Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
Introduction to Algorithms
A Triadic Approach to Formal Concept Analysis
ICCS '95 Proceedings of the Third International Conference on Conceptual Structures: Applications, Implementation and Theory
TRIAS--An Algorithm for Mining Iceberg Tri-Lattices
ICDM '06 Proceedings of the Sixth International Conference on Data Mining
What is the Dimension of Your Binary Data?
ICDM '06 Proceedings of the Sixth International Conference on Data Mining
Factor Analysis of Incidence Data via Novel Decomposition of Matrices
ICFCA '09 Proceedings of the 7th International Conference on Formal Concept Analysis
Optimal triangular decompositions of matrices with entries from residuated lattices
International Journal of Approximate Reasoning
Tensor Decompositions and Applications
SIAM Review
Discovery of optimal factors in binary data via a novel method of matrix decomposition
Journal of Computer and System Sciences
Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation
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
From triconcepts to triclusters
RSFDGrC'11 Proceedings of the 13th international conference on Rough sets, fuzzy sets, data mining and granular computing
Review: Formal Concept Analysis in knowledge processing: A survey on models and techniques
Expert Systems with Applications: An International Journal
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We present a problem of factor analysis of three-way binary data. Such data is described by a 3-dimensional binary matrix I, describing a relationship between objects, attributes, and conditions. The aim is to decompose I into three binary matrices, an object-factor matrix A, an attribute-factor matrix B, and a condition-factor matrix C, with a small number of factors. The difference from the various decomposition-based methods of analysis of three-way data consists in the composition operator and the constraint on A, B, and C to be binary. We present a theoretical analysis of the decompositions and show that optimal factors for such decompositions are provided by triadic concepts developed in formal concept analysis. Moreover, we present an illustrative example, propose a greedy algorithm for computing the decompositions.