scholarly journals Robust Structure Preserving Nonnegative Matrix Factorization for Dimensionality Reduction

2016 ◽  
Vol 2016 ◽  
pp. 1-14
Author(s):  
Bingfeng Li ◽  
Yandong Tang ◽  
Zhi Han
Keyword(s):  
Dimensionality Reduction ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Noisy Data ◽  
Nonnegative Matrix ◽  
Structure Preserving ◽  
Structure Preservation ◽  
Significant Performance ◽  
Linear Dimensionality Reduction ◽  
Low Dimensional

As a linear dimensionality reduction method, nonnegative matrix factorization (NMF) has been widely used in many fields, such as machine learning and data mining. However, there are still two major drawbacks for NMF: (a) NMF can only perform semantic factorization in Euclidean space, and it fails to discover the intrinsic geometrical structure of high-dimensional data distribution. (b) NMF suffers from noisy data, which are commonly encountered in real-world applications. To address these issues, in this paper, we present a new robust structure preserving nonnegative matrix factorization (RSPNMF) framework. In RSPNMF, a local affinity graph and a distant repulsion graph are constructed to encode the geometrical information, and noisy data influence is alleviated by characterizing the data reconstruction term of NMF withl2,1-norm instead ofl2-norm. With incorporation of the local and distant structure preservation regularization term into the robust NMF framework, our algorithm can discover a low-dimensional embedding subspace with the nature of structure preservation. RSPNMF is formulated as an optimization problem and solved by an effective iterative multiplicative update algorithm. Experimental results on some facial image datasets clustering show significant performance improvement of RSPNMF in comparison with the state-of-the-art algorithms.

The flexible recruitment of muscle synergies depends on the required force-generating capability

2014 ◽  
Vol 112 (2) ◽  
pp. 316-327 ◽  
Author(s):  
Shota Hagio ◽  
Motoki Kouzaki
Keyword(s):  
Central Nervous System ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Isometric Force ◽  
Nonnegative Matrix ◽  
Muscle Synergies ◽  
Joint Angles ◽  
Activation Patterns ◽  
The Central Nervous System ◽  
Low Dimensional

To simplify redundant motor control, the central nervous system (CNS) may modularly organize and recruit groups of muscles as “muscle synergies.” However, smooth and efficient movements are expected to require not only low-dimensional organization, but also flexibility in the recruitment or combination of synergies, depending on force-generating capability of individual muscles. In this study, we examined how the CNS controls activations of muscle synergies as changing joint angles. Subjects performed multidirectional isometric force generations around right ankle and extracted the muscle synergies using nonnegative matrix factorization across various knee and hip joint angles. As a result, muscle synergies were selectively recruited with merging or decomposition as changing the joint angles. Moreover, the activation profiles, including activation levels and the direction indicating the peak, of muscle synergies across force directions depended on the joint angles. Therefore, we suggested that the CNS selects appropriate muscle synergies and controls their activation patterns based on the force-generating capability of muscles with merging or decomposing descending neural inputs.

scholarly journals Adaptive Multiview Nonnegative Matrix Factorization Algorithm for Integration of Multimodal Biomedical Data

2017 ◽  
Vol 16 ◽  
pp. 117693511772572 ◽  
Author(s):  
Bisakha Ray ◽  
Wenke Liu ◽  
David Fenyö
Keyword(s):  
Dimensionality Reduction ◽  
Matrix Factorization ◽  
Cancer Biology ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Heterogeneous Data ◽  
Joint Analysis ◽  
Multimodal Data ◽  
Transcript Levels ◽  
Factorization Algorithm

The amounts and types of available multimodal tumor data are rapidly increasing, and their integration is critical for fully understanding the underlying cancer biology and personalizing treatment. However, the development of methods for effectively integrating multimodal data in a principled manner is lagging behind our ability to generate the data. In this article, we introduce an extension to a multiview nonnegative matrix factorization algorithm (NNMF) for dimensionality reduction and integration of heterogeneous data types and compare the predictive modeling performance of the method on unimodal and multimodal data. We also present a comparative evaluation of our novel multiview approach and current data integration methods. Our work provides an efficient method to extend an existing dimensionality reduction method. We report rigorous evaluation of the method on large-scale quantitative protein and phosphoprotein tumor data from the Clinical Proteomic Tumor Analysis Consortium (CPTAC) acquired using state-of-the-art liquid chromatography mass spectrometry. Exome sequencing and RNA-Seq data were also available from The Cancer Genome Atlas for the same tumors. For unimodal data, in case of breast cancer, transcript levels were most predictive of estrogen and progesterone receptor status and copy number variation of human epidermal growth factor receptor 2 status. For ovarian and colon cancers, phosphoprotein and protein levels were most predictive of tumor grade and stage and residual tumor, respectively. When multiview NNMF was applied to multimodal data to predict outcomes, the improvement in performance is not overall statistically significant beyond unimodal data, suggesting that proteomics data may contain more predictive information regarding tumor phenotypes than transcript levels, probably due to the fact that proteins are the functional gene products and therefore a more direct measurement of the functional state of the tumor. Here, we have applied our proposed approach to multimodal molecular data for tumors, but it is generally applicable to dimensionality reduction and joint analysis of any type of multimodal data.

scholarly journals Rank Selection in Nonnegative Matrix Factorization using Minimum Description Length

2017 ◽  
Vol 29 (8) ◽  
pp. 2164-2176 ◽  
Author(s):  
Steven Squires ◽  
Adam Prügel-Bennett ◽  
Mahesan Niranjan
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Minimum Description Length ◽  
Synthetic Data ◽  
Nonnegative Matrix ◽  
Real Data ◽  
Data Matrix ◽  
Constraint Forces ◽  
Data Points ◽  
Linear Dimensionality Reduction

Nonnegative matrix factorization (NMF) is primarily a linear dimensionality reduction technique that factorizes a nonnegative data matrix into two smaller nonnegative matrices: one that represents the basis of the new subspace and the second that holds the coefficients of all the data points in that new space. In principle, the nonnegativity constraint forces the representation to be sparse and parts based. Instead of extracting holistic features from the data, real parts are extracted that should be significantly easier to interpret and analyze. The size of the new subspace selects how many features will be extracted from the data. An effective choice should minimize the noise while extracting the key features. We propose a mechanism for selecting the subspace size by using a minimum description length technique. We demonstrate that our technique provides plausible estimates for real data as well as accurately predicting the known size of synthetic data. We provide an implementation of our code in a Matlab format.

Normalized dimensionality reduction using nonnegative matrix factorization

2010 ◽  
Vol 73 (10-12) ◽  
pp. 1783-1793 ◽  
Author(s):  
Zhenfeng Zhu ◽  
Yue-Fei Guo ◽  
Xingquan Zhu ◽  
Xiangyang Xue
Keyword(s):  
Dimensionality Reduction ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix

scholarly journals Ranking Preserving Nonnegative Matrix Factorization

2018 ◽  
Author(s):  
Jing Wang ◽  
Feng Tian ◽  
Weiwei Liu ◽  
Xiao Wang ◽  
Wenjie Zhang ◽  
...  
Keyword(s):  
Data Structure ◽  
Objective Function ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Relative Order ◽  
Structure Preserving ◽  
The Arts ◽  
Structured Representations ◽  
Clustering And Classification

Nonnegative matrix factorization (NMF),  a well-known technique  to find  parts-based representations of nonnegative data, has been widely studied. In reality,  ordinal relations often exist among data,  such as data i is more related to j than to q.  Such relative order is naturally available, and more importantly, it truly reflects the latent data structure.  Preserving the ordinal relations enables us to find structured representations of data that are faithful to the relative order, so that the learned representations become  more discriminative. However, current NMFs pay no attention to this. In this paper, we make the first attempt towards incorporating the ordinal relations and  propose a novel ranking preserving nonnegative matrix factorization (RPNMF) approach, which enforces the learned representations to be ranked according to the relations. We derive  iterative updating rules to solve RPNMF's objective function with  convergence guaranteed.  Experimental results with several datasets for clustering and classification have demonstrated that RPNMF achieves greater performance against the state-of-the-arts,  not only  in terms of  accuracy, but also interpretation of orderly data structure.

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