Dataset Information

Comparison of Penalty Functions for Sparse Canonical Correlation Analysis.

ABSTRACT: Canonical correlation analysis (CCA) is a widely used multivariate method for assessing the association between two sets of variables. However, when the number of variables far exceeds the number of subjects, such in the case of large-scale genomic studies, the traditional CCA method is not appropriate. In addition, when the variables are highly correlated the sample covariance matrices become unstable or undefined. To overcome these two issues, sparse canonical correlation analysis (SCCA) for multiple data sets has been proposed using a Lasso type of penalty. However, these methods do not have direct control over sparsity of solution. An additional step that uses Bayesian Information Criterion (BIC) has also been suggested to further filter out unimportant features. In this paper, a comparison of four penalty functions (Lasso, Elastic-net, SCAD and Hard-threshold) for SCCA with and without the BIC filtering step have been carried out using both real and simulated genotypic and mRNA expression data. This study indicates that the SCAD penalty with BIC filter would be a preferable penalty function for application of SCCA to genomic data.

SUBMITTER: Chalise P

PROVIDER: S-EPMC3185379 | biostudies-literature | 2012 Feb

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

Comparison of Penalty Functions for Sparse Canonical Correlation Analysis.

Chalise Prabhakar P Fridley Brooke L BL

Computational statistics & data analysis 20120201 2

Canonical correlation analysis (CCA) is a widely used multivariate method for assessing the association between two sets of variables. However, when the number of variables far exceeds the number of subjects, such in the case of large-scale genomic studies, the traditional CCA method is not appropriate. In addition, when the variables are highly correlated the sample covariance matrices become unstable or undefined. To overcome these two issues, sparse canonical correlation analysis (SCCA) for m ...[more]

PMID: 21984855

Similar Datasets

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:MotivationRecent developments in technology have enabled researchers to collect multiple OMICS datasets for the same individuals. The conventional approach for understanding the relationships between the collected datasets and the complex trait of interest would be through the analysis of each OMIC dataset separately from the rest, or to test for associations between the OMICS datasets. In this work we show that integrating multiple OMICS datasets together, instead of analysing them separately, improves our understanding of their in-between relationships as well as the predictive accuracy for the tested trait. Several approaches have been proposed for the integration of heterogeneous and high-dimensional (p?n) data, such as OMICS. The sparse variant of canonical correlation analysis (CCA) approach is a promising one that seeks to penalize the canonical variables for producing sparse latent variables while achieving maximal correlation between the datasets. Over the last years, a number of approaches for implementing sparse CCA (sCCA) have been proposed, where they differ on their objective functions, iterative algorithm for obtaining the sparse latent variables and make different assumptions about the original datasets.ResultsThrough a comparative study we have explored the performance of the conventional CCA proposed by Parkhomenko et al., penalized matrix decomposition CCA proposed by Witten and Tibshirani and its extension proposed by Suo et al. The aforementioned methods were modified to allow for different penalty functions. Although sCCA is an unsupervised learning approach for understanding of the in-between relationships, we have twisted the problem as a supervised learning one and investigated how the computed latent variables can be used for predicting complex traits. The approaches were extended to allow for multiple (more than two) datasets where the trait was included as one of the input datasets. Both ways have shown improvement over conventional predictive models that include one or multiple datasets.Availability and implementationhttps://github.com/theorod93/sCCA.Supplementary informationSupplementary data are available at Bioinformatics online.

Project description:It is now clear that major malignancies are heterogeneous diseases associated with diverse molecular properties and clinical outcomes, posing a great challenge for more individualized therapy. In the last decade, cancer molecular subtyping studies were mostly based on transcriptomic profiles, ignoring heterogeneity at other (epi-)genetic levels of gene regulation. Integrating multiple types of (epi)genomic data generates a more comprehensive landscape of biological processes, providing an opportunity to better dissect cancer heterogeneity. Here, we propose sparse canonical correlation analysis for cancer classification (SCCA-CC), which projects each type of single-omics data onto a unified space for data fusion, followed by clustering and classification analysis. Without loss of generality, as case studies, we integrated two types of omics data, mRNA and miRNA profiles, for molecular classification of ovarian cancer (n = 462), and breast cancer (n = 451). The two types of omics data were projected onto a unified space using SCCA, followed by data fusion to identify cancer subtypes. The subtypes we identified recapitulated subtypes previously recognized by other groups (all P- values < 0.001), but display more significant clinical associations. Especially in ovarian cancer, the four subtypes we identified were significantly associated with overall survival, while the taxonomy previously established by TCGA did not (P- values: 0.039 vs. 0.12). The multi-omics classifiers we established can not only classify individual types of data but also demonstrated higher accuracies on the fused data. Compared with iCluster, SCCA-CC demonstrated its superiority by identifying subtypes of higher coherence, clinical relevance, and time efficiency. In conclusion, we developed an integrated bioinformatic framework SCCA-CC for cancer molecular subtyping. Using two case studies in breast and ovarian cancer, we demonstrated its effectiveness in identifying biologically meaningful and clinically relevant subtypes. SCCA-CC presented a unique advantage in its ability to classify both single-omics data and multi-omics data, which significantly extends the applicability to various data types, and making more efficient use of published omics resources.

Dataset Information

Comparison of Penalty Functions for Sparse Canonical Correlation Analysis.

Publications

Comparison of Penalty Functions for Sparse Canonical Correlation Analysis.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets