Low-rank data modeling via the Minimum Description Length principle

TL;DR

This paper introduces a method for selecting the rank of low-rank matrix models using the Minimum Description Length principle, demonstrated through background extraction in video sequences.

Contribution

It applies the MDL principle to low-rank data modeling, providing a systematic way to choose the rank without prior assumptions.

Findings

Effective background extraction in videos

MDL-based rank selection outperforms heuristic methods

Practical applicability demonstrated in real-world data

Abstract

Robust low-rank matrix estimation is a topic of increasing interest, with promising applications in a variety of fields, from computer vision to data mining and recommender systems. Recent theoretical results establish the ability of such data models to recover the true underlying low-rank matrix when a large portion of the measured matrix is either missing or arbitrarily corrupted. However, if low rank is not a hypothesis about the true nature of the data, but a device for extracting regularity from it, no current guidelines exist for choosing the rank of the estimated matrix. In this work we address this problem by means of the Minimum Description Length (MDL) principle -- a well established information-theoretic approach to statistical inference -- as a guideline for selecting a model for the data at hand. We demonstrate the practical usefulness of our formal approach with results for complex background extraction in video sequences.