# Nested Cavity Classifier: performance and remedy

## TL;DR

This paper evaluates the Nested Cavity Classifier's limitations, introduces a hybrid approach with LDA called NCDA, and demonstrates through simulations that NCDA outperforms NCC and rivals traditional discriminant methods.

## Contribution

It identifies the inefficiency of NCC and proposes NCDA, a novel hybrid classifier combining NCC with LDA, improving performance in higher-dimensional spaces.

## Key findings

- NCC can be inefficient in certain scenarios.
- NCDA consistently outperforms NCC in simulations.
- NCDA competes with LDA and QDA in classification accuracy.

## Abstract

Nested Cavity Classifier (NCC) is a classification rule that pursues partitioning the feature space, in parallel coordinates, into convex hulls to build decision regions. It is claimed in some literatures that this geometric-based classifier is superior to many others, particularly in higher dimensions. First, we give an example on how NCC can be inefficient, then motivate a remedy by combining the NCC with the Linear Discriminant Analysis (LDA) classifier. We coin the term Nested Cavity Discriminant Analysis (NCDA) for the resulting classifier. Second, a simulation study is conducted to compare both, NCC and NCDA to another two basic classifiers, Linear and Quadratic Discriminant Analysis. NCC alone proves to be inferior to others, while NCDA always outperforms NCC and competes with LDA and QDA.