Classification via local manifold approximation

Abstract

Classifiers label data as belonging to one of a set of groups based on input features. It is challenging to achieve accurate classification when the feature distributions in the different classes are complex, with nonlinear, overlapping and intersecting supports. This is particularly true when training data are limited. To address this problem, we propose a new type of classifier based on obtaining a local approximation to the support of the data within each class in a neighbourhood of the feature to be classified, and assigning the feature to the class having the closest support. This general algorithm is referred to as local manifold approximation classification. As a simple and theoretically supported special case, which is shown to have excellent performance across a broad variety of examples, we use spheres for local approximation, obtaining a spherical approximation classifier.