The Annals of Applied Statistics

Joint and individual variation explained (JIVE) for integrated analysis of multiple data types

Eric F. Lock, Katherine A. Hoadley, J. S. Marron, and Andrew B. Nobel

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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.

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Ann. Appl. Stat., Volume 7, Number 1 (2013), 523-542.

First available in Project Euclid: 9 April 2013

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Data integration multi-block data principal component analysis data fusion


Lock, Eric F.; Hoadley, Katherine A.; Marron, J. S.; Nobel, Andrew B. Joint and individual variation explained (JIVE) for integrated analysis of multiple data types. Ann. Appl. Stat. 7 (2013), no. 1, 523--542. doi:10.1214/12-AOAS597.

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Supplemental materials

  • Supplementary material: Additional Material. The supplementary article Lock et al. (2012) provides additional details and further validation of the JIVE method. This includes: A proof concerning the existence and uniqueness of the decomposition. A description of the permutation approach to rank selection. Pseudocode for the algorithm. A discussion of computing time and efficiency. A discussion of invariance properties. Results from the application of JIVE to many diverse simulated data sets.