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Binary matrix factorization for analyzing gene expression data

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Abstract

The advent of microarray technology enables us to monitor an entire genome in a single chip using a systematic approach. Clustering, as a widely used data mining approach, has been used to discover phenotypes from the raw expression data. However traditional clustering algorithms have limitations since they can not identify the substructures of samples and features hidden behind the data. Different from clustering, biclustering is a new methodology for discovering genes that are highly related to a subset of samples. Several biclustering models/methods have been presented and used for tumor clinical diagnosis and pathological research. In this paper, we present a new biclustering model using Binary Matrix Factorization (BMF). BMF is a new variant rooted from non-negative matrix factorization (NMF). We begin by proving a new boundedness property of NMF. Two different algorithms to implement the model and their comparison are then presented. We show that the microarray data biclustering problem can be formulated as a BMF problem and can be solved effectively using our proposed algorithms. Unlike the greedy strategy-based algorithms, our proposed algorithms for BMF are more likely to find the global optima. Experimental results on synthetic and real datasets demonstrate the advantages of BMF over existing biclustering methods. Besides the attractive clustering performance, BMF can generate sparse results (i.e., the number of genes/features involved in each biclustering structure is very small related to the total number of genes/features) that are in accordance with the common practice in molecular biology.

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Authors and Affiliations

  1. School of Statistics, Central University of Finance and Economics, Beijing, People’s Republic of China

    Zhong-Yuan Zhang

  2. School of Computing and Information Sciences, Florida International University, Miami, FL, USA

    Tao Li

  3. Department of Computer Science and Engineering, University of Texas, Arlington, TX, USA

    Chris Ding

  4. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, People’s Republic of China

    Xian-Wen Ren & Xiang-Sun Zhang

Authors
  1. Zhong-Yuan Zhang
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  2. Tao Li
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  3. Chris Ding
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  4. Xian-Wen Ren
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  5. Xiang-Sun Zhang
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Correspondence to Tao Li.

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Responsible editor: Pierre Baldi.

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Zhang, ZY., Li, T., Ding, C. et al. Binary matrix factorization for analyzing gene expression data. Data Min Knowl Disc 20, 28–52 (2010). https://doi.org/10.1007/s10618-009-0145-2

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