Constraint-Based Mining of Closed Patterns in Noisy n-ary Relations. (Fouille Sous Contraintes de Motifs Fermés dans des Relations n-aires Bruitées)

Useful knowledge discovery processes can be based on patterns extracted from large datasets. Designing efficient data mining algorithms to compute collections of relevant patterns is an active research domain. Many datasets record whether some properties hold for some objects, e. g., whether an item is bought by a customer or whether a gene is over-expressed in a biological sample. Such datasets are binary relations and can be represented as 0/1 matrices. In such matrices, a closed itemset is a maximal rectangle of ’1’s modulo arbitrary permutations of the lines (objects) and the columns (properties). Thus, every closed itemset supports the discovery of a maximal subset of objects sharing the same maximal subset of properties. Efficiently extracting every closed itemset satisfying user-defined relevancy constraints has been extensively studied. Despite its success across many application domains, this framework often turns out to be too narrow. First of all, many datasets are n-ary relations, i. e., 0/1 tensors. Reducing their analysis to two dimensions is ignoring potentially interesting additional dimensions, e. g., where a customer buys an item (localized analysis) or when a gene expression is measured (kinetic analysis). The presence of noise in most real-life datasets is a second issue, which leads to the fragmentation of the patterns to discover. Generalizing the definition of a closed itemset to make it suit relations of higher arity and tolerate some noise is straightforward (maximal hyper-rectangle with an upper bound of ’0’s tolerated per hyper-plan). On the contrary, generalizing their extraction is very hard. Indeed, classical algorithms exploit a mathematical property (the Galois connection) of the closed itemsets that none of the two generalizations preserve. That is why our extractor browses the candidate pattern space in an original way that does not favor any dimension. This search can be guided by a very broad class of relevancy constraints the patterns must satisfy. In particular, this thesis studies constraints specifically designed for mining almost-persistent cliques in dynamic graphs. Our extractor is orders of magnitude faster than known competitors focusing on exact patterns in ternary relations or on noise-tolerant patterns in binary relations. Despite these results, such an exhaustive approach often cannot, in a reasonable time, tolerate as much noise as the dataset contains. In this case, complementing the extraction with a hierarchical agglomeration of the (insufficiently noise-tolerant) patterns increases the quality of the returned collection of patterns.