Biclustering via Sparse Singular Value Decomposition

Lee, Mihee; Shen, Haipeng; Huang, Jianhua Z.; Marron, J. S.

doi:10.1111/j.1541-0420.2010.01392.x

Cited by 230 publications

(305 citation statements)

References 28 publications

(45 reference statements)

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“…Note that the input data are standardized to mean 0 and SD 1 elementwisely for FIT-SSVD-O and LSHM-O. Although this step is not mentioned in the original papers (9,10), this simple procedure is critical for accurate mean bicluster detection. From Table 2, we can see that HSSVD-O provides the best overall performance, while HSSVD is close to the best; however, in practice, the oracle rank is unknown.…”

Section: Simulation Studymentioning

confidence: 99%

“…We compared HSSVD with the most relevant existing biclustering methods, FIT-SSVD and LSHM (9,10). HSSVD includes a rank estimation component, whereas the other methods do not automatically include this.…”

Section: Simulation Studymentioning

confidence: 99%

“…In contrast, biclustering involves clustering rows and columns simultaneously to account for the interaction of row and column sparsity. This local sparsity perspective provides an intuition for using sparse singular value decomposition (SSVD) algorithms for biclustering (8)(9)(10)(11). SSVD assumes that the signal in the data matrix can be represented by a low-rank matrix X ≈ UDV T = P r i=1 d i u i v T i with X ∈ ℜ n × p .…”

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confidence: 99%

“…The performance of different methods is evaluated based on the pattern difference of subtypes based on the mean approximations. For all methods, we set the rank of the mean signal matrix equal to 3 to maintain consistency with the ranks used in FIT-SSVD (10) and LSHM (9). Further, we use the measurement "support" to evaluate the sparsity of the estimated gene signal (10).…”

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confidence: 99%

“…We now demonstrate that even in settings without variance heterogeneity, HSSVD can better identify discriminative biclusters for different cancer subtypes than other methods, including FIT-SSVD (10), LSHM (9), and traditional SVD. We use a lung cancer data set which has been studied in the statistics literature (9,10,17). The samples are a subset of patients (21) having lung cancer with gene expression measured by the Affymetrix 95av2 GeneChip (22).…”

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confidence: 99%

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Biclustering with heterogeneous variance

Chen¹,

Sullivan²,

Kosorok

2013

Proc. Natl. Acad. Sci. U.S.A.

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In cancer research, as in all of medicine, it is important to classify patients into etiologically and therapeutically relevant subtypes to improve diagnosis and treatment. One way to do this is to use clustering methods to find subgroups of homogeneous individuals based on genetic profiles together with heuristic clinical analysis. A notable drawback of existing clustering methods is that they ignore the possibility that the variance of gene expression profile measurements can be heterogeneous across subgroups, and methods that do not consider heterogeneity of variance can lead to inaccurate subgroup prediction. Research has shown that hypervariability is a common feature among cancer subtypes. In this paper, we present a statistical approach that can capture both mean and variance structure in genetic data. We demonstrate the strength of our method in both synthetic data and in two cancer data sets. In particular, our method confirms the hypervariability of methylation level in cancer patients, and it detects clearer subgroup patterns in lung cancer data.C lustering is an important type of unsupervised learning algorithm for data exploration. Successful examples include Kmean clustering and hierarchical clustering, both of which are widely used in biological research to find cancer subtypes and to stratify patients. These and other traditional clustering algorithms depend on the distances calculated using all of the features. For example, individuals can be clustered into homogeneous groups by minimizing the summation of within-clusters sum of squares (the Euclidean distances) of their gene expression profiles. Unfortunately, this strategy is ineffective when only a subset of features is informative. This phenomenon can be demonstrated by K-means clustering (1) results for a toy example using only the variables which determine the underlying true cluster compared with using all variables (which includes many uninformative variables). As can be seen in Fig. 1, clustering performance is poor when all variables are used in the clustering algorithm (2).To solve this problem, sparse clustering methods have been proposed to allow clustering decisions to depend on only a subset of feature variables (the property of sparsity). Prominent sparse clustering methods include sparse principal component analysis (PCA) (3-5) and Sparse K-means (2), among others (6). However, sparse clustering still fails if the true sparsity is a local rather than a global phenomenon (6). More specifically, different subsets of features can be informative for some samples but not all samples, or, in other words, sparsity exists in both features and samples jointly. Biclustering methods are a potential solution to this problem, and further generalize the sparsity principle by considering samples and features as exchangeable concepts to handle local sparsity (6, 7). For example, gene expression data can be represented as a matrix with genes as columns, and subjects as rows (with various and possibly unknown diseases or tissue types). Traditiona...

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Section: Simulation Studymentioning

confidence: 99%

Section: Simulation Studymentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Biclustering with heterogeneous variance

Chen¹,

Sullivan²,

Kosorok

2013

Proc. Natl. Acad. Sci. U.S.A.

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Group‐sparsity regularization for ill‐posed subsurface flow inverse problems

Golmohammadi

Khaninezhad

Jafarpour

2015

Water Resources Research

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Sparse representations provide a flexible and parsimonious description of high‐dimensional model parameters for reconstructing subsurface flow property distributions from limited data. To further constrain ill‐posed inverse problems, group‐sparsity regularization can take advantage of possible relations among the entries of unknown sparse parameters when: (i) groups of sparse elements are either collectively active or inactive and (ii) only a small subset of the groups is needed to approximate the parameters of interest. Since subsurface properties exhibit strong spatial connectivity patterns they may lead to sparse descriptions that satisfy the above conditions. When these conditions are established, a group‐sparsity regularization can be invoked to facilitate the solution of the resulting inverse problem by promoting sparsity across the groups. The proposed regularization penalizes the number of groups that are active without promoting sparsity within each group. Two implementations are presented in this paper: one based on the multiresolution tree structure of Wavelet decomposition, without a need for explicit prior models, and another learned from explicit prior model realizations using sparse principal component analysis (SPCA). In each case, the approach first classifies the parameters of the inverse problem into groups with specific connectivity features, and then takes advantage of the grouped structure to recover the relevant patterns in the solution from the flow data. Several numerical experiments are presented to demonstrate the advantages of additional constraining power of group‐sparsity in solving ill‐posed subsurface model calibration problems.

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Singular Value Decomposition and High Dimensional Data

Allen¹,

Perry²

2012

Encyclopedia of Environmetrics

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The singular value decomposition and related principal components analysis are foundational multivariate methods used for dimension reduction and exploratory analysis of high‐dimensional data. Studying this decomposition using random matrix theory, however, reveals troubling behavior when the number of variables is larger than the number of samples. This article surveys random matrix theory results related to the singular value decomposition and high‐dimensional data as well as recent developments such as sparse principal components analysis. Software on the random matrix theory distributions related to the singular value decomposition can be found elsewhere; several software packages implementing methods for sparse principal components analysis are also available.

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Biclustering via Sparse Singular Value Decomposition

Cited by 230 publications

References 28 publications

Biclustering with heterogeneous variance

Biclustering with heterogeneous variance

Group‐sparsity regularization for ill‐posed subsurface flow inverse problems

Singular Value Decomposition and High Dimensional Data

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