Neighborhood selection for dimensionality reduction

Though a great deal of research work has been devoted to the development of dimensionality reduction algorithms, the problem is still open. The most recent and effective techniques, assuming datasets drawn from an underlying low dimensional manifold embedded into an high dimensional space, look for "small enough" neighborhoods which should represent the underlying manifold portion. Unfortunately, neighborhood selection is an open problem, for the presence of noise, outliers, points not uniformly distributed, and to unexpected high manifold curvatures, causing the inclusion of geodesically distant points in the same neighborhood. In this paper we describe our neighborhood selection algorithm, called ONeS; it exploits both distance and angular information to form neighborhoods containing nearby points that share a common local structure in terms of curvature. The reported experimental results show the enhanced quality of the neighborhoods computed by ONeS w.r.t. the commonly used k-neighborhoods solely employing the euclidean distance.