Incremental singular value decomposition of incomplete data
AssigneeMitsubishi Electric Research Laboratories, Inc.
InventorMatthew E. Brand
Life of this patent
Estimating the term…
Abstract
A method models data values acquired by measuring a natural phenomena. Samples are acquired of the natural phenomena, each sample is arranged as a vector c of the data values. Some of the data values may be missing. The vectors c are decomposed into five matrices, respectively, a subspace Upxr, singular values srxl, an encoding Vqxr, a subspace rotation U′rxr, an encoding transform V′rxr, where p indicates the number of discrete data values in each sample, q is a number of samples, and r is a rank of a decomposition of the data values. The five matrices can then be multiplied according to UU′diag(s)V′TVT to obtain a best linear approximation of the natural phenomena for any value of r less than both p and q, where T is a matrix transpose operator.
Claims13
A method for modeling data values acquired by measuring a real-world phenomena, comprising:
- acquiring a plurality of samples of the natural phenomena, each sample arranged as a vector c of the data values;
- decomposing the plurality of vectors c into five matrices, respectively, a subspace Upxr, singular values srxl, an encoding Vqxr, a subspace rotation U′rxr, and an encoding transform V′rxr, where p indicates the number of discrete data values in each sample, q is a number of samples, and r is a rank of a decomposition of the data values;
- and
- multiplying the five matrices UU′diag(s)V′TVT to obtain a best linear approximation of the real-world phenomena for any value of r less than both p and q, and where T is a matrix transpose operator.
Dependencies are inferred from the claim text.