Classification via local manifold approximation
This addresses classification challenges in domains with complex, overlapping data distributions, but it is incremental as it builds on local approximation methods.
The paper tackles the problem of accurate classification when feature distributions are complex and training data are limited, proposing a new classifier called LOMA that uses local manifold approximation, with a spherical variant (SPA) showing substantial gains over competitors in simulated and real data examples.
Classifiers label data as belonging to one of a set of groups based on input features. It is challenging to obtain accurate classification performance 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, this article proposes a new type of classifier based on obtaining a local approximation to the support of the data within each class in a neighborhood 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 (LOMA) classification. As a simple and theoretically supported special case having excellent performance in a broad variety of examples, we use spheres for local approximation, obtaining a SPherical Approximation (SPA) classifier. We illustrate substantial gains for SPA over competitors on a variety of challenging simulated and real data examples.