Discovering Knowledge from Local Patterns with Global Constraints

It is well known that local patterns are at the core of a lot of knowledge which may be discovered from data. Nevertheless, use of local patterns is limited by their huge number and computational costs. Several approaches (e.g., condensed representations, pattern set discovery) aim at grouping or synthesizing local patterns to provide a global view of the data. A global pattern is a pattern which is a set or a synthesis of local patterns coming from the data. In this paper, we propose the idea of global constraints to write queries addressing global patterns. A key point is the ability to bias the designing of global patterns according to the expectation of the user. For instance, a global pattern can be oriented towards the search of exceptions or a clustering. It requires to write queries taking into account such biases. Open issues are to design a generic framework to express powerful global constraints and solvers to mine them. We think that global constraints are a promising way to discover relevant global patterns

A Comparison of Lex Bounds for Multiset Variables in Constraint Programming

Set and multiset variables in constraint programming have typically been represented using subset bounds. However, this is a weak representation that neglects potentially useful information about a set such as its cardinality. For set variables, the length-lex (LL) representation successfully provides information about the length (cardinality) and position in the lexicographic ordering. For multiset variables, where elements can be repeated, we consider richer representations that take into account additional information. We study eight different representations in which we maintain bounds according to one of the eight different orderings: length-(co)lex (LL/LC), variety-(co)lex (VL/VC), length-variety-(co)lex (LVL/LVC), and variety-length-(co)lex (VLL/VLC) orderings. These representations integrate together information about the cardinality, variety (number of distinct elements in the multiset), and position in some total ordering. Theoretical and empirical comparisons of expressiveness and compactness of the eight representations suggest that length-variety-(co)lex (LVL/LVC) and variety-length-(co)lex (VLL/VLC) usually give tighter bounds after constraint propagation. We implement the eight representations and evaluate them against the subset bounds representation with cardinality and variety reasoning. Results demonstrate that they offer significantly better pruning and runtime.Comment: 7 pages, Proceedings of the Twenty-Fifth AAAI Conference on Artificial Intelligence (AAAI-11

Constraint Reasoning and Kernel Clustering for Pattern Decomposition with Scaling

Abstract. Motivated by an important and challenging task encountered in material discovery, we consider the problem of finding K basis patterns of numbers that jointly compose N observed patterns while enforcing additional spatial and scaling constraints. We propose a Constraint Pro-gramming (CP) model which captures the exact problem structure yet fails to scale in the presence of noisy data about the patterns. We allevi-ate this issue by employing Machine Learning (ML) techniques, namely kernel methods and clustering, to decompose the problem into smaller ones based on a global data-driven view, and then stitch the partial solu-tions together using a global CP model. Combining the complementary strengths of CP and ML techniques yields a more accurate and scalable method than the few found in the literature for this complex problem.