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Using Blind Search and Formal Concepts for Binary Factor Analysis
Using Blind Search and Formal Concepts
for Binary Factor Analysis
Aleˇs Keprt
Dept. of Computer Science, FEI, VSB Technical University Ostrava, Czech Republic
ales.keprt@vsb.cz
Abstract. Binary Factor Analysis (BFA, also known as Boolean Factor
Analysis) may help with understanding collections of binary data. Since
we can take collections of text documents as binary data too, the BFA
can be used to analyse such collections. Unfortunately, exact solving of
BFA is not easy. This article shows two BFA methods based on exact
computing, boolean algebra and the theory of formal concepts.
Keywords: Binary factor analysis, boolean algebra, formal concepts
1 Binary factor analysis
1.1 Problem definition
To describe the problem of Binary Factor Analysis (BFA) we can paraphrase
BMDP’s documentation (Bio-Medical Data Processing, see [1]).
BFA is a factor analysis of dichotomous (binary) data. This kind of analysis
differs from the classical factor analysis (see [16]) of binary valued data, even
though the goal and the model are symbolically similar. In other words, both
classical and binary analysis use symbolically the same notation, but their senses
are different.
The goal of BFA is to express p variables X = (x , x , . . . , x ) by m factors
1 2 p
(F = f , f , . . . , f ), where m p (m is considerably smaller than p ). The
1 2 m
model can be written as
X = F A
where is matrix multiplication. For n cases, data matrix X , factor scores F ,
and factor loadings A can be written as
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