Resistant lower rank approximation of matrices by iterative majorization

Peter Verboon, Willem Heiser

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

It is commonly known that many techniques for data analysis based on the least squares criterion are very sensitive to outliers in the data. Gabriel and Odoroff (1984) suggested a resistant approach for lower rank approximation of matrices. In this approach, weights are used to diminish the influence of outliers on the low-dimensional representation. The present paper uses iterative majorization to provide for a general algorithm for such resistant lower rank approximations which guarantees convergence. It is shown that the weights can be chosen in different ways corresponding with different objective functions. Some possible extensions of the algorithm are discussed.
Original languageEnglish
Pages (from-to)457-476
Number of pages21
JournalComputational Statistics & Data Analysis
Volume18
Issue number4
DOIs
Publication statusPublished - Nov 1994
Externally publishedYes

Keywords

  • lower rank approximation
  • resistance
  • robustness
  • majorization
  • huber function
  • biweight function

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