Factorization with hierarchical classes analysis and with formal concept analysis
ICFCA'11 Proceedings of the 9th international conference on Formal concept analysis
Factorizing three-way ordinal data using triadic formal concepts
FQAS'11 Proceedings of the 9th international conference on Flexible Query Answering Systems
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Triadic concept analysis departs from the dyadic case by taking into account modi, such as time instances or conditions, under which objects have attributes. That is, instead of a two-dimensional table filled with 0s and 1s (equivalently, binary relation or two-dimensional binary matrix) which represents the input data to (dyadic) formal concept analysis, the input data to triadic concept analysis consists of a three-dimensional table (equivalently, ternary relation or three-dimensional binary matrix). In the ordinary triadic concept analysis, one assumes that the ternary relationship between objects, attributes, and modi, which specifies whether a given object has a given attribute under a given modus, is a yes-or-no relationship. In the present paper, we show how triadic concept analysis may be developed in a setting in which the ternary relationship between objects, attributes, and modi is a matter of degree rather than a yes-or-no relationship. We generalize the main results of the ordinary triadic concept analysis and outline applications of the presented notions and results as well as directions for future research.