Locality Preserving Projections with adaptive neighborhood size

Abstract

Feature extraction methods are widely employed to reduce dimensionality of data and enhance the discriminative information. Among the methods, manifold learning approaches have been developed to detect the underlying manifold structure of the data based on local invariants, which are usually guaranteed by an adjacent graph of the sampled data set. The performance of the manifold learning approaches is however affected by the locality of the data, i.e. what is the neighborhood size for suitably representing the locality? In this paper, we address this issue through proposing a method to adaptively select the neighborhood size. It is applied to the manifold learning approach Locality Preserving Projections (LPP) which is a popular linear reduction algorithm. The effectiveness of the adaptive neighborhood selection method is evaluated by performing classification and clustering experiments on the real-life data sets.