LS-NMF: A modified non-negative matrix factorization algorithm utilizing uncertainty estimates

Wang, Guoli; Kossenkov, Andrew V.; Ochs, Michael F.

doi:10.1186/1471-2105-7-175

Cited by 98 publications

(37 citation statements)

References 33 publications

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“…Algorithms that allow genes to be part of multiple processes/clusters have also been extensively applied [10–12]. Among these, Singular Value Decomposition (SVD) or Principal Components Analysis (PCA) provides a linear representation of the data in terms of components that are linearly uncorrelated [12].…”

Section: Introductionmentioning

confidence: 99%

Elucidating the Altered Transcriptional Programs in Breast Cancer using Independent Component Analysis

et al. 2007

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The quantity of mRNA transcripts in a cell is determined by a complex interplay of cooperative and counteracting biological processes. Independent Component Analysis (ICA) is one of a few number of unsupervised algorithms that have been applied to microarray gene expression data in an attempt to understand phenotype differences in terms of changes in the activation/inhibition patterns of biological pathways. While the ICA model has been shown to outperform other linear representations of the data such as Principal Components Analysis (PCA), a validation using explicit pathway and regulatory element information has not yet been performed. We apply a range of popular ICA algorithms to six of the largest microarray cancer datasets and use pathway-knowledge and regulatory-element databases for validation. We show that ICA outperforms PCA and clustering-based methods in that ICA components map closer to known cancer-related pathways, regulatory modules, and cancer phenotypes. Furthermore, we identify cancer signalling and oncogenic pathways and regulatory modules that play a prominent role in breast cancer and relate the differential activation patterns of these to breast cancer phenotypes. Importantly, we find novel associations linking immune response and epithelial–mesenchymal transition pathways with estrogen receptor status and histological grade, respectively. In addition, we find associations linking the activity levels of biological pathways and transcription factors (NF1 and NFAT) with clinical outcome in breast cancer. ICA provides a framework for a more biologically relevant interpretation of genomewide transcriptomic data. Adopting ICA as the analysis tool of choice will help understand the phenotype–pathway relationship and thus help elucidate the molecular taxonomy of heterogeneous cancers and of other complex genetic diseases.

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Section: Introductionmentioning

confidence: 99%

Elucidating the Altered Transcriptional Programs in Breast Cancer using Independent Component Analysis

et al. 2007

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“…In addition, the treatment of all variances as equal raises a potential problem for eukaryotic data. Least-squares NMF (lsNMF) introduced new updating rules, effectively replacing the criterion for distance minimization with a minimization of the χ 2 error [23], given by…”

Section: Review Of Matrix Factorization Methodsmentioning

confidence: 99%

“…It is hoped as data sets grow, that cell-type gene specific variance estimates may become available. Even simple models of noise identified in early work [22] have been shown to improve estimates of biological activity from microarrays [23]. …”

Section: Matrix Factorization For Expression Datamentioning

confidence: 99%

Matrix factorization for transcriptional regulatory network inference

Ochs

Fertig

2012

2012 IEEE Symposium on Computational Intelligence in Bioinformatics and Computational Biology (CIBCB)

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Inference of Transcriptional Regulatory Networks (TRNs) provides insight into the mechanisms driving biological systems, especially mammalian development and disease. Many techniques have been developed for TRN estimation from indirect biochemical measurements. Although successful when initially tested in model organisms, these regulatory models often fail when applied to data from multicellular organisms where multiple regulation and gene reuse increase dramatically. Non-negative matrix factorization techniques were initially introduced to find non-orthogonal patterns in data, making them ideal techniques for inference in cases of multiple regulation. We review these techniques and their application to TRN analysis.

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“…For example, the least squares NMF takes into account the uncertainty measurements to better analyze the gene expression data [40]. The weighted-NMF [16] improves the NMF capabilities of representing positive local data for image classification tasks.…”

Section: Introductionmentioning

confidence: 99%

Evolutionary nonnegative matrix factorization with adaptive control of cluster quality

Gong

Wang

et al. 2018

Neurocomputing

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Nonnegative matrix factorization (NMF) approximates a given data matrix using linear combinations of a small number of nonnegative basis vectors, weighted by nonnegative encoding coefficients. This enables the exploration of the cluster structure of the data through the examination of the values of the encoding coefficients and therefore, NMF is often used as a popular tool for clustering analysis. However, its encoding coefficients do not always reveal a satisfactory cluster structure. To improve its effectiveness, a novel evolutionary strategy is proposed here to drive the iterative updating scheme of NMF and generate encoding coefficients of higher quality that are capa-

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LS-NMF: A modified non-negative matrix factorization algorithm utilizing uncertainty estimates

Cited by 98 publications

References 33 publications

Elucidating the Altered Transcriptional Programs in Breast Cancer using Independent Component Analysis

Elucidating the Altered Transcriptional Programs in Breast Cancer using Independent Component Analysis

Matrix factorization for transcriptional regulatory network inference

Evolutionary nonnegative matrix factorization with adaptive control of cluster quality

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