Research in several fields now requires the analysis of data sets in which multiple high-dimensional types of data are available for a common set of objects. In particular, The Cancer Genome Atlas (TCGA) includes data from several diverse genomic technologies on the same cancerous tumor samples. In this paper we introduce Joint and Individual Variation Explained (JIVE), a general decomposition of variation for the integrated analysis of such data sets. The decomposition consists of three terms: a low-rank approximation capturing joint variation across data types, low-rank approximations for structured variation individual to each data type, and residual noise. JIVE quantifies the amount of joint variation between data types, reduces the dimensionality of the data and provides new directions for the visual exploration of joint and individual structures. The proposed method represents an extension of Principal Component Analysis and has clear advantages over popular two-block methods such as Canonical Correlation Analysis and Partial Least Squares. A JIVE analysis of gene expression and miRNA data on Glioblastoma Multiforme tumor samples reveals gene–miRNA associations and provides better characterization of tumor types.
Documented Matlab code for running JIVE: JIVE_matlab.zip. (For an older version that uses the rank selection method described in arXiv:1102.4110v1, download JIVE_matlab_old.zip)
Gene expression and miRNA data on a common set of GBM tumor samples from TCGA : GBM_GE_miRNA.zip. (For more current, well-annotated data visit the TCGA website.)
Application of JIVE to the gene expression and miRNA data above: JIVE_Example.m
This work was supported in part by NIH Grant R01 MH090936-01, NSF Grant DMS-09-07177, NSF Grant DMS-08-54908 and NIH Grant U24-CA143848.