Is margin preserved after random projection?

TL;DR

This paper investigates how random projections affect the margin in binary and multiclass classification, providing theoretical bounds and conditions for margin preservation.

Contribution

It offers a novel analysis of margin distortion after random projection, extending to multiclass cases with theoretical bounds.

Findings

Margin can be preserved under certain conditions after random projection.

Theoretical bounds for multiclass margin preservation are established.

Analysis provides insights into the robustness of random projections in classification tasks.

Abstract

Random projections have been applied in many machine learning algorithms. However, whether margin is preserved after random projection is non-trivial and not well studied. In this paper we analyse margin distortion after random projection, and give the conditions of margin preservation for binary classification problems. We also extend our analysis to margin for multiclass problems, and provide theoretical bounds on multiclass margin on the projected data.