Deep multiple non-negative matrix factorization for multi-view clustering

2021 ◽  
Vol 25 (2) ◽  
pp. 339-357
Author(s):  
Guowang Du ◽  
Lihua Zhou ◽  
Kevin Lü ◽  
Haiyan Ding
Keyword(s):  
Matrix Factorization ◽  
Superior Performance ◽  
Dimensional Representation ◽  
Geometric Information ◽  
Heterogeneous Information ◽  
Benchmark Datasets ◽  
Abstract Level ◽  
Low Dimensional ◽  
Shallow Structure ◽  
Non Negative Matrix Factorization

Multi-view clustering aims to group similar samples into the same clusters and dissimilar samples into different clusters by integrating heterogeneous information from multi-view data. Non-negative matrix factorization (NMF) has been widely applied to multi-view clustering owing to its interpretability. However, most NMF-based algorithms only factorize multi-view data based on the shallow structure, neglecting complex hierarchical and heterogeneous information in multi-view data. In this paper, we propose a deep multiple non-negative matrix factorization (DMNMF) framework based on AutoEncoder for multi-view clustering. DMNMF consists of multiple Encoder Components and Decoder Components with deep structures. Each pair of Encoder Component and Decoder Component are used to hierarchically factorize the input data from a view for capturing the hierarchical information, and all Encoder and Decoder Components are integrated into an abstract level to learn a common low-dimensional representation for combining the heterogeneous information across multi-view data. Furthermore, graph regularizers are also introduced to preserve the local geometric information of each view. To optimize the proposed framework, an iterative updating scheme is developed. Besides, the corresponding algorithm called MVC-DMNMF is also proposed and implemented. Extensive experiments on six benchmark datasets have been conducted, and the experimental results demonstrate the superior performance of our proposed MVC-DMNMF for multi-view clustering compared to other baseline algorithms.

A zero-inflated non-negative matrix factorization for the deconvolution of mixed signals of biological data

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yixin Kong ◽  
Ariangela Kozik ◽  
Cindy H. Nakatsu ◽  
Yava L. Jones-Hall ◽  
Hyonho Chun
Keyword(s):  
Matrix Factorization ◽  
Factor Model ◽  
R Package ◽  
Biological Data ◽  
Superior Performance ◽  
Sequencing Data ◽  
Fecal Microbiome ◽  
Brain Gene Expression ◽  
Cell Transcriptome ◽  
Non Negative Matrix Factorization

Abstract A latent factor model for count data is popularly applied in deconvoluting mixed signals in biological data as exemplified by sequencing data for transcriptome or microbiome studies. Due to the availability of pure samples such as single-cell transcriptome data, the accuracy of the estimates could be much improved. However, the advantage quickly disappears in the presence of excessive zeros. To correctly account for this phenomenon in both mixed and pure samples, we propose a zero-inflated non-negative matrix factorization and derive an effective multiplicative parameter updating rule. In simulation studies, our method yielded the smallest bias. We applied our approach to brain gene expression as well as fecal microbiome datasets, illustrating the superior performance of the approach. Our method is implemented as a publicly available R-package, iNMF.

scholarly journals Recent Advances in Supervised Dimension Reduction: A Survey

2019 ◽  
Vol 1 (1) ◽  
pp. 341-358 ◽  
Author(s):  
Guoqing Chao ◽  
Yuan Luo ◽  
Weiping Ding
Keyword(s):  
Dimension Reduction ◽  
Dimensional Representation ◽  
Open Problems ◽  
Advantages And Disadvantages ◽  
Reduction Problem ◽  
Reduction Methods ◽  
Low Dimensional ◽  
Supervised Dimension Reduction ◽  
Effective Representation ◽  
Non Negative Matrix Factorization

Recently, we have witnessed an explosive growth in both the quantity and dimension of data generated, which aggravates the high dimensionality challenge in tasks such as predictive modeling and decision support. Up to now, a large amount of unsupervised dimension reduction methods have been proposed and studied. However, there is no specific review focusing on the supervised dimension reduction problem. Most studies performed classification or regression after unsupervised dimension reduction methods. However, we recognize the following advantages if learning the low-dimensional representation and the classification/regression model simultaneously: high accuracy and effective representation. Considering classification or regression as being the main goal of dimension reduction, the purpose of this paper is to summarize and organize the current developments in the field into three main classes: PCA-based, Non-negative Matrix Factorization (NMF)-based, and manifold-based supervised dimension reduction methods, as well as provide elaborated discussions on their advantages and disadvantages. Moreover, we outline a dozen open problems that can be further explored to advance the development of this topic.

Community detection enhancement using non-negative matrix factorization with graph regularization

2016 ◽  
Vol 30 (20) ◽  
pp. 1650130 ◽  
Author(s):  
Xiao Liu ◽  
Yi-Ming Wei ◽  
Jian Wang ◽  
Wen-Jun Wang ◽  
Dong-Xiao He ◽  
...  
Keyword(s):  
Community Detection ◽  
Matrix Factorization ◽  
Local Information ◽  
Superior Performance ◽  
Great Effort ◽  
Step Method ◽  
Graph Regularization ◽  
Detection Enhancement ◽  
Global And Local ◽  
Non Negative Matrix Factorization

Community detection is a meaningful task in the analysis of complex networks, which has received great concern in various domains. A plethora of exhaustive studies has made great effort and proposed many methods on community detection. Particularly, a kind of attractive one is the two-step method which first makes a preprocessing for the network and then identifies its communities. However, not all types of methods can achieve satisfactory results by using such preprocessing strategy, such as the non-negative matrix factorization (NMF) methods. In this paper, rather than using the above two-step method as most works did, we propose a graph regularized-based model to improve, specialized, the NMF-based methods for the detection of communities, namely NMFGR. In NMFGR, we introduce the similarity metric which contains both the global and local information of networks, to reflect the relationships between two nodes, so as to improve the accuracy of community detection. Experimental results on both artificial and real-world networks demonstrate the superior performance of NMFGR to some competing methods.

A Novel Discriminant Non-Negative Matrix Factorization and its Application to Facial Expression Recognition

2010 ◽  
Vol 143-144 ◽  
pp. 129-133
Author(s):  
Yan Li Zhu ◽  
Jun Chen ◽  
Pei Xin Qu
Keyword(s):  
Facial Expression ◽  
Matrix Factorization ◽  
Facial Expression Recognition ◽  
Expression Recognition ◽  
Discrimination Capability ◽  
Factorization Algorithm ◽  
Factorization Algorithms ◽  
Low Dimensional ◽  
Low Dimensional Features ◽  
Non Negative Matrix Factorization

The paper proposes a novel discriminant non-negative matrix factorization algorithm and applies it to facial expression recognition. Unlike traditional non-negative matrix factorization algorithms, the algorithm adds discriminant constraints in low-dimensional weights. The experiments on facial expression recognition indicate that the algorithm enhances the discrimination capability of low-dimensional features and achieves better performance than other non-negative matrix factorization algorithms.

scholarly journals netNMF-sc: Leveraging gene-gene interactions for imputation and dimensionality reduction in single-cell expression analysis

2019 ◽  
Author(s):  
Rebecca Elyanow ◽  
Bianca Dumitrascu ◽  
Barbara E. Engelhardt ◽  
Benjamin J. Raphael
Keyword(s):  
Single Cell ◽  
Matrix Factorization ◽  
Gene Interactions ◽  
Rna Expression ◽  
Dimensional Representation ◽  
Analysis Methods ◽  
The Matrix ◽  
Low Dimensional ◽  
Cell Expression ◽  
Zero Counts

AbstractMotivationSingle-cell RNA-sequencing (scRNA-seq) enables high throughput measurement of RNA expression in individual cells. Due to technical limitations, scRNA-seq data often contain zero counts for many transcripts in individual cells. These zero counts, or dropout events, complicate the analysis of scRNA-seq data using standard analysis methods developed for bulk RNA-seq data. Current scRNA-seq analysis methods typically overcome dropout by combining information across cells, leveraging the observation that cells generally occupy a small number of RNA expression states.ResultsWe introduce netNMF-sc, an algorithm for scRNA-seq analysis that leverages information across both cells and genes. netNMF-sc combines network-regularized non-negative matrix factorization with a procedure for handling zero inflation in transcript count matrices. The matrix factorization results in a low-dimensional representation of the transcript count matrix, which imputes gene abundance for both zero and non-zero entries and can be used to cluster cells. The network regularization leverages prior knowledge of gene-gene interactions, encouraging pairs of genes with known interactions to be close in the low-dimensional representation. We show that netNMF-sc outperforms existing methods on simulated and real scRNA-seq data, with increasing advantage at higher dropout rates (e.g. above 60%). Furthermore, we show that the results from netNMF-sc – including estimation of gene-gene covariance – are robust to choice of network, with more representative networks leading to greater performance gains.AvailabilitynetNMF-sc is available at github.com/raphael-group/[email protected]

scholarly journals Predicting miRNA-Disease Associations by Incorporating Projections in Low-Dimensional Space and Local Topological Information

Genes ◽  
2019 ◽  
Vol 10 (9) ◽  
pp. 685 ◽  
Author(s):  
Xuan ◽  
Zhang ◽  
Zhang ◽  
Li ◽  
Zhao
Keyword(s):  
Dimensional Space ◽  
Characteristic Curve ◽  
Feature Space ◽  
Superior Performance ◽  
Topological Information ◽  
Heterogeneous Information ◽  
Feature Representations ◽  
Disease Associations ◽  
Precision Recall Curve ◽  
Low Dimensional

Predicting the potential microRNA (miRNA) candidates associated with a disease helps in exploring the mechanisms of disease development. Most recent approaches have utilized heterogeneous information about miRNAs and diseases, including miRNA similarities, disease similarities, and miRNA-disease associations. However, these methods do not utilize the projections of miRNAs and diseases in a low-dimensional space. Thus, it is necessary to develop a method that can utilize the effective information in the low-dimensional space to predict potential disease-related miRNA candidates. We proposed a method based on non-negative matrix factorization, named DMAPred, to predict potential miRNA-disease associations. DMAPred exploits the similarities and associations of diseases and miRNAs, and it integrates local topological information of the miRNA network. The likelihood that a miRNA is associated with a disease also depends on their projections in low-dimensional space. Therefore, we project miRNAs and diseases into low-dimensional feature space to yield their low-dimensional and dense feature representations. Moreover, the sparse characteristic of miRNA-disease associations was introduced to make our predictive model more credible. DMAPred achieved superior performance for 15 well-characterized diseases with AUCs (area under the receiver operating characteristic curve) ranging from 0.860 to 0.973 and AUPRs (area under the precision-recall curve) ranging from 0.118 to 0.761. In addition, case studies on breast, prostatic, and lung neoplasms demonstrated the ability of DMAPred to discover potential disease-related miRNAs.

scholarly journals Efficient Retrieval of Matrix Factorization-Based Top-k Recommendations: A Survey of Recent Approaches

2021 ◽  
Vol 70 ◽  
pp. 1441-1479
Author(s):  
Dung D. Le ◽  
Hady Lauw
Keyword(s):  
Matrix Factorization ◽  
Dimensional Space ◽  
Preference Elicitation ◽  
User Preferences ◽  
Superior Performance ◽  
Recommendation Algorithms ◽  
Efficient Retrieval ◽  
Item Characteristics ◽  
Different Dimensions ◽  
Low Dimensional

Top-k recommendation seeks to deliver a personalized list of k items to each individual user. An established methodology in the literature based on matrix factorization (MF), which usually represents users and items as vectors in low-dimensional space, is an effective approach to recommender systems, thanks to its superior performance in terms of recommendation quality and scalability. A typical matrix factorization recommender system has two main phases: preference elicitation and recommendation retrieval. The former analyzes user-generated data to learn user preferences and item characteristics in the form of latent feature vectors, whereas the latter ranks the candidate items based on the learnt vectors and returns the top-k items from the ranked list. For preference elicitation, there have been numerous works to build accurate MF-based recommendation algorithms that can learn from large datasets. However, for the recommendation retrieval phase, naively scanning a large number of items to identify the few most relevant ones may inhibit truly real-time applications. In this work, we survey recent advances and state-of-the-art approaches in the literature that enable fast and accurate retrieval for MF-based personalized recommendations. Also, we include analytical discussions of approaches along different dimensions to provide the readers with a more comprehensive understanding of the surveyed works.

scholarly journals Convolutional Gaussian Embeddings for Personalized Recommendation with Uncertainty

2019 ◽  
Author(s):  
Junyang Jiang ◽  
Deqing Yang ◽  
Yanghua Xiao ◽  
Chenlu Shen
Keyword(s):  
State Of The Art ◽  
Dimensional Space ◽  
Monte Carlo Sampling ◽  
Superior Performance ◽  
Personalized Recommendation ◽  
Latent Features ◽  
Benchmark Datasets ◽  
Low Dimensional ◽  
Uncertain Preferences ◽  
Candidate Item

Most of existing embedding based recommendation models use embeddings (vectors) to represent users and items which contain latent features of users and items. Each of such embeddings corresponds to a single fixed point in low-dimensional space, thus fails to precisely represent the users/items with uncertainty which are often observed in recommender systems. Addressing this problem, we propose a unified deep recommendation framework employing Gaussian embeddings, which are proven adaptive to uncertain preferences exhibited by some users, resulting in better user representations and recommendation performance. Furthermore, our framework adopts Monte-Carlo sampling and convolutional neural networks to compute the correlation between the objective user and the candidate item, based on which precise recommendations are achieved. Our extensive experiments on two benchmark datasets not only justify that our proposed Gaussian embeddings capture the uncertainty of users very well, but also demonstrate its superior performance over the state-of-the-art recommendation models.

scholarly journals The Effect of ICA and Non-negative Matrix Factorization Analysis for EMG Signals Recorded From Multi-Channel EMG Sensors

2020 ◽  
Vol 14 ◽  
Author(s):  
Yeongdae Kim ◽  
Sorawit Stapornchaisit ◽  
Makoto Miyakoshi ◽  
Natsue Yoshimura ◽  
Yasuharu Koike
Keyword(s):  
Matrix Factorization ◽  
Decomposition Method ◽  
Index Finger ◽  
Power Source ◽  
Classification Performance ◽  
Emg Signal ◽  
Movement Artifacts ◽  
Low Dimensional ◽  
Sensor Positions ◽  
Non Negative Matrix Factorization

Surface electromyography (EMG) measurements are affected by various noises such as power source and movement artifacts and adjacent muscle activities. Hardware solutions have been found that use multi-channel EMG signal to attenuate noise signals related to sensor positions. However, studies addressing the overcoming of crosstalk from EMG and the division of overlaid superficial and deep muscles are scarce. In this study, two signal decompositions—independent component analysis and non-negative matrix factorization—were used to create a low-dimensional input signal that divides noise, surface muscles, and deep muscles and utilizes them for movement classification based on direction. In the case of index finger movement, it was confirmed that the proposed decomposition method improved the classification performance with the least input dimensions. These results suggest a new method to analyze more dexterous movements of the hand by separating superficial and deep muscles in the future using multi-channel EMG signals.

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