In Kernel-based Nonlinear Subspace (KNS) methods, the subspace dimensions have a strong influence on the performance of the subspace classifier. In order to get a high classification accuracy, a large dimension is generally required. However, if the chosen subspace dimension is too large, it leads to a low performance due to the overlapping of the resultant subspaces and, if it is too small, it increases the classification error due to the poor resulting approximation. The most common approach is of an ad hoc nature, which selects the dimensions based on the so-called cumulative proportion 13 computed from the kernel matrix for each class. In this paper, we propose a new method of systematically and efficiently selecting optimal or near-optimal subspace dimensions for KNS classifiers using a search strategy and a heuristic function termed the Overlapping criterion. The rationale for this function has been motivated in the body of the paper. The task of selecting optimal subspace dimensions is reduced to finding the best ones from a given problem-domain solution space using this criterion as a heuristic function. Thus, the search space can be pruned to very efficiently find the best solution. Our experimental results demonstrate that the proposed mechanism selects the dimensions efficiently without sacrificing the classification accuracy.

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Keywords Kernel principal component analysis (kPCA), Kernel-based nonlinear subspace (KNS) classifier, State-space search algorithms, Subspace dimension selections
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Journal IEEE Transactions on Pattern Analysis and Machine Intelligence
Kim, S.-W. (Sang-Woon), & Oommen, J. (2005). On utilizing search methods to select subspace dimensions for Kernel-Based nonlinear subspace classifiers. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(1), 136–141. doi:10.1109/TPAMI.2005.15