Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
Approximation algorithms
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
Fuzzy Relational Systems: Foundations and Principles
Fuzzy Relational Systems: Foundations and Principles
Introduction to Algorithms
Concept Data Analysis: Theory and Applications
Concept Data Analysis: Theory and Applications
What is the Dimension of Your Binary Data?
ICDM '06 Proceedings of the Sixth International Conference on Data Mining
The role mining problem: finding a minimal descriptive set of roles
Proceedings of the 12th ACM symposium on Access control models and technologies
Factor Analysis of Incidence Data via Novel Decomposition of Matrices
ICFCA '09 Proceedings of the 7th International Conference on Formal Concept Analysis
Discovery of optimal factors in binary data via a novel method of matrix decomposition
Journal of Computer and System Sciences
PKDD'06 Proceedings of the 10th European conference on Principle and Practice of Knowledge Discovery in Databases
Crisply generated fuzzy concepts
ICFCA'05 Proceedings of the Third international conference on Formal Concept Analysis
Exploring Users' Preferences in a Fuzzy Setting
Electronic Notes in Theoretical Computer Science (ENTCS)
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We study the problem of decomposition of object-attribute matrices whose entries contain degrees to which objects have attributes. The degrees are taken from a bounded partially ordered scale. Examples of such matrices are binary matrices, matrices with entries from a finite chain, or matrices with entries from the unit interval [0, 1]. We study the problem of decomposition of a given object-attribute matrix I with degrees into an object-factor matrix A with degrees and a binary factor-attribute matrix B, with the number of factors as small as possible. We present a theorem which shows that decompositions which use particular formal concepts of I as factors for the decomposition are optimal in that the number of factors involved is the smallest possible. We show that the problem of computing an optimal decomposition is NP-hard and present two heuristic algorithms for its solution along with their experimental evaluation. For the first algorithm, we provide its approximation ratio. Experiments indicate that the second algorithm, which is considerably faster than the first one, delivers decompositions whose quality is comparable to the decompositions delivered by the first algorithm. We also present an illustrative example demonstrating a factor analysis interpretation of the decomposition studied in this paper.