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With the growing surge of biological measurements, the problem of integrating and analyzing different types of genomic measurements has become an immediate challenge for elucidating events at the molecular level. In order to address the problem of integrating different data types, we present a framework that locates variation patterns in two biological inputs based on the generalized singular value decomposition (GSVD). In this work, we jointly examine gene expression and copy number data and iteratively project the data on different decomposition directions defined by the projection angle \theta in the GSVD. With the proper choice of \theta, we locate similar and dissimilar patterns of variation between both data types. We discuss the properties of our algorithm using simulated data and conduct a case study with biologically verified results. Ultimately, we demonstrate the efficacy of our method on two genome-wide breast cancer studies to identify genes with large variation in expression and copy number across numerous cell line and tumor samples. Our method identifies genes that are statistically significant in both input measurements. The proposed method is useful for a wide variety of joint copy number and expression-based studies. Supplementary information is available online, including software implementations and experimental data.
Generalized singular value decomposition, cDNA microarray data, CGH microarray data, gene expression, DNA copy numbers, breast cancer.

S. K. Mitra, S. Hautaniemi, J. Astola and J. A. Berger, "Jointly Analyzing Gene Expression and Copy Number Data in Breast Cancer Using Data Reduction Models," in IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 3, no. , pp. 2-16, 2006.
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