a higher-order generalized singular value decomposition for comparison of global mrna expression from multiple organisms高阶广义奇异值分解进行比较,从多个生物全球mrna的表达.pdfVIP

A Higher-Order Generalized Singular Value Decomposition for Comparison of Global mRNA Expression from Multiple Organisms 1 2 3 4 Sri Priya Ponnapalli , Michael A. Saunders , Charles F. Van Loan , Orly Alter * 1 Department of Electrical and Computer Engineering, University of Texas at Austin, Texas, United States of America, 2 Department of Management Science and Engineering, Stanford University, Stanford, California, United States of America, 3 Department of Computer Science, Cornell University, Ithaca, New York, United States of America, 4 Scientific Computing and Imaging (SCI) Institute and Departments of Bioengineering and Human Genetics, University of Utah, Salt Lake City, Utah, United States of America Abstract The number of high-dimensional datasets recording multiple aspects of a single phenomenon is increasing in many areas of science, accompanied by a need for mathematical frameworks that can compare multiple large-scale matrices with different row dimensions. The only such framework to date, the generalized singular value decomposition (GSVD), is limited to two matrices. We mathematically define a higher-order GSVD (HO GSVD) for N$2 matrices Di [Rmi |n , each with full column T rank. Each matrix is exactly factored as D = U S V , where V, identical in all factorizations, is obtained from the eigensystem i i i SV = VL of the arithmetic mean S of all pairwise quotients A A {1 of the matrices A ~DT D , i?j . We prove that this i j i i i decomposition extends to