Preconditioning Kernel Matrices
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چکیده
Kernel Machines and Solving Linear Systems ▶ Operate in a high-dimensional, implicit feature space; ▶ Rely on the construction of an n× n Gram matrix K; ▶ Popular kernels: – RBF : k (xi,xj) = σ exp ( − 12d 2 ) ; – Matérn : kv= 3 2 (xi,xj) = σ 2 ( 1 + √ 3d ) exp ( − √ 3d ) ; where d = (xi − xj) Λ (xi − xj). ▶ Involve the solution of linear systems Kz = v; ▶ Cholesky Decomposition: – O(n) space and O(n) time unfeasible for large n. Fig. 1: Kernel machines enable non-linear separation of data.
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تاریخ انتشار 2016