Introduction to algorithms
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
Concept Data Analysis: Theory and Applications
Concept Data Analysis: Theory and Applications
Representation of Concept Lattices by Bidirectional Associative Memories
Neural Computation
Transformation invariant component analysis for binary images
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
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
Fast factorization by similarity in formal concept analysis of data with fuzzy attributes
Journal of Computer and System Sciences
Towards a machine learning approach based on incremental concept formation
Intelligent Data Analysis
PKDD'06 Proceedings of the 10th European conference on Principle and Practice of Knowledge Discovery in Databases
Boolean Factor Analysis by Attractor Neural Network
IEEE Transactions on Neural Networks
Factor Analysis of Incidence Data via Novel Decomposition of Matrices
ICFCA '09 Proceedings of the 7th International Conference on Formal Concept Analysis
Distributed Algorithm for Computing Formal Concepts Using Map-Reduce Framework
IDA '09 Proceedings of the 8th International Symposium on Intelligent Data Analysis: Advances in Intelligent Data Analysis VIII
Optimal triangular decompositions of matrices with entries from residuated lattices
International Journal of Approximate Reasoning
RelMiCS '09/AKA '09 Proceedings of the 11th International Conference on Relational Methods in Computer Science and 6th International Conference on Applications of Kleene Algebra: Relations and Kleene Algebra in Computer Science
Comparison of Data Structures for Computing Formal Concepts
MDAI '09 Proceedings of the 6th International Conference on Modeling Decisions for Artificial Intelligence
Computing the lattice of all fixpoints of a fuzzy closure operator
IEEE Transactions on Fuzzy Systems - Special section on computing with words
A new algebraic structure for formal concept analysis
Information Sciences: an International Journal
Factorizing three-way binary data with triadic formal concepts
KES'10 Proceedings of the 14th international conference on Knowledge-based and intelligent information and engineering systems: Part I
Parallel algorithm for computing fixpoints of Galois connections
Annals of Mathematics and Artificial Intelligence
Optimal decompositions of matrices with grades into binary and graded matrices
Annals of Mathematics and Artificial Intelligence
New measure of boolean factor analysis quality
ICANNGA'11 Proceedings of the 10th international conference on Adaptive and natural computing algorithms - Volume Part I
Factorization with hierarchical classes analysis and with formal concept analysis
ICFCA'11 Proceedings of the 9th international conference on Formal concept analysis
Model order selection for boolean matrix factorization
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
Information Sciences: an International Journal
Formal context coverage based on isolated labels: An efficient solution for text feature extraction
Information Sciences: an International Journal
Knowledge discovery in data using formal concept analysis and random projections
International Journal of Applied Mathematics and Computer Science
Possibility theory and formal concept analysis: Characterizing independent sub-contexts
Fuzzy Sets and Systems
Factorizing three-way ordinal data using triadic formal concepts
FQAS'11 Proceedings of the 9th international conference on Flexible Query Answering Systems
Multi-assignment clustering for boolean data
The Journal of Machine Learning Research
ICFCA'12 Proceedings of the 10th international conference on Formal Concept Analysis
Computing Formal Concepts by Attribute Sorting
Fundamenta Informaticae - Concept Lattices and Their Applications
Review: Formal Concept Analysis in knowledge processing: A survey on models and techniques
Expert Systems with Applications: An International Journal
Granularity of attributes in formal concept analysis
Information Sciences: an International Journal
Characteristic matrix of covering and its application to Boolean matrix decomposition
Information Sciences: an International Journal
Exploring Users' Preferences in a Fuzzy Setting
Electronic Notes in Theoretical Computer Science (ENTCS)
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We present a novel method of decomposition of an nxm binary matrix I into a Boolean product A@?B of an nxk binary matrix A and a kxm binary matrix B with k as small as possible. Attempts to solve this problem are known from Boolean factor analysis where I is interpreted as an object-attribute matrix, A and B are interpreted as object-factor and factor-attribute matrices, and the aim is to find a decomposition with a small number k of factors. The method presented here is based on a theorem proved in this paper. It says that optimal decompositions, i.e. those with the least number of factors possible, are those where factors are formal concepts in the sense of formal concept analysis. Finding an optimal decomposition is an NP-hard problem. However, we present an approximation algorithm for finding optimal decompositions which is based on the insight provided by the theorem. The algorithm avoids the need to compute all formal concepts and significantly outperforms a greedy approximation algorithm for a set covering problem to which the problem of matrix decomposition is easily shown to be reducible. We present results of several experiments with various data sets including those from CIA World Factbook and UCI Machine Learning Repository. In addition, we present further geometric insight including description of transformations between the space of attributes and the space of factors.