Fast factorization by similarity in formal concept analysis of data with fuzzy attributes

被引:50
作者
Belohlavek, Radim [1 ]
Dvorak, Jiri
Outrata, Jan
机构
[1] SUNY Binghamton, Dept Syst Sci & Ind Engn, Binghamton, NY 13902 USA
[2] Palacky Univ, Dept Comp Sci, CZ-77900 Olomouc, Czech Republic
关键词
tabular data; clustering; formal concept analysis; fuzzy attributes; similarity; factorization;
D O I
10.1016/j.jcss.2007.03.016
中图分类号
TP3 [计算技术、计算机技术];
学科分类号
0812 ;
摘要
We present a method of fast factorization in formal concept analysis (FCA) of data with fuzzy attributes. The output of FCA consists of a partially ordered collection of clusters extracted from a data table describing objects and their attributes. The collection is called a concept lattice. Factorization by similarity enables us to obtain, instead of a possibly large concept lattice, its factor lattice. The elements of the factor lattice are maximal blocks of clusters which are pairwise similar to degree exceeding a user-specified threshold. The factor lattice thus represents an approximate version of the original concept lattice. We describe a fuzzy closure operator the fixed points of which are just clusters which uniquely determine the blocks of clusters of the factor lattice. This enables us to compute the factor lattice directly from the data without the need to compute the whole concept lattice. We present theoretical solution and examples demonstrating the speed-up of our method. (C) 2007 Elsevier Inc. All rights reserved.
引用
收藏
页码:1012 / 1022
页数:11
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