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Integer Matrix Approximation and Data Mining

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Abstract

Integer datasets frequently appear in many applications in science and engineering. To analyze these datasets, we consider an integer matrix approximation technique that can preserve the original dataset characteristics. Because integers are discrete in nature, to the best of our knowledge, no previously proposed technique developed for real numbers can be successfully applied. In this study, we first conduct a thorough review of current algorithms that can solve integer least squares problems, and then we develop an alternative least square method based on an integer least squares estimation to obtain the integer approximation of the integer matrices. We discuss numerical applications for the approximation of randomly generated integer matrices as well as studies of association rule mining, cluster analysis, and pattern extraction. Our computed results suggest that our proposed method can calculate a more accurate solution for discrete datasets than other existing methods.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, Liaoning, China

    Bo Dong

  2. Department of Mathematics, National Cheng Kung University, Tainan, 701, Taiwan

    Matthew M. Lin

  3. School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0765, USA

    Haesun Park

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  1. Bo Dong
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  2. Matthew M. Lin
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  3. Haesun Park
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Corresponding author

Correspondence to Matthew M. Lin.

Additional information

Bo Dong research was supported in part by the National Natural Science Foundation of China under Grant 11101067 and the Fundamental Research Funds for the Central Universities. Matthew M. Lin research was supported in part by the National Center for Theoretical Sciences of Taiwan and by the Ministry of Science and Technology of Taiwan under Grants 104-2115-M-006-017-MY3 and 105-2634-E-002-001. Haesun Park research was supported in part by the Defense Advanced Research Projects Agency (DARPA) XDATA program Grant FA8750-12-2-0309 and NSF Grants CCF-0808863, IIS-1242304, and IIS-1231742.

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Dong, B., Lin, M.M. & Park, H. Integer Matrix Approximation and Data Mining. J Sci Comput 75, 198–224 (2018). https://doi.org/10.1007/s10915-017-0531-7

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