SNP array data. The MDS plot visualised similarities between the individual samples based on information from the distance matrix. (TIF 1784 kb)Additional file 6:Table S4. Overview of the shared fusion transcripts in patient IM4, IS10, and IS11. (XLSX 13 kb)Additional file 7:Table S5.Summary of clonality tests for the RNA-seq and SNP genotyping cohort (n = 6). (XLSX 14 kb)