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Dimensionality Reduction in Boolean Data: Comparison of Four BMF Methods

机译：布尔数据中的降维：四种BMF方法的比较

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摘要

We compare four methods for Boolean matrix factorization (BMF). The oldest of these methods is the 8M method implemented in the BMDP statistical software package developed in the 1960s. The three other methods were developed recently. All the methods compute from an input object-attribute matrix I two matrices, namely an object-factor matrix A and a factor-attribute matrix B in such a way that the Boolean matrix product of A and B is approximately equal to I. Such decompositions are utilized directly in Boolean factor analysis or indirectly as a dimensionality reduction method for Boolean data in machine learning. While some compaxison of the BMF methods with matrix decomposition methods designed for real valued data exists in the literature, a mutual comparison of the various BMF methods is a severely neglected topic. In this paper, we compare the four methods on real datasets. In particular, we observe the reconstruction ability of the first few computed factors as well as the number of computed factors necessary to fully reconstruct the input matrix, i.e. the approximation to the Boolean rank of I computed by the methods. In addition, we present some general remarks on all the methods being compared.
机译：我们比较了布尔矩阵分解（BMF）的四种方法。这些方法中最早的方法是在1960年代开发的BMDP统计软件包中实现的8M方法。最近开发了其他三种方法。所有方法都从输入的对象属性矩阵I计算两个矩阵，即对象因子矩阵A和因子属性矩阵B，使A和B的布尔矩阵乘积近似等于I。直接用于布尔因子分析或间接用作机器学习中布尔数据的降维方法。虽然在文献中存在一些BMF方法与为实值数据设计的矩阵分解方法的共谋，但各种BMF方法的相互比较却是一个被严重忽略的话题。在本文中，我们在真实数据集上比较了这四种方法。特别地，我们观察到前几个计算因子的重构能力以及完全重构输入矩阵所必需的计算因子的数量，即通过这些方法计算的I的布尔秩的近似值。另外，我们对所有被比较的方法给出一些一般性的评论。

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  • 来源
    《Clustering high-dimensional data》|2012年|118-133|共16页
  • 会议地点 Naples(IT)
  • 作者

    Eduard Bartl; Radim Belohlavek; Petr Osicka; Hana Rezankova;

  • 作者单位

    Data Analysis and Modeling Laboratory (DAMOL), Department of Computer Science, Palacky Univeristy, Olomouc, Czech Republic;

    Data Analysis and Modeling Laboratory (DAMOL), Department of Computer Science, Palacky Univeristy, Olomouc, Czech Republic;

    Data Analysis and Modeling Laboratory (DAMOL), Department of Computer Science, Palacky Univeristy, Olomouc, Czech Republic;

    Department of Statistics and Probability, Faculty of Informatics and Statistics, University of Economics, Prague, Czech Republic;

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