Sparse Kernel Feature Analysis

Kernel Principal Component Analysis (KPCA) has proven to be a versatile tool for unsupervised learning, however at a high computational cost due to the dense expansions in terms of kernel functions. We overcome this problem by proposing a new class of feature extractors employing ` 1 norms in coefficient space instead of the reproducing kernel Hilbert space in which KPCA was originally formulated in. Moreover, the modified setting allows us to efficiently extract features maximizing criteria other than the variance much in a projection pursuit fashion. 1 Introduction The problems in unsupervised learning are by far less precisely defined than in the supervised counterpart. Usually no explicit cost function exists with desired outputs or anything similar. Instead, one has to make certain assumptions on the data, with respect to which several questions may be asked. A possible problem is: "Which properties of the data can be extracted with high confidence?" Or in other words, which sim..