Manifold Based Local Classifiers: Linear and Nonlinear Approaches

Abstract In case of insufficient data samples in highdimensional classification problems, sparse scatters of samples tend to have many ‘holes’—regions that have few or no nearby training samples from the class. When such regions lie close to inter-class boundaries, the nearest neighbors of a query may lie in the wrong class, thus leading to errors in the Nearest Neighbor classification rule. The K-local hyperplane distance nearest neighbor (HKNN) algorithm tackles this problem by approximating each class with a smooth nonlinear manifold, which is considered to be locally linear. The method takes advantage of the local linearity assumption by using the distances from a query sample to the affine hulls of query’s nearest neighbors for decision making. However, HKNN is limited to using the Euclidean distance metric, which is a significant limitation in practice. In this paper we reformulate HKNN in terms of subspaces, and propose a variant, the Local Discriminative Common Vector (...

• Type: Journal
• Year: 2010
• Where: VLSISP
• Authors: Hakan Cevikalp, Diane Larlus, Marian Neamtu, Bill Triggs, Frédéric Jurie
• Keywords: Manifold, Nearest Neighbors, Nonlinear Manifolds, VLSISP 2010