Patent ID: 7359550

Claim:
A computer implemented method for modeling data values acquired by measuring a real-world phenomenon, comprising the steps of: measuring a natural phenomenon to acquire a plurality of samples of the natural phenomenon, in which the samples are in a form of an extremely sparse array of consumer-product preference scores; arranging each sample as a vector c of discrete data values in a matrix M stored in a memory of a computer system; decomposing the plurality of vectors c of the matrix M into five matrices, respectively, a subspace U pxr , singular values s rxl , an encoding V qxr , a subspace rotation U′ rxr , and an encoding transform V′ rxr , where p indicates the number of the discrete data values in each sample, q is a number of the samples, and r is a rank of a decomposition of the discrete data values; multiplying the five matrices UU′ diag(s)V′ T V T obtain a best linear approximation of the real-world phenomenon for any value of the rank r less than both p and q, and where T is a matrix transpose operator; and predicting missing consumer-product preference scores using the best linear approximation in a collaborative filtering application.