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Numerous scientific studies have found a link between diverse microorganisms in the human body and complex human diseases. Because traditional experimental approaches are time-consuming and expensive, using computational methods to identify microbes correlated with diseases is critical. In this paper, a new microbe-disease association prediction model is proposed that combines a multi-view multi-modal network and a multi-scale feature fusion mechanism, called M 3 HOGAT. Firstly, a microbe-disease association network and multiple similarity views are constructed based on multi-source information. Then, consider that neighbor information from disparate orders might be more adept at learning node representations. Consequently, the higher-order graph attention network (HOGAT) is devised to aggregate neighbor information from disparate orders to extract microbe and disease features from different networks and views. Given that the embedding features of microbe and disease from different views possess varying importance, a multi-scale feature fusion mechanism is employed to learn their interaction information, thereby generating the final feature of microbes and diseases. Finally, an inner product decoder is used to reconstruct the microbe-disease association matrix. Compared with five state-of-the-art methods on the HMDAD and Disbiome datasets, the results of 5-fold cross-validations show that M 3 HOGAT achieves the best performance. Furthermore, case studies on asthma and obesity confirm the effectiveness of M 3 HOGAT in identifying potential disease-related microbes.

CircRNA has been proved to play an important role in the diseases diagnosis and treatment. Considering that the wet-lab is time-consuming and expensive, computational methods are viable alternative in these years. However, the number of circRNA-disease associations (CDAs) that can be verified is relatively few, and some methods do not take full advantage of dependencies between attributes. To solve these problems, this paper proposes a novel method based on Kernel Fusion and Deep Auto-encoder (KFDAE) to predict the potential associations between circRNAs and diseases. Firstly, KFDAE uses a non-linear method to fuse the circRNA similarity kernels and disease similarity kernels. Then the vectors are connected to make the positive and negative sample sets, and these data are send to deep auto-encoder to reduce dimension and extract features. Finally, three-layer deep feedforward neural network is used to learn features and gain the prediction score. The experimental results show that compared with existing methods, KFDAE achieves the best performance. In addition, the results of case studies prove the effectiveness and practical significance of KFDAE, which means KFDAE is able to capture more comprehensive information and generate credible candidate for subsequent wet-lab.

The roles of brain region activities and genotypic functions in the pathogenesis of Alzheimer's disease (AD) remain unclear. Meanwhile, current imaging genetics methods are difficult to identify potential pathogenetic markers by correlation analysis between brain network and genetic variation. To discover disease-related brain connectome from the specific brain structure and the fine-grained level, based on the Automated Anatomical Labeling (AAL) and human Brainnetome atlases, the functional brain network is first constructed for each subject. Specifically, the upper triangle elements of the functional connectivity matrix are extracted as connectivity features. The clustering coefficient and the average weighted node degree are developed to assess the significance of every brain area. Since the constructed brain network and genetic data are characterized by non-linearity, high-dimensionality, and few subjects, the deep subspace clustering algorithm is proposed to reconstruct the original data. Our multilayer neural network helps capture the non-linear manifolds, and subspace clustering learns pairwise affinities between samples. Moreover, most approaches in neuroimaging genetics are unsupervised learning, neglecting the diagnostic information related to diseases. We presented a label constraint with diagnostic status to instruct the imaging genetics correlation analysis. To this end, a diagnosis-guided deep subspace clustering association (DDSCA) method is developed to discover brain connectome and risk genetic factors by integrating genotypes with functional network phenotypes. Extensive experiments prove that DDSCA achieves superior performance to most association methods and effectively selects disease-relevant genetic markers and brain connectome at the coarse-grained and fine-grained levels.

Single-cell RNA sequencing (scRNA-seq) technology is famous for providing a microscopic view to help capture cellular heterogeneity. This characteristic has advanced the field of genomics by enabling the delicate differentiation of cell types. However, the properties of single-cell datasets, such as high dropout events, noise, and high dimensionality, are still a research challenge in the single-cell field. To utilize single-cell data more efficiently and to better explore the heterogeneity among cells, a new graph autoencoder (GAE)-based consensus-guided model (scGAC) is proposed in this article. The data are preprocessed into multiple top-level feature datasets. Then, feature learning is performed by using GAEs to generate new feature matrices, followed by similarity learning based on distance fusion methods. The learned similarity matrices are fed back to the GAEs to guide their feature learning process. Finally, the abovementioned steps are iterated continuously to integrate the final consistent similarity matrix and perform other related downstream analyses. The scGAC model can accurately identify critical features and effectively preserve the internal structure of the data. This can further improve the accuracy of cell type identification.

Accumulating evidence indicates that microRNAs (miRNAs) can control and coordinate various biological processes. Consequently, abnormal expressions of miRNAs have been linked to various complex diseases. Recognizable proof of miRNA-disease associations (MDAs) will contribute to the diagnosis and treatment of human diseases. Nevertheless, traditional experimental verification of MDAs is laborious and limited to small-scale. Therefore, it is necessary to develop reliable and effective computational methods to predict novel MDAs. In this work, a multi-kernel graph attention deep autoencoder (MGADAE) method is proposed to predict potential MDAs. In detail, MGADAE first employs the multiple kernel learning (MKL) algorithm to construct an integrated miRNA similarity and disease similarity, providing more biological information for further feature learning. Second, MGADAE combines the known MDAs, disease similarity, and miRNA similarity into a heterogeneous network, then learns the representations of miRNAs and diseases through graph convolution operation. After that, an attention mechanism is introduced into MGADAE to integrate the representations from multiple graph convolutional network (GCN) layers. Lastly, the integrated representations of miRNAs and diseases are input into the bilinear decoder to obtain the final predicted association scores. Corresponding experiments prove that the proposed method outperforms existing advanced approaches in MDA prediction. Furthermore, case studies related to two human cancers provide further confirmation of the reliability of MGADAE in practice.

Single-cell RNA sequencing (scRNA-Seq) technology has emerged as a powerful tool to investigate cellular heterogeneity within tissues, organs, and organisms. One fundamental question pertaining to single-cell gene expression data analysis revolves around the identification of cell types, which constitutes a critical step within the data processing workflow. However, existing methods for cell type identification through learning low-dimensional latent embeddings often overlook the intercellular structural relationships. In this paper, we present a novel non-negative low-rank similarity correction model (NLRSIM) that leverages subspace clustering to preserve the global structure among cells. This model introduces a novel manifold learning process to address the issue of imbalanced neighbourhood spatial density in cells, thereby effectively preserving local geometric structures. This procedure utilizes a position-sensitive hashing algorithm to construct the graph structure of the data. The experimental results demonstrate that the NLRSIM surpasses other advanced models in terms of clustering effects and visualization experiments. The validated effectiveness of gene expression information after calibration by the NLRSIM model has been duly ascertained in the realm of relevant biological studies. The NLRSIM model offers unprecedented insights into gene expression, states, and structures at the individual cellular level, thereby contributing novel perspectives to the field.

Advances in omics technology have enriched the understanding of the biological mechanisms of diseases, which has provided a new approach for cancer research. Multi-omics data contain different levels of cancer information, and comprehensive analysis of them has attracted wide attention. However, limited by the dimensionality of matrix models, traditional methods cannot fully use the key high-dimensional global structure of multi-omics data. Moreover, besides global information, local features within each omics are also critical. It is necessary to consider the potential local information together with the high-dimensional global information, ensuring that the shared and complementary features of the omics data are comprehensively observed. In view of the above, this article proposes a new tensor integrative framework called the strong complementarity tensor decomposition model (BioSTD) for cancer multi-omics data. It is used to identify cancer subtype specific genes and cluster subtype samples. Different from the matrix framework, BioSTD utilizes multi-view tensors to coordinate each omics to maximize high-dimensional spatial relationships, which jointly considers the different characteristics of different omics data. Meanwhile, we propose the concept of strong complementarity constraint applicable to omics data and introduce it into BioSTD. Strong complementarity is used to explore the potential local information, which can enhance the separability of different subtypes, allowing consistency and complementarity in the omics data to be fully represented. Experimental results on real cancer datasets show that our model outperforms other advanced models, which confirms its validity.

Determining the association between drug and disease is important in drug development. However, existing approaches for drug-disease associations (DDAs) prediction are too homogeneous in terms of feature extraction. Here, a novel graph representation approach based on light gradient boosting machine (GRLGB) is proposed for prediction of DDAs. After the introduction of the protein into a heterogeneous network, nodes features were extracted from two perspectives: network topology and biological knowledge. Finally, the GRLGB classifier was applied to predict potential DDAs. GRLGB achieved satisfactory results on Bdataset and Fdataset through 10-fold cross-validation. To further prove the reliability of the GRLGB, case studies involving anxiety disorders and clozapine were conducted. The results suggest that GRLGB can identify novel DDAs.

Clinical trials indicate that the dysregulation of microRNAs (miRNAs) is closely associated with the development of diseases. Therefore, predicting miRNA-disease associations is significant for studying the pathogenesis of diseases. Since traditional wet-lab methods are resource-intensive, cost-saving computational models can be an effective complementary tool in biological experiments. In this work, a locality-constrained linear coding is proposed to predict associations (ILLCEL). Among them, ILLCEL adopts miRNA sequence similarity, miRNA functional similarity, disease semantic similarity, and interaction profile similarity obtained by locality-constrained linear coding (LLC) as the priori information. Next, features and similarities extracted from multiperspectives are input to the ensemble learning framework to improve the comprehensiveness of the prediction. Significantly, the introduction of hypergraph-regular terms improves the accuracy of prediction by describing complex associations between samples. The results under fivefold cross validation indicate that ILLCEL achieves superior prediction performance. In case studies, known associations are accurately predicted and novel associations are verified in HMDD v3.2, miRCancer, and existing literature. It is concluded that ILLCEL can be served as a powerful tool for inferring potential associations.

Identifying drug-disease associations (DDAs) is critical to the development of drugs. Traditional methods to determine DDAs are expensive and inefficient. Therefore, it is imperative to develop more accurate and effective methods for DDAs prediction. Most current DDAs prediction methods utilize original DDAs matrix directly. However, the original DDAs matrix is sparse, which greatly affects the prediction consequences. Hence, a prediction method based on multi-similarities graph convolutional autoencoder (MSGCA) is proposed for DDAs prediction. First, MSGCA integrates multiple drug similarities and disease similarities using centered kernel alignment-based multiple kernel learning (CKA-MKL) algorithm to form new drug similarity and disease similarity, respectively. Second, the new drug and disease similarities are improved by linear neighborhood, and the DDAs matrix is reconstructed by weighted K nearest neighbor profiles. Next, the reconstructed DDAs and the improved drug and disease similarities are integrated into a heterogeneous network. Finally, the graph convolutional autoencoder with attention mechanism is utilized to predict DDAs. Compared with extant methods, MSGCA shows superior results on three datasets. Furthermore, case studies further demonstrate the reliability of MSGCA.

With the development of bioinformatics, the important role played by lncRNAs in various intractable diseases has aroused the interest of many experts. In recent studies, researchers have found that several human diseases are related to lncRANs. Moreover, it is very difficult and expensive to explore the unknown lncRNA-disease associations (LDAs), so only a few associations have been confirmed. It is vital to find a more accurate and effective method to identify potential LDAs. In this study, a method of collaborative matrix factorization based on correntropy (LDCMFC) is proposed for the identification of potential LDAs. To improve the robustness of the algorithm, the traditional minimization of the Euclidean distance is replaced with the maximized correntropy. In addition, the weighted K nearest known neighbor (WKNKN) method is used to rebuild the adjacency matrix. Finally, the performance of LDCMFC is tested by 5-fold cross-validation. Compared with other traditional methods, LDACMFC obtains a higher AUC of 0.8628. In different types of studies of three important cancer cases, most of the potentially relevant lncRNAs derived from the experiments have been validated in the databases. The final result shows that LDCMFC is a feasible method to predict LDAs.

Many experiments have proved that long non-coding RNAs (lncRNAs) in humans have been implicated in disease development. The prediction of lncRNA-disease association is essential in promoting disease treatment and drug development. It is time-consuming and laborious to explore the relationship between lncRNA and diseases in the laboratory. The computation-based approach has clear advantages and has become a promising research direction. This paper proposes a new lncRNA disease association prediction algorithm BRWMC. Firstly, BRWMC constructed several lncRNA (disease) similarity networks based on different measurement angles and fused them into an integrated similarity network by similarity network fusion (SNF). In addition, the random walk method is used to preprocess the known lncRNA-disease association matrix and calculate the estimated scores of potential lncRNA-disease associations. Finally, the matrix completion method accurately predicts the potential lncRNA-disease associations. Under the framework of leave-one-out cross-validation and 5-fold cross-validation, the AUC values obtained by BRWMC are 0.9610 and 0.9739, respectively. In addition, case studies of three common diseases show that BRWMC is a reliable method for prediction., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier Ltd. All rights reserved.)

With the high-quality development of bioinformatics technology, miRNA-disease associations (MDAs) are gradually being uncovered. At present, convenient and efficient prediction methods, which solve the problem of resource-consuming in traditional wet experiments, need to be further put forward. In this study, a space projection model based on block matrix is presented for predicting MDAs (BMPMDA). Specifically, two block matrices are first composed of the known association matrix and similarity to increase comprehensiveness. For the integrity of information in the heterogeneous network, matrix completion (MC) is utilized to mine potential MDAs. Considering the neighborhood information of data points, linear neighborhood similarity (LNS) is regarded as a measure of similarity. Next, LNS is projected onto the corresponding completed association matrix to derive the projection score. Finally, the AUC and AUPR values for BMPMDA reach 0.9691 and 0.6231, respectively. Additionally, the majority of novel MDAs in three disease cases are identified in existing databases and literature. It suggests that BMPMDA can serve as a reliable prediction model for biological research., (© 2022. International Association of Scientists in the Interdisciplinary Areas.)

Studies have revealed that microbes have an important effect on numerous physiological processes, and further research on the links between diseases and microbes is significant. Given that laboratory methods are expensive and not optimized, computational models are increasingly used for discovering disease-related microbes. Here, a new neighbor approach based on two-tier Bi-Random Walk is proposed for potential disease-related microbes, known as NTBiRW. In this method, the first step is to construct multiple microbe similarities and disease similarities. Then, three kinds of microbe/disease similarity are integrated through two-tier Bi-Random Walk to obtain the final integrated microbe/disease similarity network with different weights. Finally, Weighted K Nearest Known Neighbors (WKNKN) is used for prediction based on the final similarity network. In addition, leave-one-out cross-validation (LOOCV) and 5-fold cross-validation (5-fold CV) are applied for evaluating the performance of NTBiRW. Multiple evaluating indicators are taken to show the performance from multiple perspectives. And most of the evaluation index values of NTBiRW are better than those of the compared methods. Moreover, in case studies on atopic dermatitis and psoriasis, most of the first 10 candidates in the final result can be proven. This also demonstrates the capability of NTBiRW for discovering new associations. Therefore, this method can contribute to the discovery of disease-related microbes and thus offer new thoughts for further understanding the pathogenesis of diseases.

An Increase in microbial activity is shown to be intimately connected with the pathogenesis of diseases. Considering the expense of traditional verification methods, researchers are working to develop high-efficiency methods for detecting potential disease-related microbes. In this article, a new prediction method, MSF-LRR, is established, which uses Low-Rank Representation (LRR) to perform multi-similarity information fusion to predict disease-related microbes. Considering that most existing methods only use one class of similarity, three classes of microbe and disease similarity are added. Then, LRR is used to obtain low-rank structural similarity information. Additionally, the method adaptively extracts the local low-rank structure of the data from a global perspective, to make the information used for the prediction more effective. Finally, a neighbor-based prediction method that utilizes the concept of collaborative filtering is applied to predict unknown microbe-disease pairs. As a result, the AUC value of MSF-LRR is superior to other existing algorithms under 5-fold cross-validation. Furthermore, in case studies, excluding originally known associations, 16 and 19 of the top 20 microbes associated with Bacterial Vaginosis and Irritable Bowel Syndrome, respectively, have been confirmed by the recent literature. In summary, MSF-LRR is a good predictor of potential microbe-disease associations and can contribute to drug discovery and biological research.

With the development of research on the complex aetiology of many diseases, computational drug repositioning methodology has proven to be a shortcut to costly and inefficient traditional methods. Therefore, developing more promising computational methods is indispensable for finding new candidate diseases to treat with existing drugs. In this paper, a model integrating a new variant of message passing neural network and a novel-gated fusion mechanism called GLGMPNN is proposed for drug-disease association prediction. First, a light-gated message passing neural network (LGMPNN), including message passing, aggregation and updating, is proposed to separately extract multiple pieces of information from the similarity networks and the association network. Then, a gated fusion mechanism consisting of a forget gate and an output gate is applied to integrate the multiple pieces of information to extent. The forget gate calculated by the multiple embeddings is built to integrate the association information into the similarity information. Furthermore, the final node representations are controlled by the output gate, which fuses the topology information of the networks and the initial similarity information. Finally, a bilinear decoder is adopted to reconstruct an adjacency matrix for drug-disease associations. Evaluated by 10-fold cross-validations, GLGMPNN achieves excellent performance compared with the current models. The following studies show that our model can effectively discover novel drug-disease associations., (© The Author(s) 2022. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.)

Extracting genes involved in cancer lesions from gene expression data is critical for cancer research and drug development. The method of feature selection has attracted much attention in the field of bioinformatics. Principal Component Analysis (PCA) is a widely used method for learning low-dimensional representation. Some variants of PCA have been proposed to improve the robustness and sparsity of the algorithm. However, the existing methods ignore the high-order relationships between data. In this paper, a new model named Robust Principal Component Analysis via Hypergraph Regularization (HRPCA) is proposed. In detail, HRPCA utilizes L2,1-norm to reduce the effect of outliers and make data sufficiently row-sparse. And the hypergraph regularization is introduced to consider the complex relationship among data. Important information hidden in the data are mined, and this method ensures the accuracy of the resulting data relationship information. Extensive experiments on multi-view biological data demonstrate that the feasible and effective of the proposed approach.

A growing number of clinical studies have provided substantial evidence of a close relationship between the microbe and the disease. Thus, it is necessary to infer potential microbe-disease associations. But traditional approaches use experiments to validate these associations that often spend a lot of materials and time. Hence, more reliable computational methods are expected to be applied to predict disease-associated microbes. In this article, an innovative mean for predicting microbe-disease associations is proposed, which is based on network consistency projection and label propagation (NCPLP). Given that most existing algorithms use the Gaussian interaction profile (GIP) kernel similarity as the similarity criterion between microbe pairs and disease pairs, in this model, Medical Subject Headings descriptors are considered to calculate disease semantic similarity. In addition, 16S rRNA gene sequences are borrowed for the calculation of microbe functional similarity. In view of the gene-based sequence information, we use two conventional methods (BLAST+ and MEGA7) to assess the similarity between each pair of microbes from different perspectives. Especially, network consistency projection is added to obtain network projection scores from the microbe space and the disease space. Ultimately, label propagation is utilized to reliably predict microbes related to diseases. NCPLP achieves better performance in various evaluation indicators and discovers a greater number of potential associations between microbes and diseases. Also, case studies further confirm the reliable prediction performance of NCPLP. To conclude, our algorithm NCPLP has the ability to discover these underlying microbe-disease associations and can provide help for biological study.

Tensor Robust Principal Component Analysis (TRPCA) has achieved promising results in the analysis of genomics data. However, the TRPCA model under the existing tensor singular value decomposition ([Formula: see text]-SVD) framework insufficiently extracts the potential low-rank structure of the data, resulting in suboptimal restored components. Simultaneously, the tensor nuclear norm (TNN) defined based on [Formula: see text]-SVD uses the same standard to handle various singular values. TNN ignores the difference of singular values, leading to the failure of the main information that needs to be well preserved. To preserve the heterogeneous structure in the low-rank information, we propose a novel TNN and extend it to the TRPCA model. Potential low-rank space may contain important information. We learn the low-rank structural information from the core tensor. The singular value space contains the association information between genes and cancers. The [Formula: see text]-shrinkage generalized threshold function is utilized to preserve the low-rank properties of larger singular values. The optimization problem is solved by the alternating direction method of the multiplier (ADMM) algorithm. Clustering and feature selection experiments are performed on the TCGA data set. The experimental results show that the proposed model is more promising than other state-of-the-art tensor decomposition methods.

The rapid development of single-cell RNA sequencing (scRNA-seq)technology reveals the gene expression status and gene structure of individual cells, reflecting the heterogeneity and diversity of cells. The traditional methods of scRNA-seq data analysis treat data as the same subspace, and hide structural information in other subspaces. In this paper, we propose a low-rank subspace ensemble clustering framework (LRSEC)to analyze scRNA-seq data. Assuming that the scRNA-seq data exist in multiple subspaces, the low-rank model is used to find the lowest rank representation of the data in the subspace. It is worth noting that the penalty factor of the low-rank kernel function is uncertain, and different penalty factors correspond to different low-rank structures. Moreover, the single cluster model is difficult to find the cellular structure of all datasets. To strengthen the correlation between model solutions, we construct a new ensemble clustering framework LRSEC by using the low-rank model as the basic learner. The LRSEC framework captures the global structure of data through low-rank subspaces, which has better clustering performance than a single clustering model. We validate the performance of the LRSEC framework on seven small datasets and one large dataset and obtain satisfactory results.

The development of single-cell RNA sequencing (scRNA-seq) technology has made it possible to measure gene expression levels at the resolution of a single cell, which further reveals the complex growth processes of cells such as mutation and differentiation. Recognizing cell heterogeneity is one of the most critical tasks in scRNA-seq research. To solve it, we propose a non-negative matrix factorization framework based on multi-subspace cell similarity learning for unsupervised scRNA-seq data analysis (MscNMF). MscNMF includes three parts: data decomposition, similarity learning, and similarity fusion. The three work together to complete the data similarity learning task. MscNMF can learn the gene features and cell features of different subspaces, and the correlation and heterogeneity between cells will be more prominent in multi-subspaces. The redundant information and noise in each low-dimensional feature space are eliminated, and its gene weight information can be further analyzed to calculate the optimal number of subpopulations. The final cell similarity learning will be more satisfactory due to the fusion of cell similarity information in different subspaces. The advantage of MscNMF is that it can calculate the number of cell types and the rank of Non-negative matrix factorization (NMF) reasonably. Experiments on eight real scRNA-seq datasets show that MscNMF can effectively perform clustering tasks and extract useful genetic markers. To verify its clustering performance, the framework is compared with other latest clustering algorithms and satisfactory results are obtained. The code of MscNMF is free available for academic (https://github.com/wangchuanyuan1/project-MscNMF).

Non-negative matrix factorization (NMF) is a dimensionality reduction technique based on high-dimensional mapping. It can learn part-based representations effectively. In this paper, we propose a method called Dual Hyper-graph Regularized Supervised Non-negative Matrix Factorization (HSNMF). To encode the geometric information of the data, the hyper-graph is introduced into the model as a regularization term. The advantage of hyper-graph learning is to find higher order data relationship to enhance data relevance. This method constructs the data hyper-graph and the feature hyper-graph to find the data manifold and the feature manifold simultaneously. The application of hyper-graph theory in cancer datasets can effectively find pathogenic genes. The discrimination information is further introduced into the objective function to obtain more information about the data. Supervised learning with label information greatly improves the classification effect. Furthermore, the real datasets of cancer usually contain sparse noise, so the L 2,1 -norm is applied to enhance the robustness of HSNMF algorithm. Experiments under The Cancer Genome Atlas (TCGA) datasets verify the feasibility of the HSNMF method.

High-throughput sequencing of single-cell gene expression reveals a complex mechanism of individual cell's heterogeneity in a population. An important purpose for analyzing single-cell RNA sequencing (scRNA-seq) data is to identify cell subtypes and functions by cell clustering. To deal with high levels of noise and cellular heterogeneity, we introduced a new single cell data analysis model called Adaptive Total-Variation Regularized Low-Rank Representation (ATV-LRR). In scRNA-seq data, ATV-LRR can reconstruct the low-rank subspace structure to learn the similarity of cells. The low-rank representation can not only segment multiple linear subspaces, but also extract important information. Moreover, adaptive total variation also can remove cell noise and preserve cell feature details by learning the gradient information of the data. At the same time, to analyze scRNA-seq data with unknown prior information, we introduced the maximum eigenvalue method into the ATV-LRR model to automatically identify cell populations. The final clustering results show that the ATV-LRR model can detect cell types more effectively and stably., (© 2021. International Association of Scientists in the Interdisciplinary Areas.)

The identification of differentially expressed genes plays an increasingly important role biologically. Therefore, the feature selection approach has attracted much attention in the field of bioinformatics. The most popular method of principal component analysis studies two-dimensional data without considering the spatial geometric structure of the data. The recently proposed tensor robust principal component analysis method performs sparse and low-rank decomposition on three-dimensional tensors and effectively preserves the spatial structure. Based on this approach, the L 2,1 - norm regularization term is introduced into the DSTPCA (Double-Sparse Constrained Tensor Principal Component Analysis) method. The DSTPCA method removes the redundant noise by double sparse constraints on the objective function to obtain sufficiently sparse results. After the regularization norm is introduced into the model, the ADMM (alternating direction method of multipliers) algorithm is used to solve the optimal problem. In the experiment of feature selection, while the more redundant genes were filtered out, the more genes closely associated with disease were screened. Experimental results using different datasets indicate that our method outperforms other methods.

Background: In the development of science and technology, there are increasing evidences that there are some associations between lncRNAs and human diseases. Therefore, finding these associations between them will have a huge impact on our treatment and prevention of some diseases. However, the process of finding the associations between them is very difficult and requires a lot of time and effort. Therefore, it is particularly important to find some good methods for predicting lncRNA-disease associations (LDAs)., Results: In this paper, we propose a method based on dual sparse collaborative matrix factorization (DSCMF) to predict LDAs. The DSCMF method is improved on the traditional collaborative matrix factorization method. To increase the sparsity, the L 2,1 -norm is added in our method. At the same time, Gaussian interaction profile kernel is added to our method, which increase the network similarity between lncRNA and disease. Finally, the AUC value obtained by the experiment is used to evaluate the quality of our method, and the AUC value is obtained by the ten-fold cross-validation method., Conclusions: The AUC value obtained by the DSCMF method is 0.8523. At the end of the paper, simulation experiment is carried out, and the experimental results of prostate cancer, breast cancer, ovarian cancer and colorectal cancer are analyzed in detail. The DSCMF method is expected to bring some help to lncRNA-disease associations research. The code can access the https://github.com/Ming-0113/DSCMF website.

As is known to all, constructing experiments to predict unknown miRNA-disease association is time-consuming, laborious and costly. Accordingly, new prediction model should be conducted to predict novel miRNA-disease associations. What's more, the performance of this method should be high and reliable. In this paper, a new computation model Logistic Weighted Profile-based Collaborative Matrix Factorization (LWPCMF) is put forward. In this method, weighted profile (WP) is combined with collaborative matrix factorization (CMF) to increase the performance of this model. And, the neighbor information is considered. In addition, logistic function is applied to miRNA functional similarity matrix and disease semantic similarity matrix to extract valuable information. At the same time, by adding WP and logistic function, the known correlation can be protected. And, Gaussian Interaction Profile (GIP) kernels of miRNAs and diseases are added to miRNA functional similarity network and disease semantic similarity network to augment kernel similarities. Then, a five-fold cross validation is implemented to evaluate the predictive ability of this method. Besides, case studies are conducted to view the experimental results. The final result contains not only known associations but also newly predicted ones. And, the result proves that our method is better than other existing methods. This model is able to predict potential miRNA-disease associations.

As we all know, science and technology are developing faster and faster. Many experts and scholars have demonstrated that human diseases are related to lncRNA, but only a few associations have been confirmed, and many unknown associations need to be found. In the process of finding associations, it takes a lot of time, so finding an efficient way to predict the associations between lncRNAs and diseases is particularly important. In this paper, we propose a multi-label fusion collaborative matrix factorization (MLFCMF) approach for predicting lncRNA-disease associations (LDAs). Firstly, the lncRNA space and disease space are optimized by multi-label to enhance the intrinsic link between lncRNA and disease and to tap potential information. Multi-label learning can encode a variety of data information from the sample space. Secondly, to learn multi-label information in the data space, the fusion method is used to handle the relationship between multiple labels. More comprehensive information will be obtained by weighing the effects of different labels. The addition of Gaussian interaction profile (GIP) kernel can increase the network similarity. Finally, the lncRNA-disease associations are predicted by the method of collaborative matrix factorization. The ten-fold cross-validation method is used to evaluate the MLFCMF method, and our method finally obtains an AUC value of 0.8612. Detailed analysis of ovarian cancer, colorectal cancer, and lung cancer in the simulation experiment results. So it can be seen that our method MLFCMF is an effective model for predicting lncRNA-disease associations.

Non-negative Matrix Factorization (NMF) is a popular data dimension reduction method in recent years. The traditional NMF method has high sensitivity to data noise. In the paper, we propose a model called Sparse Robust Graph-regularized Non-negative Matrix Factorization based on Correntropy (SGNMFC). The maximized correntropy replaces the traditional minimized Euclidean distance to improve the robustness of the algorithm. Through the kernel function, correntropy can give less weight to outliers and noise in data but give greater weight to meaningful data. Meanwhile, the geometry structure of the high-dimensional data is completely preserved in the low-dimensional manifold through the graph regularization. Feature selection and sample clustering are commonly used methods for analyzing genes. Sparse constraints are applied to the loss function to reduce matrix complexity and analysis difficulty. Comparing the other five similar methods, the effectiveness of the SGNMFC model is proved by selection of differentially expressed genes and sample clustering experiments in three The Cancer Genome Atlas (TCGA) datasets.

In recent years, many human diseases have been determined to be associated with certain lncRNAs. Only a small percentage of all lncRNA-disease associations (LDAs) have been discovered by researchers. Predicting novel LDAs is time-consuming and costly. It is crucial to propose a method that can effectively identify potential LDAs to solve this problem based on the available datasets. Although some current methods can effectively predict potential LDAs, the prediction accuracy needs to be improved, and there are few known associations. Moreover, there are notable errors in the method of constructing the network and the bipartite graph, which interfere with the final results. A weighted graph regularized collaborative matrix factorization (WGRCMF) method is proposed to predict novel LDAs. We introduce the graph regularization terms into the collaborative matrix factorization. Considering that manifold learning can recover low-dimensional manifold structures from high-dimensional sampled data, we can find low-dimensional manifolds in high-dimensional space. In addition, a weight matrix is also introduced into the method, the significance of which is to prevent unknown associations from contributing to the final prediction matrix. Finally, the prediction accuracy of this method is better than those of other methods. In several cancer cases, we implemented the corresponding simulation experiments. According to the experimental results, the proposed method is feasible and effective.

With the development of cancer research, various gene expression datasets containing cancer information show an explosive growth trend. In addition, due to the continuous maturity of single-cell RNA sequencing (scRNA-seq) technology, the protein information and pedigree information of a single cell are also continuously mined. It is a technical problem of how to classify these high-dimensional data correctly. In recent years, Extreme Learning Machine (ELM) has been widely used in the field of supervised learning and unsupervised learning. However, the traditional ELM does not consider the robustness of the method. To improve the robustness of ELM, in this paper, a novel ELM method based on L 2,1 -norm named L 2,1 -Extreme Learning Machine (L 2,1 -ELM) has been proposed. The method introduces L 2,1 -norm on loss function to improve the robustness, and minimizes the influence of noise and outliers. Firstly, we evaluate the new method on five UCI datasets. The experiment results prove that our method can achieve competitive results. Next, the novel method is applied to the problem of classification of cancer samples and single-cell RNA sequencing datasets. The experimental results on The Cancer Genome Atlas (TCGA) datasets and scRNA-seq datasets prove that ELM and its variants has great potential in the classification of cancer samples., (Copyright © 2020 Elsevier Ltd. All rights reserved.)

Background: MicroRNAs (miRNAs) are non-coding RNAs with regulatory functions. Many studies have shown that miRNAs are closely associated with human diseases. Among the methods to explore the relationship between the miRNA and the disease, traditional methods are time-consuming and the accuracy needs to be improved. In view of the shortcoming of previous models, a method, collaborative matrix factorization based on matrix completion (MCCMF) is proposed to predict the unknown miRNA-disease associations., Results: The complete matrix of the miRNA and the disease is obtained by matrix completion. Moreover, Gaussian Interaction Profile kernel is added to the miRNA functional similarity matrix and the disease semantic similarity matrix. Then the Weight K Nearest Known Neighbors method is used to pretreat the association matrix, so the model is close to the reality. Finally, collaborative matrix factorization method is applied to obtain the prediction results. Therefore, the MCCMF obtains a satisfactory result in the fivefold cross-validation, with an AUC of 0.9569 (0.0005)., Conclusions: The AUC value of MCCMF is higher than other advanced methods in the fivefold cross validation experiment. In order to comprehensively evaluate the performance of MCCMF, accuracy, precision, recall and f-measure are also added. The final experimental results demonstrate that MCCMF outperforms other methods in predicting miRNA-disease associations. In the end, the effectiveness and practicability of MCCMF are further verified by researching three specific diseases.

Background: As a machine learning method with high performance and excellent generalization ability, extreme learning machine (ELM) is gaining popularity in various studies. Various ELM-based methods for different fields have been proposed. However, the robustness to noise and outliers is always the main problem affecting the performance of ELM., Results: In this paper, an integrated method named correntropy induced loss based sparse robust graph regularized extreme learning machine (CSRGELM) is proposed. The introduction of correntropy induced loss improves the robustness of ELM and weakens the negative effects of noise and outliers. By using the L 2,1 -norm to constrain the output weight matrix, we tend to obtain a sparse output weight matrix to construct a simpler single hidden layer feedforward neural network model. By introducing the graph regularization to preserve the local structural information of the data, the classification performance of the new method is further improved. Besides, we design an iterative optimization method based on the idea of half quadratic optimization to solve the non-convex problem of CSRGELM., Conclusions: The classification results on the benchmark dataset show that CSRGELM can obtain better classification results compared with other methods. More importantly, we also apply the new method to the classification problems of cancer samples and get a good classification effect.

Non-negative Matrix Factorization (NMF) is a dimensionality reduction approach for learning a parts-based and linear representation of non-negative data. It has attracted more attention because of that. In practice, NMF not only neglects the manifold structure of data samples, but also overlooks the priori label information of different classes. In this paper, a novel matrix decomposition method called Hyper-graph regularized Constrained Non-negative Matrix Factorization (HCNMF) is proposed for selecting differentially expressed genes and tumor sample classification. The advantage of hyper-graph learning is to capture local spatial information in high dimensional data. This method incorporates a hyper-graph regularization constraint to consider the higher order data sample relationships. The application of hyper-graph theory can effectively find pathogenic genes in cancer datasets. Besides, the label information is further incorporated in the objective function to improve the discriminative ability of the decomposition matrix. Supervised learning with label information greatly improves the classification effect. We also provide the iterative update rules and convergence proofs for the optimization problems of HCNMF. Experiments under The Cancer Genome Atlas (TCGA) datasets confirm the superiority of HCNMF algorithm compared with other representative algorithms through a set of evaluations.

In recent years, with the diversity and variability of cancer information, the multi-omics data have been applied in various fields. Many existing models of principal component analysis can only process single data, which makes limitations on cancer research. Therefore, in this paper, a new model called integrative principal component analysis (IPCA) is proposed to achieve the unification of multi-omics data. In addition, in order to preserve the high-order manifold structure between the data, an integrative hypergraph regularization principal component analysis (IHPCA) is further proposed by applying the hypergraph regularization constraint. The effectiveness of IHPCA method is tested on four multi-omics datasets. Experimental results show that the proposed method has better performance than other representative methods on sample clustering and common expression genes (co-expression genes) network analysis.

There is much evidence that long non-coding RNA (lncRNA) is associated with many diseases. However, it is time-consuming and expensive to identify meaningful lncRNA-disease associations (LDAs) through medical or biological experiments. Therefore, investigating how to identify more meaningful LDAs is necessary, and at the same time it is conducive to the prevention, diagnosis and treatment of complex diseases. Considering the limitations of some current prediction models, a novel model based on bipartite local model with nearest profile-based association inferring, BLM-NPAI, is developed for predicting LDAs. This model predicts novel LDAs from the lncRNA side and the disease side, respectively. More importantly, for some lncRNAs and diseases without any association, the model can also be predicted by their nearest neighbors. Leave-one-out cross validation (LOOCV) and 5-fold cross validation are implemented for BLM-NPAI to evaluate the performance of this model. Our model is superior to current advanced methods in most cases. In addition, to verify the validity and reliability of BLM-NPAI, three disease cases and three lncRNA cases are analyzed to further evaluate BLM-NPAI. Finally, these predicted novel LDAs are confirmed by using the LncRNA-disease database.

Background: Gene co-expression network is a favorable method to reveal the nature of disease. With the development of cancer, the way to build gene co-expression networks based on cancer data has been become a hot spot. However, there are still a limited number of current node measurement methods and node mining strategies for multi-cancers network construction., Methods: In this paper, we introduce a new method for mining information of co-expression network based on multi-cancers integrated data, named PMN. We construct the network by combining the different types of relevant measures (linear and nonlinear rules) for different nodes based on integrated gene expression data of multi-cancers from The Cancer Genome Atlas (TCGA). For mining genes, we combine different properties (local and global characteristics) of the nodes., Results: We uncover more suspicious abnormally expressed genes and shared pathways of different cancers. And we have also found some proven genes and pathways; of course, there are some suspicious factors and molecules that need clinical validation., Conclusions: The results demonstrate that our method is very effective in excavating gene co-expression genes of multi-cancers.

Background: Predicting miRNA-disease associations (MDAs) is time-consuming and expensive. It is imminent to improve the accuracy of prediction results. So it is crucial to develop a novel computing technology to predict new MDAs. Although some existing methods can effectively predict novel MDAs, there are still some shortcomings. Especially when the disease matrix is processed, its sparsity is an important factor affecting the final results., Results: A robust collaborative matrix factorization (RCMF) is proposed to predict novel MDAs. The L 2,1 -norm are introduced to our method to achieve the highest AUC value than other advanced methods., Conclusions: 5-fold cross validation is used to evaluate our method, and simulation experiments are used to predict novel associations on Gold Standard Dataset. Finally, our prediction accuracy is better than other existing advanced methods. Therefore, our approach is effective and feasible in predicting novel MDAs.

Background: As one of the most popular data representation methods, non-negative matrix decomposition (NMF) has been widely concerned in the tasks of clustering and feature selection. However, most of the previously proposed NMF-based methods do not adequately explore the hidden geometrical structure in the data. At the same time, noise and outliers are inevitably present in the data., Results: To alleviate these problems, we present a novel NMF framework named robust hypergraph regularized non-negative matrix factorization (RHNMF). In particular, the hypergraph Laplacian regularization is imposed to capture the geometric information of original data. Unlike graph Laplacian regularization which captures the relationship between pairwise sample points, it captures the high-order relationship among more sample points. Moreover, the robustness of the RHNMF is enhanced by using the L 2,1 -norm constraint when estimating the residual. This is because the L 2,1 -norm is insensitive to noise and outliers., Conclusions: Clustering and common abnormal expression gene (com-abnormal expression gene) selection are conducted to test the validity of the RHNMF model. Extensive experimental results on multi-view datasets reveal that our proposed model outperforms other state-of-the-art methods.

Principal component analysis (PCA) has been used to study the pathogenesis of diseases. To enhance the interpretability of classical PCA, various improved PCA methods have been proposed to date. Among these, a typical method is the so-called sparse PCA, which focuses on seeking sparse loadings. However, the performance of these methods is still far from satisfactory due to their limitation of using unsupervised learning methods; moreover, the class ambiguity within the sample is high. To overcome this problem, this paper developed a new PCA method, which is named the supervised discriminative sparse PCA (SDSPCA). The main innovation of this method is the incorporation of discriminative information and sparsity into the PCA model. Specifically, in contrast to the traditional sparse PCA, which imposes sparsity on the loadings, here, sparse components are obtained to represent the data. Furthermore, via the linear transformation, the sparse components approximate the given label information. On the one hand, sparse components improve interpretability over the traditional PCA, while on the other hand, they are have discriminative abilities suitable for classification purposes. A simple algorithm is developed, and its convergence proof is provided. SDSPCA has been applied to the common-characteristic gene selection and tumor classification on multiview biological data. The sparsity and classification performance of SDSPCA are empirically verified via abundant, reasonable, and effective experiments, and the obtained results demonstrate that SDSPCA outperforms other state-of-the-art methods.

Background: Predicting meaningful miRNA-disease associations (MDAs) is costly. Therefore, an increasing number of researchers are beginning to focus on methods to predict potential MDAs. Thus, prediction methods with improved accuracy are under development. An efficient computational method is proposed to be crucial for predicting novel MDAs. For improved experimental productivity, large biological datasets are used by researchers. Although there are many effective and feasible methods to predict potential MDAs, the possibility remains that these methods are flawed., Results: A simple and effective method, known as Nearest Profile-based Collaborative Matrix Factorization (NPCMF), is proposed to identify novel MDAs. The nearest profile is introduced to our method to achieve the highest AUC value compared with other advanced methods. For some miRNAs and diseases without any association, we use the nearest neighbour information to complete the prediction., Conclusions: To evaluate the performance of our method, five-fold cross-validation is used to calculate the AUC value. At the same time, three disease cases, gastric neoplasms, rectal neoplasms and colonic neoplasms, are used to predict novel MDAs on a gold-standard dataset. We predict the vast majority of known MDAs and some novel MDAs. Finally, the prediction accuracy of our method is determined to be better than that of other existing methods. Thus, the proposed prediction model can obtain reliable experimental results.

Background: Predicting drug-target interactions is time-consuming and expensive. It is important to present the accuracy of the calculation method. There are many algorithms to predict global interactions, some of which use drug-target networks for prediction (ie, a bipartite graph of bound drug pairs and targets known to interact). Although these algorithms can predict some drug-target interactions to some extent, there is little effect for some new drugs or targets that have no known interaction., Results: Since the datasets are usually located at or near low-dimensional nonlinear manifolds, we propose an improved GRMF (graph regularized matrix factorization) method to learn these flow patterns in combination with the previous matrix-decomposition method. In addition, we use one of the pre-processing steps previously proposed to improve the accuracy of the prediction., Conclusions: Cross-validation is used to evaluate our method, and simulation experiments are used to predict new interactions. In most cases, our method is superior to other methods. Finally, some examples of new drugs and new targets are predicted by performing simulation experiments. And the improved GRMF method can better predict the remaining drug-target interactions.

With the development of biological research and scientific experiments, it has been discovered that microRNAs (miRNAs) are closely related to many serious human diseases; however, finding the correct miRNA-disease associations is both time consuming and challenging. Therefore, it is very necessary to develop some new methods. Although the existing methods are very helpful in this regard, they all present some shortcomings; thus, some new methods need to be developed to overcome these shortcomings. In this study, a method based on dual network sparse graph regularized matrix factorization (DNSGRMF) was proposed, which increased the sparsity by adding the L 2,1 -norm. Moreover, Gaussian interaction profile kernels were introduced. The experiments showed that our method was feasible and had a high AUC value. Additionally, the five-fold cross-validation method was used to evaluate this method. A simulation experiment was used to predict some new associations on the datasets, and the obtained experimental results were satisfactory, which proved that our method was indeed feasible.

The noise problem of cancer sequencing data has been a problem that can't be ignored. Utilizing considerable way to reduce noise of these cancer data is an important issue in the analysis of gene co-expression network. In this paper, we apply a sparse and low-rank method which is Robust Principal Component Analysis (RPCA) to solve the noise problem for integrated data of multi-cancers from The Cancer Genome Atlas (TCGA). And then we build the gene co-expression network based on the integrated data after noise reduction. Finally, we perform nodes and pathways mining on the denoising networks. Experiments in this paper show that after denoising by RPCA, the gene expression data tend to be orderly and neat than before, and the constructed networks contain more pathway enrichment information than unprocessed data. Moreover, learning from the betweenness centrality of the nodes in the network, we find some abnormally expressed genes and pathways proven that are associated with many cancers from the denoised network. The experimental results indicate that our method is reasonable and effective, and we also find some candidate suspicious genes that may be linked to multi-cancers., (Copyright © 2018 Elsevier Ltd. All rights reserved.)

Background: Predicting drug-disease interactions (DDIs) is time-consuming and expensive. Improving the accuracy of prediction results is necessary, and it is crucial to develop a novel computing technology to predict new DDIs. The existing methods mostly use the construction of heterogeneous networks to predict new DDIs. However, the number of known interacting drug-disease pairs is small, so there will be many errors in this heterogeneous network that will interfere with the final results., Results: A novel method, known as the dual-network L 2,1 -collaborative matrix factorization, is proposed to predict novel DDIs. The Gaussian interaction profile kernels and L 2,1 -norm are introduced in our method to achieve better results than other advanced methods. The network similarities of drugs and diseases with their chemical and semantic similarities are combined in this method., Conclusions: Cross validation is used to evaluate our method, and simulation experiments are used to predict new interactions using two different datasets. Finally, our prediction accuracy is better than other existing methods. This proves that our method is feasible and effective.

Principal component analysis (PCA) is a widely used method for evaluating low-dimensional data. Some variants of PCA have been proposed to improve the interpretation of the principal components (PCs). One of the most common methods is sparse PCA which aims at finding a sparse basis to improve the interpretability over the dense basis of PCA. However, the performances of these improved methods are still far from satisfactory because the data still contain redundant PCs. In this paper, a novel method called PCA based on graph Laplacian and double sparse constraints (GDSPCA) is proposed to improve the interpretation of the PCs and consider the internal geometry of the data. In detail, GDSPCA utilizes L2,1-norm and L1-norm regularization terms simultaneously to enforce the matrix to be sparse by filtering redundant and irrelative PCs, where the L2,1-norm regularization term can produce row sparsity, while the L1-norm regularization term can enforce element sparsity. This way, we can make a better interpretation of the new PCs in low-dimensional subspace. Meanwhile, the method of GDSPCA integrates graph Laplacian into PCA to explore the geometric structure hidden in the data. A simple and effective optimization solution is provided. Extensive experiments on multi-view biological data demonstrate the feasibility and effectiveness of the proposed approach., (© 2019 S. Karger AG, Basel.)

Cancer genomic data contain views from different sources that provide complementary information about genetic activity. This provides a new way for cancer research. Feature selection and multi-view clustering are hot topics in bioinformatics, and they can make full use of complementary information to improve the effect. In this paper, a novel integrated model called Multi-view Non-negative Matrix Factorization (MvNMF) is proposed for the selection of common differential genes (co-differential genes) and multi-view clustering. In order to encode the geometric information in the multi-view genomic data, graph regularized MvNMF (GMvNMF) is further proposed by applying the graph regularization constraint in the objective function. GMvNMF can not only obtain the potential shared feature structure and shared cluster group structure, but also capture the manifold structure of multi-view data. The validity of the proposed GMvNMF method was tested in four multi-view genomic data. Experimental results showed that the GMvNMF method has better performance than other representative methods., Competing Interests: The authors declare no conflict of interest.

Non-negative Matrix Factorization (NMF), a classical method for dimensionality reduction, has been applied in many fields. It is based on the idea that negative numbers are physically meaningless in various data-processing tasks. Apart from its contribution to conventional data analysis, the recent overwhelming interest in NMF is due to its newly discovered ability to solve challenging data mining and machine learning problems, especially in relation to gene expression data. This survey paper mainly focuses on research examining the application of NMF to identify differentially expressed genes and to cluster samples, and the main NMF models, properties, principles, and algorithms with its various generalizations, extensions, and modifications are summarized. The experimental results demonstrate the performance of the various NMF algorithms in identifying differentially expressed genes and clustering samples.

Background: Traditional drug identification methods follow the "one drug-one target" thought. But those methods ignore the natural characters of human diseases. To overcome this limitation, many identification methods of drug-pathway association pairs have been developed, such as the integrative penalized matrix decomposition (iPaD) method. The iPaD method imposes the L 1 -norm penalty on the regularization term. However, lasso-type penalties have an obvious disadvantage, that is, the sparsity produced by them is too dispersive., Results: Therefore, to improve the performance of the iPaD method, we propose a novel method named L 2,1 -iPaD to identify paired drug-pathway associations. In the L 2,1 -iPaD model, we use the L 2,1 -norm penalty to replace the L 1 -norm penalty since the L 2,1 -norm penalty can produce row sparsity., Conclusions: By applying the L 2,1 -iPaD method to the CCLE and NCI-60 datasets, we demonstrate that the performance of L 2,1 -iPaD method is superior to existing methods. And the proposed method can achieve better enrichment in terms of discovering validated drug-pathway association pairs than the iPaD method by performing permutation test. The results on the two real datasets prove that our method is effective.

Identifying differentially expressed genes from the thousands of genes is a challenging task. Robust principal component analysis (RPCA) is an efficient method in the identification of differentially expressed genes. RPCA method uses nuclear norm to approximate the rank function. However, theoretical studies showed that the nuclear norm minimizes all singular values, so it may not be the best solution to approximate the rank function. The truncated nuclear norm is defined as the sum of some smaller singular values, which may achieve a better approximation of the rank function than nuclear norm. In this paper, a novel method is proposed by replacing nuclear norm of RPCA with the truncated nuclear norm, which is named robust principal component analysis regularized by truncated nuclear norm (TRPCA). The method decomposes the observation matrix of genomic data into a low-rank matrix and a sparse matrix. Because the significant genes can be considered as sparse signals, the differentially expressed genes are viewed as the sparse perturbation signals. Thus, the differentially expressed genes can be identified according to the sparse matrix. The experimental results on The Cancer Genome Atlas data illustrate that the TRPCA method outperforms other state-of-the-art methods in the identification of differentially expressed genes.

The traditional methods of drug discovery follow the "one drug-one target" approach, which ignores the cellular and physiological environment of the action mechanism of drugs. However, pathway-based drug discovery methods can overcome this limitation. This kind of method, such as the Integrative Penalized Matrix Decomposition (iPaD) method, identifies the drug-pathway associations by taking the lasso-type penalty on the regularization term. Moreover, instead of imposing the L1-norm regularization, the L2,1-Integrative Penalized Matrix Decomposition (L2,1-iPaD) method imposes the L2,1-norm penalty on the regularization term. In this paper, based on the iPaD and L2,1-iPaD methods, we propose a novel method named L1L2,1-iPaD (L1L2,1-Integrative Penalized Matrix Decomposition), which takes the sum of the L1-norm and L2,1-norm penalties on the regularization term. Besides, we perform permutation test to assess the significance of the identified drug-pathway association pairs and compute the P-values. Compared with the existing methods, our method can identify more drug-pathway association pairs which have been validated in the CancerResource database. In order to identify drug-pathway associations which are not validated in the CancerResource database, we retrieve published papers to prove these associations. The results on two real datasets prove that our method can achieve better enrichment for identified association pairs than the iPaD and L2,1-iPaD methods.