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Incremental Singular Value Decomposition of Uncertain Data with Missing Values

  • Matthew Brand
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2350)

Abstract

We introduce an incremental singular value decomposition (svd) of incomplete data. The svd is developed as data arrives, and can handle arbitrary missing/untrusted values, correlated uncertainty across rows or columns of the measurement matrix, and user priors. Since incomplete data does not uniquely specify an svd, the procedure selects one having minimal rank. For a dense p × q matrix of low rank r, the incremental method has time complexity O(pqr) and space complexity O((p + q)r)—better than highly optimized batch algorithms such as matlab’s svd(). In cases of missing data, it produces factorings of lower rank and residual than batch svd algorithms applied to standard missing-data imputations. We show applications in computer vision and audio feature extraction. In computer vision, we use the incremental svd to develop an efficient and unusually robust subspace-estimating flow-based tracker, and to handle occlusions/missing points in structure-from-motion factorizations.

Keywords

Singular Vector Uncertain Data Minimal Rank Lanczos Method User Prior 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Matthew Brand
    • 1
  1. 1.Mitsubishi Electric Research LabsCambridgeUSA

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