Enforcement of Minimal Size and Area Constraints before and while Mining Patterns in Fuzzy Tensors

Abstract

Fuzzy tensors, i. e., n-way tensors with values in [0, 1], indicate to what extent n-tuples satisfy a Boolean predicate. In that very general context, the multidupehack algorithm mines itemset-like patterns. They are sub-tensors with values "close to 1" and can be further constrained. In particular, the analyst usually wants to focus on large-enough patterns and specifies minimal numbers of elements every pattern must contain in some of its n dimensions and/or a minimal number of n-tuples inside the pattern. Not only constraints filter out irrelevant patterns, they lower the time multidupehack takes to discover the relevant ones too. This article aims to further lower that time when minimal size/area constraints are enforced. Two algorithms are proposed. Both discard elements that no large-enough pattern can involve, i. e., they losslessly reduce the pattern space. The first algorithm runs before mining the patterns with multidupehack or with another algorithm that similarly defines them. The second algorithm, less effective but more efficient, is used while mining the patterns. Experiments on real-world fuzzy tensors show that the two algorithms sometimes divide by more than 80,000 the time multidupehack takes to discover the valid patterns.