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  4. Deterministic CUR for improved large-scale data analysis: An empirical study
 
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2012
Konferenzbeitrag
Titel

Deterministic CUR for improved large-scale data analysis: An empirical study

Abstract
Low-rank approximations which are computed from selected rows and columns of a given data matrix have attracted considerable attention lately. They have been proposed as an alternative to the SVD because they naturally lead to interpretable decompositions which was shown to be successful in application such as fraud detection, fMRI segmentation, and collaborative filtering. The CUR decomposition of large matrices, for example, samples rows and columns according to a probability distribution that depends on the Euclidean norm of rows or columns or on other measures of statistical leverage. At the same time, there are various deterministic approaches that do not resort to sampling and were found to often yield factorization of superior quality with respect to reconstruction accuracy. However , these are hardly applicable to large matrices as they typically suffer from high computational costs. Consequently, many practitioners in the field of data mining have abandon deterministic approaches in favor of randomized ones when dealing with today's large-scale data sets. In this paper, we empirically disprove this prejudice. We do so by introducing a novel, linear-time, deterministic CUR approach that adopts the recently introduced Simplex Volume Maximization approach for column selection. The latter has already been proven to be successful for NMF-like decompositions of matrices of billions of entries. Our exhaustive empirical study on more than $30$ synthetic and real-world data sets demonstrates that it is also beneficial for CUR-like decompositions. Compared to other determinis tic CUR-like methods, it provides comparable reconstruction quality but operates much faster so that it easily scales to matrices of billions of elements. Compared to sampling-based methods, it provides competitive reconstruction quality while staying in the same run-time complexity class.
Author(s)
Thurau, Christian
Kersting, Kristian
Bauckhage, Christian
Hauptwerk
12th SIAM International Conference on Data Mining. Proceedings
Konferenz
International Conference on Data Mining 2012
File(s)
001.pdf (890.07 KB)
Language
Englisch
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IAIS
Tags
  • data mining

  • large-scale data

  • CUR decomposition

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