Multivariate and functional classification using depth and distance

TL;DR

This paper introduces a robust, invariant distance-based classification method for multivariate and functional data, utilizing the DistSpace transform combined with kNN, and compares it with existing approaches through experiments.

Contribution

It proposes a novel classification framework using distance measures based on depth functions, enhancing robustness and invariance in multivariate and functional data analysis.

Findings

The method performs well on real and simulated data.

It outperforms some existing classifiers in robustness.

The approach is simple, effective, and widely applicable.

Abstract

We construct classifiers for multivariate and functional data. Our approach is based on a kind of distance between data points and classes. The distance measure needs to be robust to outliers and invariant to linear transformations of the data. For this purpose we can use the bagdistance which is based on halfspace depth. It satisfies most of the properties of a norm but is able to reflect asymmetry when the class is skewed. Alternatively we can compute a measure of outlyingness based on the skew-adjusted projection depth. In either case we propose the DistSpace transform which maps each data point to the vector of its distances to all classes, followed by k-nearest neighbor (kNN) classification of the transformed data points. This combines invariance and robustness with the simplicity and wide applicability of kNN. The proposal is compared with other methods in experiments with real and simulated data.