Kernel-based adaptive-subspace self-organizing map as a nonlinear subspace pattern recognition

The Adaptive-Subspace Self-Organizing Map (ASSOM) has been proposed for extracting subspace detectors from the input data. In the ASSOM, each computation unit referred by neuron, has a linear subspace which consists of a set of basis vectors. After the training, each unit results in a set of subspace detector. In this paper, the ASSOM on the high-dimensional feature space with the kernel methods is proposed in order to achieve the classification for more general data such as images. By using the kernel methods, the linear subspaces in the ASSOM arc extended to the nonlinear subspaces. This leads to increase the ability of representation as a subspace. The effectiveness of the proposed method is verified by applying it in a face recognition problem under varying illumination.