Model Averaging and Dimension Selection for the Singular Value Decomposition

Abstract

Many multivariate data analysis techniques for an m x n matrix Y are related to the model Y = M+E, where Y is an m x n matrix of full rank and M is an unobserved mean matrix of rank K < (m^n). Typically the rank of M is estimated in a heuristic way and then the least-squares estimate of M is obtained via the singular value decomposition of Y, yielding an estimate that can have a very high variance. In this paper we suggest a model-based alternative to the above approach by providing prior distributions and posterior estimation for the rank of M and the components of its singular value decomposition.

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Document Details

Document Type
Technical Report
Publication Date
Jan 10, 2006
Accession Number
ADA454966

Entities

People

  • Peter D. Hoff

Organizations

  • University of Washington

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Algorithms
  • Bessel Functions
  • Data Analysis
  • Data Mining
  • Data Science
  • Decomposition
  • Eigenvalues
  • Factor Analysis
  • Information Processing
  • Information Science
  • Markov Chains
  • Monte Carlo Method
  • Normal Distribution
  • Probability
  • Random Variables
  • Sampling
  • Statistical Algorithms

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Statistical inference.