Fast singular value decomposition for expediting computer analysis system and application thereof
AssigneeMetison Technologies Corporation
InventorJengnan Tzeng
Life of this patent
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Abstract
The present invention uses a computer analysis system of a fast singular value decomposition to overcome the bottleneck of a traditional singular value decomposition that takes much computing time for decomposing a huge number of objects, and the invention can also process a matrix in any form without being limited to symmetric matrixes only. The decomposition and subgroup concept of the fast singular value decomposition works together with the decomposition of a variance matrix and the adjustment of an average vector of a column vector are used for optimizing the singular value decomposition to improve the overall computing speed of the computer analysis system.
Claims6
A fast singular value decomposition for expediting a computer analysis system, comprising the steps of:
- (a) inputting a first matrix into the computer analysis system, wherein the first matrix is a N*p matrix, and N is the quantity of a first object, and p is the quantity of a variable;
- (b) computing an average vector of a column vector of the first matrix by the computer analysis system;
- (c) performing an overlapped random number sub-grouping for a row vector of the first matrix to randomly decompose the N first objects into K partially overlapped subgroups;
- (d) computing a variance matrix for the row vector of each subgroup;
- (e) computing a multidimensional scaling for each of the variance matrixes;
- (f) reorganizing space coordinates of the multidimensional scaling;
- (g) converting the reorganized multidimensional scaling coordinates into a principal component analysis (PCA) result;
- and
- (h) using the PCA result and the average vector to output a complete matrix data sequence by the computer analysis system.
Dependencies are inferred from the claim text.