scholarly journals A Review on Initialization Methods for Nonnegative Matrix Factorization: Towards Omics Data Experiments

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1006
Author(s):  
Flavia Esposito
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Biological Information ◽  
Relevant Role ◽  
Initialization Scheme ◽  
The Cost ◽  
The Impact ◽  
Omic Data

Nonnegative Matrix Factorization (NMF) has acquired a relevant role in the panorama of knowledge extraction, thanks to the peculiarity that non-negativity applies to both bases and weights, which allows meaningful interpretations and is consistent with the natural human part-based learning process. Nevertheless, most NMF algorithms are iterative, so initialization methods affect convergence behaviour, the quality of the final solution, and NMF performance in terms of the residual of the cost function. Studies on the impact of NMF initialization techniques have been conducted for text or image datasets, but very few considerations can be found in the literature when biological datasets are studied, even though NMFs have largely demonstrated their usefulness in better understanding biological mechanisms with omic datasets. This paper aims to present the state-of-the-art on NMF initialization schemes along with some initial considerations on the impact of initialization methods when microarrays (a simple instance of omic data) are evaluated with NMF mechanisms. Using a series of measures to qualitatively examine the biological information extracted by a given NMF scheme, it preliminary appears that some information (e.g., represented by genes) can be extracted regardless of the initialization scheme used.

scholarly journals Comparison of Initialization Techniques for the Accurate Extraction of Muscle Synergies from Myoelectric Signals via Nonnegative Matrix Factorization

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Mumtaz Hussain Soomro ◽  
Silvia Conforto ◽  
Gaetano Giunta ◽  
Simone Ranaldi ◽  
Cristiano De Marchis
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Simulated Data ◽  
Surface Emg ◽  
Muscle Synergies ◽  
Accurate Identification ◽  
Experimental Surface ◽  
Factorization Algorithms

The main goal of this work was to assess the performance of different initializations of matrix factorization algorithms for an accurate identification of muscle synergies. Currently, nonnegative matrix factorization (NNMF) is the most commonly used method to identify muscle synergies. However, it has been shown that NNMF performance might be affected by different kinds of initialization. The present study aims at optimizing the traditional NNMF initialization for data with partial or complete temporal dependencies. For this purpose, three different initializations are used: random, SVD-based, and sparse. NNMF was used to identify muscle synergies from simulated data as well as from experimental surface EMG signals. Simulated data were generated from synthetic independent and dependent synergy vectors (i.e., shared muscle components), whose activation coefficients were corrupted by simulating controlled degrees of correlation. Similarly, EMG data were artificially modified, making the extracted activation coefficients temporally dependent. By measuring the quality of identification of the original synergies underlying the data, it was possible to compare the performance of different initialization techniques. Simulation results demonstrate that sparse initialization performs significantly better than all other kinds of initialization in reconstructing muscle synergies, regardless of the correlation level in the data.

Optimizing modularity with nonnegative matrix factorization

2021 ◽  
pp. 2150142
Author(s):  
Zhenhai Chang ◽  
Zhong-Yuan Zhang ◽  
Huimin Cheng ◽  
Chao Yan ◽  
Xianjun Yin
Keyword(s):  
Community Structure ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Frobenius Norm ◽  
Structure Detection ◽  
Clustering Quality ◽  
Modularity Maximization ◽  
And Function

Community structure detection is one of the fundamental problems in complex network analysis towards understanding the topology structure and function of the network. Modularity is a criterion to evaluate the quality of community structures, and optimization of this quality function over the possible divisions of a network is a sensitive detection method for community structure. However, the direct application of this method is computationally costly. Nonnegative matrix factorization (NMF) is a widely used method for community detection. In this paper, we show that modularity maximization can be approximately reformulated under the framework of NMF with Frobenius norm, especially when [Formula: see text] is large. A new algorithm for detecting community structure is proposed based on the above finding. The new method is compared with four state-of-the-art methods on both synthetic and real-world networks, showing its higher clustering quality over the existing methods.

Local Smoothness Constrained Nonnegative Matrix Factorization with Nonlinear Convergence Rate for Spectral Decomposition

2017 ◽  
Vol 31 (09) ◽  
pp. 1750030 ◽  
Author(s):  
Kan Xie ◽  
Yue Lai ◽  
Sihui Huang ◽  
Jie Xu
Keyword(s):  
Convergence Rate ◽  
Cost Function ◽  
Matrix Factorization ◽  
Spectral Decomposition ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Biomedical Signal Processing ◽  
Lipschitz Continuous ◽  
Local Smoothness ◽  
The Cost

With the development of the detection technology using multispectra sensors, spectral decomposition (SD) attracts more and more attention in the biomedical signal processing and image processing. In this paper, a local smoothness constrained nonnegative matrix factorization (NMF) with nonlinear convergence rate (NMF-NCR) is proposed to solve SD problem and our contributions are as follows. First, it proves that the gradients of the cost function with respect to each variable matrix are Lipschitz continuous. Then, a proximal function is constructed for optimizing the cost function. As a result, our method can achieve an NCR much faster than the traditional methods. Simulations show the advantage in solving SD of our algorithm over the compared methods.

scholarly journals Joint Nonnegative Matrix Factorization Based on Sparse and Graph Laplacian Regularization for Clustering and Co-Differential Expression Genes Analysis

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Ling-Yun Dai ◽  
Rong Zhu ◽  
Juan Wang
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Graph Laplacian ◽  
Biological Information ◽  
Joint Analysis ◽  
Characteristic Matrix ◽  
Graph Regularization ◽  
Laplacian Regularization ◽  
Joint Nonnegative Matrix Factorization

The explosion of multiomics data poses new challenges to existing data mining methods. Joint analysis of multiomics data can make the best of the complementary information that is provided by different types of data. Therefore, they can more accurately explore the biological mechanism of diseases. In this article, two forms of joint nonnegative matrix factorization based on the sparse and graph Laplacian regularization (SG-jNMF) method are proposed. In the method, the graph regularization constraint can preserve the local geometric structure of data. L 2,1 -norm regularization can enhance the sparsity among the rows and remove redundant features in the data. First, SG-jNMF1 projects multiomics data into a common subspace and applies the multiomics fusion characteristic matrix to mine the important information closely related to diseases. Second, multiomics data of the same disease are mapped into the common sample space by SG-jNMF2, and the cluster structures are detected clearly. Experimental results show that SG-jNMF can achieve significant improvement in sample clustering compared with existing joint analysis frameworks. SG-jNMF also effectively integrates multiomics data to identify co-differentially expressed genes (Co-DEGs). SG-jNMF provides an efficient integrative analysis method for mining the biological information hidden in heterogeneous multiomics data.

scholarly journals Stability-driven nonnegative matrix factorization to interpret spatial gene expression and build local gene networks

2016 ◽  
Vol 113 (16) ◽  
pp. 4290-4295 ◽  
Author(s):  
Siqi Wu ◽  
Antony Joseph ◽  
Ann S. Hammonds ◽  
Susan E. Celniker ◽  
Bin Yu ◽  
...  
Keyword(s):  
Gene Expression ◽  
Matrix Factorization ◽  
Gene Networks ◽  
Regulatory Networks ◽  
Nonnegative Matrix Factorization ◽  
Expression Patterns ◽  
Selection Criterion ◽  
Nonnegative Matrix ◽  
Biological Information ◽  
Expression Data

Spatial gene expression patterns enable the detection of local covariability and are extremely useful for identifying local gene interactions during normal development. The abundance of spatial expression data in recent years has led to the modeling and analysis of regulatory networks. The inherent complexity of such data makes it a challenge to extract biological information. We developed staNMF, a method that combines a scalable implementation of nonnegative matrix factorization (NMF) with a new stability-driven model selection criterion. When applied to a set of Drosophila early embryonic spatial gene expression images, one of the largest datasets of its kind, staNMF identified 21 principal patterns (PP). Providing a compact yet biologically interpretable representation of Drosophila expression patterns, PP are comparable to a fate map generated experimentally by laser ablation and show exceptional promise as a data-driven alternative to manual annotations. Our analysis mapped genes to cell-fate programs and assigned putative biological roles to uncharacterized genes. Finally, we used the PP to generate local transcription factor regulatory networks. Spatially local correlation networks were constructed for six PP that span along the embryonic anterior–posterior axis. Using a two-tail 5% cutoff on correlation, we reproduced 10 of the 11 links in the well-studied gap gene network. The performance of PP with the Drosophila data suggests that staNMF provides informative decompositions and constitutes a useful computational lens through which to extract biological insight from complex and often noisy gene expression data.

LOCALITY PRESERVING NONNEGATIVE MATRIX FACTORIZATION WITH APPLICATION TO FACE RECOGNITION

2010 ◽  
Vol 08 (05) ◽  
pp. 835-846 ◽  
Author(s):  
TAIPING ZHANG ◽  
BIN FANG ◽  
YUAN Y. TANG ◽  
ZHAOWEI SHANG
Keyword(s):  
Face Recognition ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
High Dimensional ◽  
Face Space ◽  
Manifold Structure ◽  
Locality Preserving ◽  
The Cost ◽  
Dimensional Face

In this paper, we propose a Locality Preserving Nonnegative Matrix Factorization (LPNMF) method to discover the manifold structure embedded in high-dimensional face space that is applied for face recognition. It is done by incorporating locality preserving constraints inside the cost function of NMF, then a new decomposition of a face with locality preserving can be obtained. As a result, the proposed LPNMF method shares some properties with the Locality Preserving Projection (LPP) such that it can effectively discover the manifold structure embedded in a high-dimensional face space. Experimental results show that LPNMF provides a better representation and achieves higher recognition rates in face recognition.

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