Depth and depth-based classification with R-package ddalpha

TL;DR

The paper introduces the R-package ddalpha, which implements data depth concepts and depth-based classifiers for multivariate and functional data, facilitating classification, visualization, and customization.

Contribution

It provides comprehensive tools for computing data depth, implementing depth-based classifiers, and visualizing data geometry, with options for user-defined methods and benchmarks.

Findings

Efficient implementation of exact and approximate data depth calculations.

Effective depth-based classifiers for multivariate and functional data.

Visualization tools for data geometry and pattern recognition quality.

Abstract

Following the seminal idea of Tukey, data depth is a function that measures how close an arbitrary point of the space is located to an implicitly defined center of a data cloud. Having undergone theoretical and computational developments, it is now employed in numerous applications with classification being the most popular one. The R-package ddalpha is a software directed to fuse experience of the applicant with recent achievements in the area of data depth and depth-based classification. ddalpha provides an implementation for exact and approximate computation of most reasonable and widely applied notions of data depth. These can be further used in the depth-based multivariate and functional classifiers implemented in the package, where the $DD\alpha$-procedure is in the main focus. The package is expandable with user-defined custom depth methods and separators. The implemented functions for depth visualization and the built-in benchmark procedures may also serve to provide insights into the geometry of the data and the quality of pattern recognition.