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RCUR: an R package for CUR matrix decomposition.

ABSTRACT: BACKGROUND: Many methods for dimensionality reduction of large data sets such as those generated in microarray studies boil down to the Singular Value Decomposition (SVD). Although singular vectors associated with the largest singular values have strong optimality properties and can often be quite useful as a tool to summarize the data, they are linear combinations of up to all of the data points, and thus it is typically quite hard to interpret those vectors in terms of the application domain from which the data are drawn. Recently, an alternative dimensionality reduction paradigm, CUR matrix decompositions, has been proposed to address this problem and has been applied to genetic and internet data. CUR decompositions are low-rank matrix decompositions that are explicitly expressed in terms of a small number of actual columns and/or actual rows of the data matrix. Since they are constructed from actual data elements, CUR decompositions are interpretable by practitioners of the field from which the data are drawn. RESULTS: We present an implementation to perform CUR matrix decompositions, in the form of a freely available, open source R-package called rCUR. This package will help users to perform CUR-based analysis on large-scale data, such as those obtained from different high-throughput technologies, in an interactive and exploratory manner. We show two examples that illustrate how CUR-based techniques make it possible to reduce significantly the number of probes, while at the same time maintaining major trends in data and keeping the same classification accuracy. CONCLUSIONS: The package rCUR provides functions for the users to perform CUR-based matrix decompositions in the R environment. In gene expression studies, it gives an additional way of analysis of differential expression and discriminant gene selection based on the use of statistical leverage scores. These scores, which have been used historically in diagnostic regression analysis to identify outliers, can be used by rCUR to identify the most informative data points with respect to which to express the remaining data points.

SUBMITTER: Bodor A

PROVIDER: S-EPMC3546429 | biostudies-literature | 2012

REPOSITORIES: biostudies-literature

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Project description:Exploratory analysis of human microbiome data is often based on dimension-reduced graphical displays derived from similarities based on non-Euclidean distances, such as UniFrac or Bray-Curtis. However, a display of this type, often referred to as the principal-coordinate analysis (PCoA) plot, does not reveal which taxa are related to the observed clustering because the configuration of samples is not based on a coordinate system in which both the samples and variables can be represented. The reason is that the PCoA plot is based on the eigen-decomposition of a similarity matrix and not the singular value decomposition (SVD) of the sample-by-abundance matrix. We propose a novel biplot that is based on an extension of the SVD, called the generalized matrix decomposition biplot (GMD-biplot), which involves an arbitrary matrix of similarities and the original matrix of variable measures, such as taxon abundances. As in a traditional biplot, points represent the samples, and arrows represent the variables. The proposed GMD-biplot is illustrated by analyzing multiple real and simulated data sets which demonstrate that the GMD-biplot provides improved clustering capability and a more meaningful relationship between the arrows and points.IMPORTANCE Biplots that simultaneously display the sample clustering and the important taxa have gained popularity in the exploratory analysis of human microbiome data. Traditional biplots, assuming Euclidean distances between samples, are not appropriate for microbiome data, when non-Euclidean distances are used to characterize dissimilarities among microbial communities. Thus, incorporating information from non-Euclidean distances into a biplot becomes useful for graphical displays of microbiome data. The proposed GMD-biplot accounts for any arbitrary non-Euclidean distances and provides a robust and computationally efficient approach for graphical visualization of microbiome data. In addition, the proposed GMD-biplot displays both the samples and taxa with respect to the same coordinate system, which further allows the configuration of future samples.

Project description:Recently, a growing number of biological research and scientific experiments have demonstrated that microRNA (miRNA) affects the development of human complex diseases. Discovering miRNA-disease associations plays an increasingly vital role in devising diagnostic and therapeutic tools for diseases. However, since uncovering associations via experimental methods is expensive and time-consuming, novel and effective computational methods for association prediction are in demand. In this study, we developed a computational model of Matrix Decomposition and Heterogeneous Graph Inference for miRNA-disease association prediction (MDHGI) to discover new miRNA-disease associations by integrating the predicted association probability obtained from matrix decomposition through sparse learning method, the miRNA functional similarity, the disease semantic similarity, and the Gaussian interaction profile kernel similarity for diseases and miRNAs into a heterogeneous network. Compared with previous computational models based on heterogeneous networks, our model took full advantage of matrix decomposition before the construction of heterogeneous network, thereby improving the prediction accuracy. MDHGI obtained AUCs of 0.8945 and 0.8240 in the global and the local leave-one-out cross validation, respectively. Moreover, the AUC of 0.8794+/-0.0021 in 5-fold cross validation confirmed its stability of predictive performance. In addition, to further evaluate the model's accuracy, we applied MDHGI to four important human cancers in three different kinds of case studies. In the first type, 98% (Esophageal Neoplasms) and 98% (Lymphoma) of top 50 predicted miRNAs have been confirmed by at least one of the two databases (dbDEMC and miR2Disease) or at least one experimental literature in PubMed. In the second type of case study, what made a difference was that we removed all known associations between the miRNAs and Lung Neoplasms before implementing MDHGI on Lung Neoplasms. As a result, 100% (Lung Neoplasms) of top 50 related miRNAs have been indexed by at least one of the three databases (dbDEMC, miR2Disease and HMDD V2.0) or at least one experimental literature in PubMed. Furthermore, we also tested our prediction method on the HMDD V1.0 database to prove the applicability of MDHGI to different datasets. The results showed that 50 out of top 50 miRNAs related with the breast neoplasms were validated by at least one of the three databases (HMDD V2.0, dbDEMC, and miR2Disease) or at least one experimental literature.

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RCUR: an R package for CUR matrix decomposition.

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