Directional Statistics in Machine Learning: a Brief Review

TL;DR

This paper reviews statistical models for directional data in machine learning, focusing on high-dimensional vectors on spheres and projective planes, discussing mathematical foundations, applications, and open challenges.

Contribution

It provides a concise overview of models, technical considerations, and open problems related to directional statistics in high-dimensional machine learning.

Findings

Summarizes common mathematical models for directional data.

Highlights technical aspects and software tools.

Identifies open mathematical challenges.

Abstract

The modern data analyst must cope with data encoded in various forms, vectors, matrices, strings, graphs, or more. Consequently, statistical and machine learning models tailored to different data encodings are important. We focus on data encoded as normalized vectors, so that their "direction" is more important than their magnitude. Specifically, we consider high-dimensional vectors that lie either on the surface of the unit hypersphere or on the real projective plane. For such data, we briefly review common mathematical models prevalent in machine learning, while also outlining some technical aspects, software, applications, and open mathematical challenges.