Rank Matrix Factorisation

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• 作者：Thanh Le Van (10)
  Matthijs van Leeuwen (10)
  Siegfried Nijssen (10) (11)
  Luc De Raedt (10)
  
  10. Department of Computer Science ; KU Leuven ; Leuven ; Belgium
  11. Leiden Institute for Advanced Computer Science ; Universiteit Leiden ; Leiden ; The Netherlands
  
• 关键词：Matrix factorisation ; Rank data ; Integer linear programming
• 刊名：Lecture Notes in Computer Science
• 出版年：2015
• 出版时间：2015
• 年：2015
• 卷：9077
• 期：1
• 页码：734-746
• 全文大小：455 KB
• 参考文献：1. Van, T, Leeuwen, M, Nijssen, S, Fierro, AC, Marchal, K, Raedt, L Ranked tiling. In: Calders, T, Esposito, F, H眉llermeier, E, Meo, R eds. (2014) Machine Learning and Knowledge Discovery in Databases. Springer, Heidelberg, pp. 98-113 CrossRef
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  11. Kluger, Y, Basri, R, Chang, JT, Gerstein, M (2003) Spectral Biclustering of Microarray Data : Coclustering Genes and Conditions. Genome Research 13: pp. 703-716 CrossRef
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  16. Truong, D.T., Battiti, R., Brunato, M.: Discovering non-redundant overlapping biclusters on gene expression data. In: ICDM 2013, pp. 747鈥?56. IEEE (2013)
  17. Deng, K, Han, S, Li, KJ, Liu, JS (2014) Bayesian Aggregation of Order-Based Rank Data. Journal of the American Statistical Association 109: pp. 1023-1039 CrossRef
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• 作者单位：Advances in Knowledge Discovery and Data Mining
• 丛书名：978-3-319-18037-3
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349

文摘

We introduce the problem of rank matrix factorisation (RMF). That is, we consider the decomposition of a rank matrix, in which each row is a (partial or complete) ranking of all columns. Rank matrices naturally appear in many applications of interest, such as sports competitions. Summarising such a rank matrix by two smaller matrices, in which one contains partial rankings that can be interpreted as local patterns, is therefore an important problem. After introducing the general problem, we consider a specific instance called Sparse RMF, in which we enforce the rank profiles to be sparse, i.e., to contain many zeroes. We propose a greedy algorithm for this problem based on integer linear programming. Experiments on both synthetic and real data demonstrate the potential of rank matrix factorisation.