scholarly journals A Convex Model for Nonnegative Matrix Factorization and Dimensionality Reduction on Physical Space

2012 ◽  
Vol 21 (7) ◽  
pp. 3239-3252 ◽  
Author(s):  
E. Esser ◽  
M. Moller ◽  
S. Osher ◽  
G. Sapiro ◽  
J. Xin
Keyword(s):  
Dimensionality Reduction ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Physical Space ◽  
Convex Model

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.

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 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.

Discriminative Nonnegative Matrix Factorization for dimensionality reduction

2016 ◽  
Vol 173 ◽  
pp. 212-223 ◽  
Author(s):  
Mohammadreza Babaee ◽  
Stefanos Tsoukalas ◽  
Maryam Babaee ◽  
Gerhard Rigoll ◽  
Mihai Datcu
Keyword(s):  
Dimensionality Reduction ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix
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