Patent ID: 7685080

Claim:
A computer-implemented methodology for regularized least squares (RLS) classification or regression, the method executed by one or more computer systems comprising a processor and a memory, the method comprising: receiving, by a processor, a training set of data; generating a kernel matrix K based on the training set, wherein the kernel matrix is represented explicitly in an n by n matrix satisfying K ij =K( x i , x j ) and having a form K ⁡ ( x _ i , x _ j ) = exp ⁡ (  x _ i - x _ j  2 2 ⁢ σ 2 ) , where x is a vector of data points included in the training set and σ is a user-selected bandwidth parameter; computing, by the processor, an eigendecomposition of the kernel matrix K; receiving a plurality of regularization parameters λ; computing, by the processor, coefficients c for each regularization parameter λ based on the eigendecomposition of the kernel matrix K; computing, by the processor, a leave-one-out (LOO) error for each of the regularization parameters λ, wherein the LOO error for all the regularization parameters λ are computed in O(n 3 +n 2 d) time and O(n 2 ) space, where n is the number of points in d dimensions of the training set; selecting the regularization parameter λ with the lowest LOO error; identifying a hyperplane function w based on the selected regularization parameter λ and the training set of data; and storing the hyperplane function w in the memory.