Non-negative Matrix Factorization Algorithm Research Articles

The Generalization of Non-Negative Matrix Factorization Based on Algorithmic Stability

The Non-negative Matrix Factorization (NMF) is a popular technique for intelligent systems, which can be widely used to decompose a nonnegative matrix into two factor matrices: a basis matrix and a coefficient one, respectively. The main objective of NMF is to ensure that the operation results of the two matrices are as close to the original matrix as possible. Meanwhile, the stability and generalization ability of the algorithm should be ensured. Therefore, the generalization performance of NMF algorithms is analyzed from the perspective of algorithm stability and the generalization error bounds are given, which is named AS-NMF. Firstly, a general NMF prediction algorithm is proposed, which can predict the labels for new samples, and then the corresponding loss function is defined further. Secondly, the stability of the NMF algorithm is defined according to the loss function, and two generalization error bounds can be obtained by employing uniform stability in the case where U is fixed and it is not fixed under the multiplicative update rule. The bounds numerically show that its stability parameter depends on the upper bound on the module length of the input data, dimension of hidden matrix and Frobenius norm of the basis matrix. Finally, a general and stable framework is established, which can analyze and measure generalization error bounds for the NMF algorithm. The experimental results demonstrate the advantages of new methods on three widely used benchmark datasets, which indicate that our AS-NMF can not only achieve efficient performance, but also outperform the state-of-the-art of recommending tasks in terms of model stability.

A fast two-stage algorithm for non-negative matrix factorization in smoothly varying data.

This article reports the study of algorithms for non-negative matrix factorization (NMF) in various applications involving smoothly varying data such as time or temperature series diffraction data on a dense grid of points. Utilizing the continual nature of the data, a fast two-stage algorithm is developed for highly efficient and accurate NMF. In the first stage, an alternating non-negative least-squares framework is used in combination with the active set method with a warm-start strategy for the solution of subproblems. In the second stage, an interior point method is adopted to accelerate the local convergence. The convergence of the proposed algorithm is proved. The new algorithm is compared with some existing algorithms in benchmark tests using both real-world data and synthetic data. The results demonstrate the advantage of the algorithm in finding high-precision solutions.

TIMEAS, a promising method for the stratification of testicular germ cell tumor patients with distinct immune microenvironment, clinical outcome and sensitivity to frontline therapies.

With the heterogeneous genetic background, prognosis prediction and therapeutic targets for testicular germ cell tumors (TGCTs) are still unclear. We defined the tumor immune microenvironment activation status (TIMEAS). We collected a total of 314 TGCT patients from four cohorts, including a 48-case microarray. A nonnegative matrix factorization algorithm was applied to identify the "immune factor", derived the top 150 weighted genes to divide patients into immune and non-immune classes, and further separated the immune class into activated and exhausted subgroups by nearest template prediction. Tumor mutant burden, gene mutation, and copy number alteration were compared with our recently developed package "MOVICS". A random forest algorithm was performed to establish a prediction model with fewer genes. Immunohistochemistry staining was performed to identify TIMEAS in the microarray. We constructed the TIMEAS in the TCGA-TGCT cohort and further validated it in the GSE3218 and GSE99420 cohorts. The immune class contained the activated status of T-lymphocytes, B-lymphocytes, and macrophages, while Treg cells and the WNT/TGFβ signature were more activated in the immune-suppressed subgroup. Patients in the immune-exhausted subgroup had the worst prognosis, and 22.9% of patients in the immune-activated subgroup had KRAS mutations, which might stimulate the response of the immune system and lead to a favorable prognosis. The immune-exhausted group benefited more from chemotherapy, while the immune-activated subgroup responded well to anti-PD-1/PD-L1 therapy. FSCN1 was validated as the target of the immune-exhausted microenvironment by immunohistochemistry. TIMEAS classification can separate TGCT patients; patients in the immune-activated subgroup could benefit more from anti-PD-L1 immunotherapy, and those in the immune-exhausted subgroup are more suitable for chemotherapy.

Imaging genetic association analysis of triple-negative breast cancer based on the integration of prior sample information.

Triple-negative breast cancer (TNBC) is one of the more aggressive subtypes of breast cancer. The prognosis of TNBC patients remains low. Therefore, there is still a need to continue identifying novel biomarkers to improve the prognosis and treatment of TNBC patients. Research in recent years has shown that the effective use and integration of information in genomic data and image data will contribute to the prediction and prognosis of diseases. Considering that imaging genetics can deeply study the influence of microscopic genetic variation on disease phenotype, this paper proposes a sample prior information-induced multidimensional combined non-negative matrix factorization (SPID-MDJNMF) algorithm to integrate the Whole-slide image (WSI), mRNAs expression data, and miRNAs expression data. The algorithm effectively fuses high-dimensional data of three modalities through various constraints. In addition, this paper constructs an undirected graph between samples, uses an adjacency matrix to constrain the similarity, and embeds the clinical stage information of patients in the algorithm so that the algorithm can identify the co-expression patterns of samples with different labels. We performed univariate and multivariate Cox regression analysis on the mRNAs and miRNAs in the screened co-expression modules to construct a TNBC-related prognostic model. Finally, we constructed prognostic models for 2-mRNAs (IL12RB2 and CNIH2) and 2-miRNAs (miR-203a-3p and miR-148b-3p), respectively. The prognostic model can predict the survival time of TNBC patients with high accuracy. In conclusion, our proposed SPID-MDJNMF algorithm can efficiently integrate image and genomic data. Furthermore, we evaluated the prognostic value of mRNAs and miRNAs screened by the SPID-MDJNMF algorithm in TNBC, which may provide promising targets for the prognosis of TNBC patients.

Identification of potential tumor antigens and immune subtypes for lung adenocarcinoma.

In lung adenocarcinoma (LUAD), tumor antigens and immune phenotypes are important for cancer immunotherapy. This study aims to identify potential tumor antigens and immune subtypes for LUAD. In this study, the gene expression profiles and related clinical data of LUAD patients were collected from the TCGA and the GEO database. Then, we first identified four genes with copy number variation and mutation related to the survival of LUAD patients, in which FAM117A, INPP5J, and SLC25A42 were screened as potential tumor antigens. The expressions of these genes were significantly correlated with the infiltration of B cells CD4+ T cells and dendritic cells using TIMER and CIBERSORT algorithms. LUAD patients were divided into three immune clusters: C1(immune-desert), C2(immune-active), and C3(inflamed) using the Non-negative matrix factorization algorithm by using survival-related immune genes. The C2 cluster showed favorable overall survival compared to C1 and C3 clusters in both TCGA and two GEO LUAD cohorts. Different immune cell infiltration patterns, immune-associated molecular characteristics, and drug sensitivity were found among the three clusters. Moreover, different positions in the immune landscape map exhibited different prognostic characteristics using dimensionality reduction, providing further evidence of the immune clusters. The Weighted Gene Co-Expression Network Analysis was used to identify the co-expression modules of these immune genes. the three subtypes were significantly positively correlated with the turquoise module gene list, indicating a good prognosis with high scores. We hope that the identified tumor antigens and immune subtypes can be used for immunotherapy and prognosis in LUAD patients.

Estimating Soil Salinity with Different Levels of Vegetation Cover by Using Hyperspectral and Non-Negative Matrix Factorization Algorithm.

Hyperspectral technology has proven to be an effective method for monitoring soil salt content (SSC). However, hyperspectral estimation capabilities are limited when the soil surface is partially vegetated. This work aimed to (1) quantify the influences of different fraction vegetation coverage (FVC) on SSC estimation by hyperspectra and (2) explore the potential for a non-negative matrix factorization algorithm (NMF) to reduce the influence of various FVCs. Nine levels of mixed hyperspectra were measured from simulated mixed scenes, which were performed by strictly controlling SSC and FVC in the laboratory. NMF was implemented to extract soil spectral signals from mixed hyperspectra. The NMF-extracted soil spectra were used to estimate SSC using partial least squares regression. Results indicate that SSC could be estimated based on the original mixed spectra within a 25.76% FVC (R2cv = 0.68, RMSEcv = 5.18 g·kg-1, RPD = 1.43). Compared with the mixed spectra, NMF extraction of soil spectrum improved the estimation accuracy. The NMF-extracted soil spectra from FVC below 63.55% of the mixed spectra provided acceptable estimation accuracies for SSC with the lowest results of determination of the estimation R2cv = 0.69, RMSEcv = 4.15 g·kg-1, and RPD = 1.8. Additionally, we proposed a strategy for the model performance investigation that combines spearman correlation analysis and model variable importance projection analysis. The NMF-extracted soil spectra retained the sensitive wavelengths that were significantly correlated with SSC and participated in the operation as important variables of the model.

Identification of the Subtypes of Renal Ischemia-Reperfusion Injury Based on Pyroptosis-Related Genes.

Ischemia-reperfusion injury (IRI) often occurs in the process of kidney transplantation, which significantly impacts the subsequent treatment and prognosis of patients. The prognosis of patients with different subtypes of IRI is quite different. Therefore, in this paper, the gene expression data of multiple IRI samples were downloaded from the GEO database, and a double Laplacian orthogonal non-negative matrix factorization (DL-ONMF) algorithm was proposed to classify them. In this algorithm, various regularization constraints are added based on the non-negative matrix factorization algorithm, and the prior information is fused into the algorithm from different perspectives. The connectivity information between different samples and features is added to the algorithm by Laplacian regularization constraints on samples and features. In addition, orthogonality constraints on the basis matrix and coefficient matrix obtained by the algorithm decomposition are added to reduce the influence of redundant samples and redundant features on the results. Based on the DL-ONMF algorithm for clustering, two PRGs-related IRI isoforms were obtained in this paper. The results of immunoassays showed that the immune microenvironment was different among PRGS-related IRI types. Based on the differentially expressed PRGs between subtypes, we used LASSO and SVM-RFE algorithms to construct a diagnostic model related to renal transplantation. ROC analysis showed that the diagnostic model could predict the outcome of renal transplant patients with high accuracy. In conclusion, this paper presents an algorithm, DL-ONMF, which can identify subtypes with different disease characteristics. Comprehensive bioinformatic analysis showed that pyroptosis might affect the outcome of kidney transplantation by participating in the immune response of IRI.

Single-channel blind source separation of underwater acoustic signals using improved NMF and FastICA

When automatic monitoring buoys receive mixed acoustic signals from multiple underwater acoustic targets, the statistical blind source separation (BSS) task is used to separate the signals and identify vessel features, which is overly complex and needs improvement, especially noting that noise cancellation and stealth technologies are advancing rapidly. To fill this gap in capability, an improved non-negative matrix factorization (NMF) based BSS algorithm is built on a FastICA machine learning backbone. With this tool, the spatial and spectral correlation of underwater acoustic signals is introduced into the NMF algorithm improved by to resolve the non-convex and feature correlation problems commonly encountered by contemporary NMF algorithms. Moreover, the improved modulation feature adaptability of the NMF increases the local expressivity and independence of the decomposed base matrix, which is proven to meet the requirements of FastICA and used to improve the BSS effect of the FastICA. Simulated and empirical results show that compared with state-of-the-art FastICA and NMF based BSS algorithms, our novel approach obtains better signal-to-noise reduction and separation accuracy while maintaining superior target signal recognition features.

Senescence-associated lncRNAs indicate distinct molecular subtypes associated with prognosis and androgen response in patients with prostate cancer

Cellular senescence has been considered as a hallmark of aging. In this study, we aimed to establish two novel prognostic subtypes for prostate cancer patients using senescence-related lncRNAs. Nonnegative matrix factorization algorithm was used to identify molecular subtypes. We completed analyses using software R 3.6.3 and its suitable packages. Using SNHG1, MIAT and SNHG3, 430 patients in TCGA database were classified into two subtypes associated with biochemical recurrence (BCR)-free survival and subtype 2 was prone to BCR (HR: 19.62, p < 0.001). The similar results were observed in the GSE46602 and GSE116918. For hallmark gene set enrichment, we found that protein secretion and androgen response were highly enriched in subtype 1 and G2M checkpoint was highly enriched in subtype 2. For tumor heterogeneity and stemness, homologous recombination deficiency and tumor mutation burden were significantly higher in subtype 2 than subtype 1. The top ten genes between subtype 2 and subtype 1 were CUBN, DNAH9, PTCHD4, NOD1, ARFGEF1, HRAS, PYHIN1, ARHGEF2, MYOM1 and ITGB6 with statistical significance. In terms of immune checkpoints, only CD47 was significantly higher in subtype 1 than that in subtype 2. For the overall assessment, no significant difference was detected between two subtypes, while B cells score was significantly higher in subtype 1 than subtype 2. Overall, we found two distinct subtypes closely associated with BCR-free survival and androgen response for prostate cancer. These subtypes might facilitate future research in the field of prostate cancer.

Speech Separation Methodology for Hearing Aid

In the design of hearing aids (HA), the real-time speech-enhancement is done. The digital hearing aids should provide high signal-to-noise ratio, gain improvement and should eliminate feedback. In generic hearing aids the performance towards different frequencies varies and non uniform. Existing noise cancellation and speech separation methods drops the voice magnitude under the noise environment. The performance of the HA for frequency response is non uniform. Existing noise suppression methods reduce the required signal strength also. So, the performance of uniform sub band analysis is poor when hearing aid is concern. In this paper, a speech separation method using Non-negative Matrix Factorization (NMF) algorithm is proposed for wavelet decomposition. The Proposed non-uniform filter-bank was validated by parameters like band power, Signal-to-noise ratio (SNR), Mean Square Error (MSE), Signal to Noise and Distortion Ratio (SINAD), Spurious-free dynamic range (SFDR), error and time. The speech recordings before and after separation was evaluated for quality using objective speech quality measures International Telecommunication Union -Telecommunication standard ITU-T P.862.

Network-Based Structural Learning Nonnegative Matrix Factorization Algorithm for Clustering of scRNA-Seq Data.

Single-cell RNA sequencing (scRNA-seq) measures expression profiles at the single-cell level, which sheds light on revealing the heterogeneity and functional diversity among cell populations. The vast majority of current algorithms identify cell types by directly clustering transcriptional profiles, which ignore indirect relations among cells, resulting in an undesirable performance on cell type discovery and trajectory inference. Therefore, there is a critical need for inferring cell types and trajectories by exploiting the interactions among cells. In this study, we propose a network-based structural learning nonnegative matrix factorization algorithm (aka SLNMF) for the identification of cell types in scRNA-seq, which is transformed into a constrained optimization problem. SLNMF first constructs the similarity network for cells and then extracts latent features of the cells by exploiting the topological structure of the cell-cell network. To improve the clustering performance, the structural constraint is imposed on the model to learn the latent features of cells by preserving the structural information of the networks, thereby significantly improving the performance of algorithms. Finally, we track the trajectory of cells by exploring the relationships among cell types. Fourteen scRNA-seq datasets are adopted to validate the performance of algorithms with the number of single cells varying from 49 to 26,484. The experimental results demonstrate that SLNMF significantly outperforms fifteen state-of-the-art methods with 15.32% improvement in terms of accuracy, and it accurately identifies the trajectories of cells. The proposed model and methods provide an effective strategy to analyze scRNA-seq data. (The software is coded using matlab, and is freely available for academic https://github.com/xkmaxidian/SLNMF).

An algorithm of nonnegative matrix factorization under structure constraints for image clustering

An algorithm of nonnegative matrix factorization under structure constraints for image clustering

Comprehensive analysis of the amino acid metabolism-related gene signature for prognosis, tumor immune microenvironment, and candidate drugs in hepatocellular carcinoma.

Metabolic rewiring satisfies increased nutritional demands and modulates many oncogenic processes in tumors. Amino acid metabolism is abnormal in many malignancies. Metabolic reprogramming of amino acids not only plays a crucial role in sustaining tumor cell proliferation but also influences the tumor immune microenvironment. Herein, the aim of our study was to elucidate the metabolic signature of amino acids in hepatocellular carcinoma (HCC). Transcriptome profiles of HCC were obtained from the TCGA and ICGC databases. Based on the expression of amino acid metabolism-related genes (AAMRGs), we clustered the HCC samples into two molecular subtypes using the non-negative matrix factorization algorithm. Then, we constructed the amino acid metabolism-related gene signature (AAMRGS) by Cox regression and LASSO regression. Afterward, the clinical significance of the AAMRGS was evaluated. Additionally, we comprehensively analyzed the differences in mutational profiles, immune cell infiltration, immune checkpoint expression, and drug sensitivity between different risk subgroups. Furthermore, we examined three key gene expressions in liver cancer cells by quantitative real-time PCR and conducted the CCK8 assay to evaluate the influence of two chemotherapy drugs on different liver cancer cells. A total of 81 differentially expressed AAMRGs were screened between the two molecular subtypes, and these AAMRGs were involved in regulating amino acid metabolism. The AAMRGS containing GLS, IYD, and NQO1 had a high value for prognosis prediction in HCC patients. Besides this, the two AAMRGS subgroups had different genetic mutation probabilities. More importantly, the immunosuppressive cells were more enriched in the AAMRGS-high group. The expression level of inhibitory immune checkpoints was also higher in patients with high AAMRGS scores. Additionally, the two AAMRGS subgroups showed different susceptibility to chemotherapeutic and targeted drugs. In vitro experiments showed that gemcitabine significantly reduced the proliferative capacity of SNU449 cells, and rapamycin remarkedly inhibited Huh7 proliferation. The five HCC cells displayed different mRNA expression levels of GLS, IYD, and NQO1. Our study explored the features of amino acid metabolism in HCC and identified the novel AAMRGS to predict the prognosis, immune microenvironment, and drug sensitivity of HCC patients. These findings might help to guide personalized treatment and improve the clinical outcomes of HCC.

A prognostic signature based on adenosine metabolism related genes for ovarian cancer.

Ovarian cancer is one of the most common cause of cancer death in women due to its late diagnosis and susceptibility to drug resistance. Adenosine (ADO) signaling plays a key role in immune activity and tumor progression. In this study, we constructed a signature of ADO metabolism related genes expression in patients with ovarian cancer. A total of 372 ovarian cancer patients from TCGA was used as training set and 1,137 patients from six GEO datasets were as validation set. The gene expression and drug response inhibitory concentration values for ovarian cancer cell line from GDSC were used for drug sensitivity analysis. The non-negative matrix factorization algorithm and ssGSVA were used to construct the ADO score. Patients with high ADO score had shorter overall survival (OS) than those with low ADO score in both training set (HR = 1.42, 95% CI, 1.06-1.88) and validation sets (pooled HR = 1.24, 95% CI = 1.02-1.51). In GSEA analysis, genes in ATP synthesis related pathways were enriched in the low ADO score group (adjusted P value = 0.02). Further, we observed that the high ADO score group had significantly higher levels of most cancer hallmark signatures (all adjusted P values < 0.01) and T cell dysfunction and exclusion signatures than the low ADO score group (all adjusted P values < 0.001). Patients with lower ADO score tended to be sensitive to common drugs including Olaparib and Paclitaxel (adjusted P values = 0.05 and 0.04, respectively). In conclusion, the established ADO signature could be used as a prognostic biomarker to stratify ovarian cancer patients and had the potential to guide the drug exploitation and personalized therapy selection.

A system for biomedical audio signal processing based on high performance computing techniques

In this paper, a noninvasive portable prototype is presented for biomedical audio signal processing. The proposed prototype is suitable for monitoring the health of patients. The proposed hardware setup consists of a cost-effective microphone, multipurpose microcontroller and computing node that could be a mobile phone or general-purpose computer. Using parallel and high-performance techniques, this setup allows one to register and wirelessly multicast the recorded biomedical signals to computing nodes in real time. The developed prototype was used as a case study to estimate the heart rate (HR) from the captured biomedical audio signal. In this regard, the developed algorithm for estimating HR comprises three stages: preprocessing, separation, and HR estimation. In the first stage, the signal captured by the microphone is adapted for processing. Subsequently, a separation stage was proposed to alleviate the acoustic interference between the lungs and heart. The separation is performed by combining a non-negative matrix factorization algorithm, clustering approach, and soft-filter strategy. Finally, HR estimation was obtained using a novel and efficient method based on the autocorrelation function. The developed prototype could be used not only for the estimation of the HR, but also for the retrieval of other biomedical information related to the recording of cardiac or respiratory audio signals. The proposed method was evaluated using well-known datasets and compared with state-of-the-art algorithms for source-separation. The results showed that it is possible to obtain an accurate separation and reliable real-time estimation in terms of source separation metrics and relative error in the tested scenarios by combining multi-core architectures with parallel and high-performance techniques. Finally, the proposed prototype was validated in a real-world scenario.

Identification of subtypes of hepatocellular carcinoma and screening of prognostic molecular diagnostic markers based on cell adhesion molecule related genes.

Cell adhesion molecules can predict liver hepatocellular carcinoma (LIHC) metastasis and determine prognosis, while the mechanism of the role of cell adhesion molecules in LIHC needs to be further explored. LIHC-related expression data were sourced from The Cancer Genome Atlas (TCGA) and the gene expression omnibus (GEO) databases, and genes related to cell adhesion were sourced from the Kyoto Encyclopedia of Genes and Genomes (KEGG) database. First, the TCGA-LIHC dataset was clustered by the nonnegative matrix factorization (NMF) algorithm to find different subtypes of LIHC. Then the difference of prognosis and immune microenvironment between patients of different subtypes was evaluated. In addition, a prognostic risk model was obtained by least shrinkage and selection operator (LASSO) and Cox analysis, while a nomogram was drawn. Furthermore, functional enrichment analysis between high and low risk groups was conducted. Finally, the expressions of model genes were explored by quantitative real-time polymerase chain reaction (qRT-PCR). The 371 LIHC patients were classified into four subtypes by NMF clustering, and survival analysis revealed that disease-free survival (DFS) of these four subtypes were clearly different. Cancer-related pathways and immune microenvironment among these four subtypes were dysregulated. Moreover, 58 common differentially expressed genes (DEGs) between four subtypes were identified and were mainly associated with PPAR signaling pathway and amino acid metabolism. Furthermore, a prognostic model consisting of IGSF11, CD8A, ALCAM, CLDN6, JAM2, ITGB7, SDC3, CNTNAP1, and MPZ was built. A nomogram consisting of pathologic T and riskScore was built, and the calibration curve illustrated that the nomogram could better forecast LIHC prognosis. Gene Set Enrichment Analysis (GSEA) demonstrated that DEGs between high and low risk groups were mainly involved in cell cycle. Finally, the qRT-PCR illustrated the expressions of nine model genes between normal and LIHC tissue. A prognostic model consisting of IGSF11, CD8A, ALCAM, CLDN6, JAM2, ITGB7, SDC3, CNTNAP1, and MPZ was obtained, which provides an important reference for the molecular diagnosis of patient prognosis.

A Novel Prognostic Model for Acute Myeloid Leukemia Based on Gene Set Variation Analysis.

Acute myeloid leukemia (AML) is a malignant hematological malignancy with a poor prognosis. Risk stratification of patients with AML is mainly based on the characteristics of cytogenetics and molecular genetics; however, patients with favorable genetics may have a poor prognosis. Here, we focused on the activity changes of immunologic and hallmark gene sets in the AML population. Based on the enrichment score of gene sets by gene set variation analysis (GSVA), we identified three AML subtypes by the nonnegative matrix factorization (NMF) algorithm in the TCGA cohort. AML patients in subgroup 1 had worse overall survival (OS) than subgroups 2 and 3 (P < 0.001). The median overall survival (mOS) of subgroups 1-3 was 0.4, 2.2, and 1.7 years, respectively. Clinical characteristics, including age and FAB classification, were significantly different among each subgroup. Using the least absolute shrinkage and selection operator (LASSO) regression method, we discovered three prognostic gene sets and established the final prognostic model based on them. Patients in the high-risk group had significantly shorter OS than those in the low-risk group in the TCGA cohort (P < 0.001) with mOS of 2.2 and 0.7 years in the low- and high-risk groups, respectively. The results were further validated in the GSE146173 and GSE12417 cohorts. We further identified the key genes of prognostic gene sets using a protein-protein interaction network. In conclusion, the study established and validated a novel prognostic model for risk stratification in AML, which provides a new perspective for accurate prognosis assessment.

Matrix-wise $$\ell _0$$-constrained sparse nonnegative least squares

Nonnegative least squares problems with multiple right-hand sides (MNNLS) arise in models that rely on additive linear combinations. In particular, they are at the core of most nonnegative matrix factorization algorithms and have many applications. The nonnegativity constraint is known to naturally favor sparsity, that is, solutions with few non-zero entries. However, it is often useful to further enhance this sparsity, as it improves the interpretability of the results and helps reducing noise, which leads to the sparse MNNLS problem. In this paper, as opposed to most previous works that enforce sparsity column- or row-wise, we first introduce a novel formulation for sparse MNNLS, with a matrix-wise sparsity constraint. Then, we present a two-step algorithm to tackle this problem. The first step divides sparse MNNLS in subproblems, one per column of the original problem. It then uses different algorithms to produce, either exactly or approximately, a Pareto front for each subproblem, that is, to produce a set of solutions representing different tradeoffs between reconstruction error and sparsity. The second step selects solutions among these Pareto fronts in order to build a sparsity-constrained matrix that minimizes the reconstruction error. We perform experiments on facial and hyperspectral images, and we show that our proposed two-step approach provides more accurate results than state-of-the-art sparse coding heuristics applied both column-wise and globally.

SOJNMF: Identifying Multidimensional Molecular Regulatory Modules by Sparse Orthogonality-Regularized Joint Non-Negative Matrix Factorization Algorithm.

Cancer is not only a very aggressive but also a very diverse disease. Recent advances in high-throughput omics technologies of cancer have enabled biomedical researchers to have more opportunities for studying its multi-level biological regulatory mechanism. However, there are few methods to explore the underlying mechanism of cancer by identifying its multidimensional molecular regulatory modules from the multidimensional omics data of cancer. In this paper, we propose a sparse orthogonality-regularized joint non-negative matrix factorization (SOJNMF) algorithm which can integratively analyze multidimensional omics data. This method can not only identify multidimensional molecular regulatory modules, but reduce the overlap rate of features among the multidimensional modules while ensuring the sparsity of the coefficient matrix after decomposition. Gene expression data, miRNA expression data and gene methylation data of liver cancer are integratively analyzed based on SOJNMF algorithm. Then, we obtain 238 multidimensional molecular regulatory modules. The results of permutation test indicate that different omics features within these modules are significantly correlated in statistics. Meanwhile, the results of functional enrichment analysis show that these multidimensional modules are significantly related to the underlying mechanism of the occurrence and development of liver cancer.

The involvement of high succinylation modification in the development of prostate cancer.

Succinylation modification of the lysine site plays an important role in tumorigenesis and development, but it is rarely reported in prostate cancer (PCa), so this study aims to elucidate its expression in and clinical correlation with PCa. A total of 95 tumor, 3 normal and 52 paired adjacent tissue of PCa were involved for succinylation stanning. 498 PCa samples with 20 succinylation modification-related genes from TCGA were downloaded for model construction. Statistical methods were employed to analyze the data, including Non-Negative Matrix Factorization (NMF) algorithm, t-Distributed Stochastic Neighbor Embedding (t-SNE) algorithm and Cox regression analysis. The pan-succinyllysine antibody stanning indicated that tumor tissues showed higher succinyllysine level than adjacent tissues (p<0.001). Gleason grade and PDL1 expression levels were significantly different (p<0.001) among the high, medium and low succinylation staining scores. The types of PCa tissue were divided into four clusters using RNA-seq data of 20 succinylation-related genes in TCGA database. Clinical characterize of age, PSA level, and pathological stage showed differences among four clusters. The expression of succinylation-related genes (KAT5, SDHD and GLYATL1) and PCa related genes (PDL1, AR and TP53) were significantly different in 52 matched tumor and adjacent tissues (p<0.001). GLYATL1 and AR gene expression was significantly related to the pathological stage of PCa. Succinylation was significantly increased in PCa tissues and was closely related to Gleason grade and PD-L1 expression. Model construction of 20 genes related to succinylation modification showed that the later the pathological stage of PCa, the higher the level of succinylation modification.