Non-negative Matrix Factorization Algorithm Research Articles

Construction of an interferon regulatory factors-related risk model for predicting prognosis, immune microenvironment and immunotherapy in clear cell renal cell carcinoma.

Interferon regulatory factors (IRFs) played complex and essential roles in progression, prognosis, and immune microenvironment in clear cell renal cell carcinoma (ccRCC). The purpose of this study was to construct a novel IRFs-related risk model to predict prognosis, tumor microenvironment (TME) and immunotherapy response in ccRCC. Multi-omics analysis of IRFs in ccRCC was performed based on bulk RNA sequencing and single cell RNA sequencing data. According to the expression profiles of IRFs, the ccRCC samples were clustered by non-negative matrix factorization (NMF) algorithm. Then, least absolute shrinkage and selection operator (LASSO) and Cox regression analyses were applied to construct a risk model to predict prognosis, immune cells infiltration, immunotherapy response and targeted drug sensitivity in ccRCC. Furthermore, a nomogram comprising the risk model and clinical characteristics was established. Two molecular subtypes with different prognosis, clinical characteristics and infiltration levels of immune cells were identified in ccRCC. The IRFs-related risk model was developed as an independent prognostic indicator in the TCGA-KIRC cohort and validated in the E-MTAB-1980 cohort. The overall survival of patients in the low-risk group was better than that in the high-risk group. The risk model was superior to clinical characteristics and the ClearCode34 model in predicting the prognosis. In addition, a nomogram was developed to improve the clinical utility of the risk model. Moreover, the high-risk group had higher infiltration levels of CD8+ T cell, macrophages, T follicular helper cells and T helper (Th1) cells and activity score of type I IFN response but lower infiltration levels of mast cells and activity score of type II IFN response. Cancer immunity cycle showed that the immune activity score of most steps was remarkably higher in the high-risk group. TIDE scores indicated that patients in the low-risk group were more likely responsive to immunotherapy. Patients in different risk groups showed diverse drug sensitivity to axitinib, sorafenib, gefitinib, erlotinib, dasatinib and rapamycin. In brief, a robust and effective risk model was developed to predict prognosis, TME characteristics and responses to immunotherapy and targeted drugs in ccRCC, which might provide new insights into personalized and precise therapeutic strategies.

Conic optimization-based algorithms for nonnegative matrix factorization

Nonnegative matrix factorization is the following problem: given a nonnegative input matrix V and a factorization rank K, compute two nonnegative matrices, W with K columns and H with K rows, such that WH approximates V as well as possible. In this paper, we propose two new approaches for computing high-quality NMF solutions using conic optimization. These approaches rely on the same two steps. First, we reformulate NMF as minimizing a concave function over a product of convex cones – one approach is based on the exponential cone and the other on the second-order cone. Then, we solve these reformulations iteratively: at each step, we minimize exactly, over the feasible set, a majorization of the objective functions obtained via linearization at the current iterate. Hence these subproblems are convex conic programs and can be solved efficiently using dedicated algorithms. We prove that our approaches reach a stationary point with an accuracy decreasing as , where i denotes the iteration number. To the best of our knowledge, our analysis is the first to provide a convergence rate to stationary points for NMF. Furthermore, in the particular cases of rank-1 factorizations (i.e. K = 1), we show that one of our formulations can be expressed as a convex optimization problem, implying that optimal rank-1 approximations can be computed efficiently. Finally, we show on several numerical examples that our approaches are able to frequently compute exact NMFs (i.e. with V = WH) and compete favourably with the state of the art.

Fragmentation landscape of cell-free DNA revealed by deconvolutional analysis of end motifs

Cell-free DNA (cfDNA) fragmentation is nonrandom, at least partially mediated by various DNA nucleases, forming characteristic cfDNA end motifs. However, there is a paucity of tools for deciphering the relative contributions of cfDNA cleavage patterns related to underlying fragmentation factors. In this study, through non-negative matrix factorization algorithm, we used 256 5' 4-mer end motifs to identify distinct types of cfDNA cleavage patterns, referred to as "founder" end-motif profiles (F-profiles). F-profiles were associated with different DNA nucleases based on whether such patterns were disrupted in nuclease-knockout mouse models. Contributions of individual F-profiles in a cfDNA sample could be determined by deconvolutional analysis. We analyzed 93 murine cfDNA samples of different nuclease-deficient mice and identified six types of F-profiles. F-profiles I, II, and III were linked to deoxyribonuclease 1 like 3 (DNASE1L3), deoxyribonuclease 1 (DNASE1), and DNA fragmentation factor subunit beta (DFFB), respectively. We revealed that 42.9% of plasma cfDNA molecules were attributed to DNASE1L3-mediated fragmentation, whereas 43.4% of urinary cfDNA molecules involved DNASE1-mediated fragmentation. We further demonstrated that the relative contributions of F-profiles were useful to inform pathological states, such as autoimmune disorders and cancer. Among the six F-profiles, the use of F-profile I could inform the human patients with systemic lupus erythematosus. F-profile VI could be used to detect individuals with hepatocellular carcinoma, with an area under the receiver operating characteristic curve of 0.97. F-profile VI was more prominent in patients with nasopharyngeal carcinoma undergoing chemoradiotherapy. We proposed that this profile might be related to oxidative stress.

Measuring the Effect of Vision on the Synergy of Lower Extremity Muscles during Walking using Nonnegative Matrix Factorization (NNMF) Algorithm Method.

Lack of visual information in blind people during walking can affect the choice of muscle synergy from among the many incoming messages that reach the central nervous system (CNS). This study aimed to determine the effect of vision on the synergy of lower limb muscles during walking using the nonnegative matrix factorization algorithm (NNMF). Ten blind people and 10 people with normal vision participated in this study. Activities of involved muscles were recorded during walking. Muscle synergy matrix and synergy activation coefficient were calculated using the NNMF algorithm, while the variance accounted for criterion was used to determine the number of synergies required during walking. In order to assess the similarity of muscle synergy pattern and the relative weight of each muscle in each synergy in each group, Pearson correlation and independent samples t-test at a significance level of α ≤ 0.05 were used. Four muscle synergies were extracted from EMG data during walking. The first (r = 0.431) and the second (r = 0.457) synergy patterns showed a moderate correlation between the two groups. However, the third (r = 0.302) and the fourth (r = 0.329) synergy patterns showed a weak correlation between the two groups. In the blind group, the relative weight of the muscles in the first synergy was significant for the external extensor muscle (P = 0.023), and in the second synergy for the biceps femoris. Also, in the third synergy, the relative weight was found to be significant in none of the muscles. In the fourth synergy, however, the relative weight of external extensor muscle in the blind group showed a significant decrease, as compared to the group with normal vision. These changes can be the strategy of the CNS to preserve the optimal functioning in the motor system of blind people.

Continuous Estimation of the Lower-Limb Multi-Joint Angles Based on Muscle Synergy Theory and State-Space Model

Continuous joint angle estimation is essential for enhancing man-machine collaboration performance. However, it is challenging to estimate the complex multi-joint angle of the lower limb accurately. Firstly, a non-redundant feature extraction algorithm for muscle synergy was proposed. The non-negative matrix factorization (NMF) algorithm was used to extract the muscle activation coefficient matrix, and the muscle activation coefficient matrix was divided into non-redundant and redundant feature vectors. Then, a state-space frame model with non-redundant features as input and redundant features as measurement output to reduce system error was proposed. The square root unscented Kalman filter (SRUKF) algorithm was used to estimate the multi-joint angle of lower limbs. We recruited ten subjects to participate in seven daily activities, including going upstairs (US), downing stairs (DS), going uphill (UH), going downhill (DH), and walking at three speeds of 0.6 m/s, 1.0 m/s, and 1.4 m/s. The results showed that the average RMSE of the proposed approach for estimating hip and knee joint angles was 0.44±0.1 and 0.73±0.5, respectively, which was significantly smaller than the common neural networks (p<0.05). Particularly, the anti-interference performance of the proposed model was tested. Meanwhile, the adaptability test was carried out through the developed lower-limb multi-joint angle estimation verification system, which proved that the proposed approach could provide accurate and stable estimation results by making full use of redundant features. It can improve the safety of online applications for sEMG auxiliary equipment.

Study subnetwork developing pattern of autism children by non-negative matrix factorization

Background:As a developmental disorder, the brain networks of autism children show abnormal patterns compared with that of typically developing. The differences between them are not stable due to the developing progress of children. It has become a choice to study the differences of developing trajectories between autistic and typically developing children by investigating the change of each group respectively. Related researches studied the developing of brain network by analyzing the relationship between network indices of the entire or sub brain networks and the cognitive developing scores. Methods:As a matrix decomposition algorithm, non-negative matrix factorization (NMF) was applied to decompose the association matrices of brain networks. By NMF, we can obtain subnetworks in an unsupervised way. The association matrices of autism and control children were estimated by their magnetoencephalography data. NMF was applied to decompose the matrices to obtain common subnetworks of both groups. Then we calculated the expression of each subnetwork in each child’s brain network by two indices, energy and entropy. The relationship between the expression and the cognitive and development indices were investigated. Results:We found a subnetwork with left lateralization pattern in α band showed different expression tendency in two groups. The expression indices of two groups were correlated with cognitive indices in autism and control group in an opposite way. In γ band, a subnetwork with strong connections on right hemisphere of brain showed a negative correlation between the expression indices and development indices in autism group. Conclusion:NMF algorithm can effectively decompose brain network to meaningful subnetworks. The finding of α band subnetworks confirms the results of abnormal lateralization of autistic children mentioned in relevant studies. We assume the results of decrease of expression of the subnetwork may relate to the dysfunction of mirror neuron. The decrease expression of γ subnetwork of autism may be related to the weaken process of high-frequency neurons in the neurotrophic competition.

Robust dual-graph discriminative NMF for data classification

In this paper, we propose a new supervised non-negative matrix factorization algorithm, named Robust Dual-graph Discriminative Non-negative Matrix Factorization (RDGDNMF). This model not only considers the differentiability between data samples, but also explores the intrinsic geometric structure information of data and feature space simultaneously, so it can obtain a more effective low-dimensional representation. Considering that the real data usually contains noise and outliers, we adopt ℓ2,12 norm to minimize the loss function of Non-negative Matrix Factorization (NMF) to improve the robustness of the algorithm. In addition, we also give the multiplication update rules and prove the convergence of the algorithm. Then, we use this model and K-Nearest Neighbor (KNN) to reduce dimension and classify data. By comparing the classification results with other advanced methods on multiple datasets, the effectiveness and robustness of the proposed method are demonstrated.

Single-cell and bulk RNA sequencing identifies T cell marker genes score to predict the prognosis of pancreatic ductal adenocarcinoma

Pancreatic ductal adenocarcinoma (PDAC) is one of the lethal malignancies, with limited biomarkers identified to predict its prognosis and treatment response of immune checkpoint blockade (ICB). This study aimed to explore the predictive ability of T cell marker genes score (TMGS) to predict their overall survival (OS) and treatment response to ICB by integrating single-cell RNA sequencing (scRNA-seq) and bulk RNA-seq data. Multi-omics data of PDAC were applied in this study. The uniform manifold approximation and projection (UMAP) was utilized for dimensionality reduction and cluster identification. The non-negative matrix factorization (NMF) algorithm was applied to molecular subtypes clustering. The Least Absolute Shrinkage and Selection Operator (LASSO)-Cox regression was adopted for TMGS construction. The prognosis, biological characteristics, mutation profile, and immune function status between different groups were compared. Two molecular subtypes were identified via NMF: proliferative PDAC (C1) and immune PDAC (C2). Distinct prognoses and biological characteristics were observed between them. TMGS was developed based on 10 T cell marker genes (TMGs) through LASSO-Cox regression. TMGS is an independent prognostic factor of OS in PDAC. Enrichment analysis indicated that cell cycle and cell proliferation-related pathways are significantly enriched in the high-TMGS group. Besides, high-TMGS is related to more frequent KRAS, TP53, and CDKN2A germline mutations than the low-TMGS group. Furthermore, high-TMGS is significantly associated with attenuated antitumor immunity and reduced immune cell infiltration compared to the low-TMGS group. However, high TMGS is correlated to higher tumor mutation burden (TMB), a low expression level of inhibitory immune checkpoint molecules, and a low immune dysfunction score, thus having a higher ICB response rate. On the contrary, low TMGS is related to a favorable response rate to chemotherapeutic agents and targeted therapy. By combining scRNA-seq and bulk RNA-seq data, we identified a novel biomarker, TMGS, which has remarkable performance in predicting the prognosis and guiding the treatment pattern for patients with PDAC.

Single-cell dissection reveals the role of DNA damage response patterns in tumor microenvironment components contributing to colorectal cancer progression and immunotherapy.

Colorectal cancer (CRC) is one of the leading malignant cancers. DNA damage response (DDR), referring to the molecular process of DNA damage, is emerging as a promising field in targeted cancer therapy. However, the engagement of DDR in the remodeling of the tumor microenvironment is rarely studied. In this study, by sequential nonnegative matrix factorization (NMF) algorithm, pseudotime analysis, cell-cell interaction analysis, and SCENIC analysis, we have shown that DDR genes demonstrate various patterns among different cell types in CRC TME (tumor microenvironment), especially in epithelial cells, cancer-associated fibroblasts, CD8+ T cells, tumor-associated macrophages, which enhance the intensity of intercellular communication and transcription factor activation. Furthermore, based on the newly identified DDR-related TME signatures, cell subtypes including MNAT+CD8+T_cells-C5, POLR2E+Mac-C10, HMGB2+Epi-C4, HMGB1+Mac-C11, PER1+Mac-C5, PER1+CD8+T_cells-C1, POLR2A+Mac-C1, TDG+Epi-C5, TDG+CD8+T_cells-C8 are determined as critical prognostic factors for CRC patients and predictors of immune checkpoint blockade (ICB) therapy efficacy in two public CRC cohorts, TCGA-COAD and GSE39582. Our novel and systematic analysis on the level of the single-cell analysis has revealed the unique role of DDR in remodeling CRC TME for the first time, facilitating the prediction of prognosis and guidance of personalized ICB regimens in CRC.

Identification of the mitophagy-related diagnostic biomarkers in hepatocellular carcinoma based on machine learning algorithm and construction of prognostic model.

As a result of increasing numbers of studies most recently, mitophagy plays a vital function in the genesis of cancer. However, research on the predictive potential and clinical importance of mitophagy-related genes (MRGs) in hepatocellular carcinoma (HCC) is currently lacking. This study aimed to uncover and analyze the mitophagy-related diagnostic biomarkers in HCC using machine learning (ML), as well as to investigate its biological role, immune infiltration, and clinical significance. In our research, by using Least absolute shrinkage and selection operator (LASSO) regression and support vector machine- (SVM-) recursive feature elimination (RFE) algorithm, six mitophagy genes (ATG12, CSNK2B, MTERF3, TOMM20, TOMM22, and TOMM40) were identified from twenty-nine mitophagy genes, next, the algorithm of non-negative matrix factorization (NMF) was used to separate the HCC patients into cluster A and B based on the six mitophagy genes. And there was evidence from multi-analysis that cluster A and B were associated with tumor immune microenvironment (TIME), clinicopathological features, and prognosis. After then, based on the DEGs (differentially expressed genes) between cluster A and cluster B, the prognostic model (riskScore) of mitophagy was constructed, including ten mitophagy-related genes (G6PD, KIF20A, SLC1A5, TPX2, ANXA10, TRNP1, ADH4, CYP2C9, CFHR3, and SPP1). This study uncovered and analyzed the mitophagy-related diagnostic biomarkers in HCC using machine learning (ML), as well as to investigate its biological role, immune infiltration, and clinical significance. Based on the mitophagy-related diagnostic biomarkers, we constructed a prognostic model(riskScore). Furthermore, we discovered that the riskScore was associated with somatic mutation, TIME, chemotherapy efficacy, TACE and immunotherapy effectiveness in HCC patients. Mitophagy may play an important role in the development of HCC, and further research on this issue is necessary. Furthermore, the riskScore performed well as a standalone prognostic marker in terms of accuracy and stability. It can provide some guidance for the diagnosis and treatment of HCC patients.

An algorithm of non-negative matrix factorization with the nearest neighbor after per-treatments

An algorithm of non-negative matrix factorization with the nearest neighbor after per-treatments

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 &lt; 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.