Dataset Information

Tensor canonical correlation analysis.

ABSTRACT: Canonical correlation analysis (CCA) is a multivariate analysis technique for estimating a linear relationship between two sets of measurements. Modern acquisition technologies, for example, those arising in neuroimaging and remote sensing, produce data in the form of multidimensional arrays or tensors. Classic CCA is not appropriate for dealing with tensor data due to the multidimensional structure and ultrahigh dimensionality of such modern data. In this paper, we present tensor CCA (TCCA) to discover relationships between two tensors while simultaneously preserving multidimensional structure of the tensors and utilizing substantially fewer parameters. Furthermore, we show how to employ a parsimonious covariance structure to gain additional stability and efficiency. We delineate population and sample problems for each model and propose efficient estimation algorithms with global convergence guarantees. Also we describe a probabilistic model for TCCA that enables the generation of synthetic data with desired canonical variates and correlations. Simulation studies illustrate the performance of our methods.

SUBMITTER: Min EJ

PROVIDER: S-EPMC7351364 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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Tensor canonical correlation analysis.

Min Eun Jeong EJ Chi Eric C EC Zhou Hua H

Stat 20200102 1

Canonical correlation analysis (CCA) is a multivariate analysis technique for estimating a linear relationship between two sets of measurements. Modern acquisition technologies, for example, those arising in neuroimaging and remote sensing, produce data in the form of multidimensional arrays or tensors. Classic CCA is not appropriate for dealing with tensor data due to the multidimensional structure and ultrahigh dimensionality of such modern data. In this paper, we present tensor CCA (TCCA) to ...[more]

PMID: 32655193

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Project description:The emergence of high-throughput genomic datasets from different sources and platforms (e.g., gene expression, single nucleotide polymorphisms (SNP), and copy number variation (CNV)) has greatly enhanced our understandings of the interplay of these genomic factors as well as their influences on the complex diseases. It is challenging to explore the relationship between these different types of genomic data sets. In this paper, we focus on a multivariate statistical method, canonical correlation analysis (CCA) method for this problem. Conventional CCA method does not work effectively if the number of data samples is significantly less than that of biomarkers, which is a typical case for genomic data (e.g., SNPs). Sparse CCA (sCCA) methods were introduced to overcome such difficulty, mostly using penalizations with l-1 norm (CCA-l1) or the combination of l-1and l-2 norm (CCA-elastic net). However, they overlook the structural or group effect within genomic data in the analysis, which often exist and are important (e.g., SNPs spanning a gene interact and work together as a group).We propose a new group sparse CCA method (CCA-sparse group) along with an effective numerical algorithm to study the mutual relationship between two different types of genomic data (i.e., SNP and gene expression). We then extend the model to a more general formulation that can include the existing sCCA models. We apply the model to feature/variable selection from two data sets and compare our group sparse CCA method with existing sCCA methods on both simulation and two real datasets (human gliomas data and NCI60 data). We use a graphical representation of the samples with a pair of canonical variates to demonstrate the discriminating characteristic of the selected features. Pathway analysis is further performed for biological interpretation of those features.The CCA-sparse group method incorporates group effects of features into the correlation analysis while performs individual feature selection simultaneously. It outperforms the two sCCA methods (CCA-l1 and CCA-group) by identifying the correlated features with more true positives while controlling total discordance at a lower level on the simulated data, even if the group effect does not exist or there are irrelevant features grouped with true correlated features. Compared with our proposed CCA-group sparse models, CCA-l1 tends to select less true correlated features while CCA-group inclines to select more redundant features.

Project description:BackgroundAlternative polyadenylation (APA) has emerged as a pervasive mechanism that contributes to the transcriptome complexity and dynamics of gene regulation. The current tsunami of whole genome poly(A) site data from various conditions generated by 3' end sequencing provides a valuable data source for the study of APA-related gene expression. Cluster analysis is a powerful technique for investigating the association structure among genes, however, conventional gene clustering methods are not suitable for APA-related data as they fail to consider the information of poly(A) sites (e.g., location, abundance, number, etc.) within each gene or measure the association among poly(A) sites between two genes.ResultsHere we proposed a computational framework, named PASCCA, for clustering genes from replicated or unreplicated poly(A) site data using canonical correlation analysis (CCA). PASCCA incorporates multiple layers of gene expression data from both the poly(A) site level and gene level and takes into account the number of replicates and the variability within each experimental group. Moreover, PASCCA characterizes poly(A) sites in various ways including the abundance and relative usage, which can exploit the advantages of 3' end deep sequencing in quantifying APA sites. Using both real and synthetic poly(A) site data sets, the cluster analysis demonstrates that PASCCA outperforms other widely-used distance measures under five performance metrics including connectivity, the Dunn index, average distance, average distance between means, and the biological homogeneity index. We also used PASCCA to infer APA-specific gene modules from recently published poly(A) site data of rice and discovered some distinct functional gene modules. We have made PASCCA an easy-to-use R package for APA-related gene expression analyses, including the characterization of poly(A) sites, quantification of association between genes, and clustering of genes.ConclusionsBy providing a better treatment of the noise inherent in repeated measurements and taking into account multiple layers of poly(A) site data, PASCCA could be a general tool for clustering and analyzing APA-specific gene expression data. PASCCA could be used to elucidate the dynamic interplay of genes and their APA sites among various biological conditions from emerging 3' end sequencing data to address the complex biological phenomenon.

Dataset Information

Tensor canonical correlation analysis.

Publications

Tensor canonical correlation analysis.

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