An Efficient Incremental KernelPrincipal ComponentAnalysis forOnlineFeature Selection

In thispaper,a feature extraction methodfor online classification problems isproposed byextending Kernel Principal Component Analysis (KPCA).Inourprevious work, we proposed an incremental KPCA algorithm whichcould learnanewinputincrementally without keeping allthepast training data. Inthisalgorithm, eigenvectors arerepresented byalinear sumoflinearly independent datawhichareselected fromgiven training data. A serious drawbackoftheprevious IKPCAisthatmanyindependent dataarepronetobeselected during learning andthis causes large computation andmemory costs. Forthisproblem, we propose a novelapproach tothe selection ofindependent data; thatis,theyarenotselected in thehigh-dimensional feature spacebutinthelow-dimensional eigenspace spannedbythecurrenteigenvectors. Usingthis method, thenumberofindependent dataisrestricted tothe numberofeigenvectors. Thisrestriction makesthelearning of themodified IKPCA(M-IKPCA) veryfast without loosing the approximation accuracy against trueeigenvectors. Toverify the effectiveness ofM-IKPCA,thelearning timeandtheaccuracy of eigenspaces areevaluated using twoUCIbenchmark datasets. Asa result, we confirm thatthelearning ofM-IKPCAisat least 5timesfaster thantheprevious version ofIKPCA.