Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
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
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
Triadic Concept Analysis of Data with Fuzzy Attributes
GRC '10 Proceedings of the 2010 IEEE International Conference on Granular Computing
Optimal Factorization of Three-Way Binary Data
GRC '10 Proceedings of the 2010 IEEE International Conference on Granular Computing
Boolean Factor Analysis for Data Preprocessing in Machine Learning
ICMLA '10 Proceedings of the 2010 Ninth International Conference on Machine Learning and Applications
PKDD'06 Proceedings of the 10th European conference on Principle and Practice of Knowledge Discovery in Databases
Optimal decompositions of matrices with entries from residuated lattices
Journal of Logic and Computation
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The paper presents a new approach to factor analysis of three-way ordinal data, i.e. data described by a 3-dimensional matrix I with values in an ordered scale. The matrix describes a relationship between objects, attributes, and conditions. The problem consists in finding factors for I, i.e. finding a decomposition of I into three matrices, an object-factor matrix A, an attribute-factor matrix B, and a condition-factor matrix C, with the number of factors as small as possible. The difference from the decomposition-based methods of analysis of three-way data consists in the composition operator and the constraint on A, B, and C to be matrices with values in an ordered scale. We prove that optimal decompositions are achieved by using triadic concepts of I, developed within formal concept analysis, and provide results on natural transformations between the space of attributes and conditions and the space of factors. We present an illustrative example demonstrating the usefulness of finding factors and a greedy algorithm for computing decompositions.