# Classification via local manifold approximation

## TL;DR

This paper introduces a novel local manifold approximation classifier called LOMA, which improves classification accuracy for complex, overlapping, and intersecting data supports, especially with limited training data.

## Contribution

It proposes a new local approximation-based classification method, with a specific sphere-based implementation called SPA, demonstrating superior performance over existing methods.

## Key findings

- SPA outperforms competitors on simulated data
- SPA achieves substantial accuracy gains on real datasets
- The method effectively handles complex, nonlinear class supports

## Abstract

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.