Low-Rank Data Modeling via the Minimum Description Length Principle

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.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 2011
Accession Number
ADA557786

Entities

People

  • Guillermo Sapiro
  • Ignacio Ramirez

Organizations

  • University of Minnesota

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Algorithms
  • Coding
  • Computer Programming
  • Computer Vision
  • Data Analysis
  • Data Mining
  • Data Modeling
  • Data Processing
  • Data Science
  • Dimensionality Reduction
  • Eigenvectors
  • Feature Selection
  • Information Science
  • Predictive Modeling
  • Probability
  • Random Variables
  • Signal Processing

Fields of Study

  • Computer science

Readers

  • Neural Network Machine Learning.
  • Systems Analysis and Design

Technology Areas

  • AI & ML
  • AI & ML - Machine Learning Algorithms