Projection pursuit for discrete data

TL;DR

This paper introduces a method for exploratory analysis of discrete data using projection pursuit with the discrete Radon transform, identifying informative views that deviate from uniformity.

Contribution

It develops a novel approach for discrete data analysis combining projection pursuit with the discrete Radon transform, including an automated procedure for finding informative projections.

Findings

Most projections of discrete data are close to uniform.

Informative summaries are projections that deviate from uniformity.

The method effectively analyzes syllabic data from classical texts.

Abstract

This paper develops projection pursuit for discrete data using the discrete Radon transform. Discrete projection pursuit is presented as an exploratory method for finding informative low dimensional views of data such as binary vectors, rankings, phylogenetic trees or graphs. We show that for most data sets, most projections are close to uniform. Thus, informative summaries are ones deviating from uniformity. Syllabic data from several of Plato's great works is used to illustrate the methods. Along with some basic distribution theory, an automated procedure for computing informative projections is introduced.