Tensor GSVD of patient- and platform-matched tumor and normal DNA copy-number profiles uncovers chromosome arm-wide patterns of tumor-exclusive platform-consistent alterations encoding for cell transformation and predicting ovarian cancer survival.

The number of large-scale high-dimensional datasets recording different aspects of a single disease is growing, accompanied by a need for frameworks that can create one coherent model from multiple tensors of matched columns, e.g., patients and platforms, but independent rows, e.g., probes. We define and prove the mathematical properties of a novel tensor generalized singular value decomposition (GSVD), which can simultaneously find the similarities and dissimilarities, i.e., patterns of varying relative significance, between any two such tensors. We demonstrate the tensor GSVD in comparative modeling of patient- and platform-matched but probe-independent ovarian serous cystadenocarcinoma (OV) tumor, mostly high-grade, and normal DNA copy-number profiles, across each chromosome arm, and combination of two arms, separately. The modeling uncovers previously unrecognized patterns of tumor-exclusive platform-consistent co-occurring copy-number alterations (CNAs). We find, first, and validate that each of the patterns across only 7p and Xq, and the combination of 6p+12p, is correlated with a patient's prognosis, is independent of the tumor's stage, the best predictor of OV survival to date, and together with stage makes a better predictor than stage alone. Second, these patterns include most known OV-associated CNAs that map to these chromosome arms, as well as several previously unreported, yet frequent focal CNAs. Third, differential mRNA, microRNA, and protein expression consistently map to the DNA CNAs. A coherent picture emerges for each pattern, suggesting roles for the CNAs in OV pathogenesis and personalized therapy. In 6p+12p, deletion of the p21-encoding CDKN1A and p38-encoding MAPK14 and amplification of RAD51AP1 and KRAS encode for human cell transformation, and are correlated with a cell's immortality, and a patient's shorter survival time. In 7p, RPA3 deletion and POLD2 amplification are correlated with DNA stability, and a longer survival. In Xq, PABPC5 deletion and BCAP31 amplification are correlated with a cellular immune response, and a longer survival.