Directional Statistics in Machine Learning: a Brief Review
It addresses the need for tailored models in machine learning for data where direction is more important than magnitude, but it is incremental as it primarily reviews existing methods.
The paper reviews mathematical models for machine learning with directional data, focusing on normalized vectors on the unit hypersphere or real projective plane, and outlines technical aspects, software, applications, and open challenges.
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.