Combining fuzzy information from multiple systems (extended abstract)
PODS '96 Proceedings of the fifteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Combining fuzzy information: an overview
ACM SIGMOD Record
Introduction to Algorithms
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
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
Boolean Factor Analysis by Attractor Neural Network
IEEE Transactions on Neural Networks
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
Optimal decompositions of matrices with grades into binary and graded matrices
Annals of Mathematics and Artificial Intelligence
Factorization with hierarchical classes analysis and with formal concept analysis
ICFCA'11 Proceedings of the 9th international conference on Formal concept analysis
What is a fuzzy concept lattice? II
RSFDGrC'11 Proceedings of the 13th international conference on Rough sets, fuzzy sets, data mining and granular computing
Creating fuzzy concepts: the one-sided threshold, fuzzy closure and factor analysis methods
RSFDGrC'11 Proceedings of the 13th international conference on Rough sets, fuzzy sets, data mining and granular computing
From triconcepts to triclusters
RSFDGrC'11 Proceedings of the 13th international conference on Rough sets, fuzzy sets, data mining and granular computing
RSKT'11 Proceedings of the 6th international conference on Rough sets and knowledge technology
Factorizing three-way ordinal data using triadic formal concepts
FQAS'11 Proceedings of the 9th international conference on Flexible Query Answering Systems
Closure spaces of isotone galois connections and their morphisms
AI'11 Proceedings of the 24th international conference on Advances in Artificial Intelligence
A macroscopic approach to FCA and its various fuzzifications
ICFCA'12 Proceedings of the 10th international conference on Formal Concept Analysis
Row and Column Spaces of Matrices over Residuated Lattices
Fundamenta Informaticae - Concept Lattices and Their Applications
Hi-index | 0.00 |
Matrix decomposition methods provide representations of an object-variable data matrix by a product of two different matrices, one describing relationship between objects and hidden variables or factors, and the other describing relationship between the factors and the original variables. We present a novel approach to decomposition and factor analysis of matrices with incidence data. The matrix entries are grades to which objects represented by rows satisfy attributes represented by columns, e.g. grades to which an image is red or a person performs well in a test. We assume that the grades belong to a scale bounded by 0 and 1 which is equipped with certain aggregation operators and forms a complete residuated lattice. We present an approximation algorithm for the problem of decomposition of such matrices with grades into products of two matrices with grades with the number of factors as small as possible. Decomposition of binary matrices into Boolean products of binary matrices is a special case of this problem in which 0 and 1 are the only grades. Our algorithm is based on a geometric insight provided by a theorem identifying particular rectangular-shaped submatrices as optimal factors for the decompositions. These factors correspond to formal concepts of the input data and allow for an easy interpretation of the decomposition. We present the problem formulation, basic geometric insight, algorithm, illustrative example, experimental evaluation.