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(Neural Computation. 2006;18:2928-2935.)
© 2006 The MIT Press

Note

Kernel Least-Squares Models Using Updates of the Pseudoinverse

E. Andelic

andelic{at}iesk.et.uni-magdeburg.de

M. Schafföner

schaffoe{at}iesk.et.uni-magdeburg.de

M. Katz

katz{at}iesk.et.uni-magdeburg.de

S. E. Krüger

skruger{at}iesk.et.uni-magdeburg.de

A. Wendemuth

wendemu{at}iesk.et.uni-magdeburg.de Cognitive Systems Group, IESK, Otto-von-Guericke-University, 39016 Magdeburg, Germany

Sparse nonlinear classification and regression models in reproducing kernel Hilbert spaces (RKHSs) are considered. The use of Mercer kernels and the square loss function gives rise to an overdetermined linear least-squares problem in the corresponding RKHS. When we apply a greedy forward selection scheme, the least-squares problem may be solved by an order-recursive update of the pseudoinverse in each iteration step. The computational time is linear with respect to the number of the selected training samples.






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