Enforcing local consistencies in cost function networks is performed by applying so-called Equivalent Preserving Transformations (EPTs) to the cost functions. As EPTs transform the cost functions, they may break the property that was making local consistency enforcement tractable on a global cost function. A global cost function is called tractable projection-safe when applying an EPT to it is tractable and does not break the tractability property. In this paper, we prove that depending on the size r of the smallest scopes used for performing EPTs, the tractability of global cost functions can be preserved (r = 0) or destroyed (r > 1). When r = 1, the answer is indefinite. We show that on a large family of cost functions, EPTs can be computed via dynamic programming-based algorithms, leading to tractable projection-safety. We also show that when a global cost function can be decomposed into a Berge acyclic network of bounded arity cost functions, soft local consistencies such as soft Directed or Virtual Arc Consistency can directly emulate dynamic programming. These different approaches to decomposable cost functions are then embedded in a solver for extensive experiments that confirm the feasibility and efficiency of our proposal.
Constraint-based pattern discovery is at the core of numerous data mining tasks. Patterns are extracted with respect to a given set of constraints (frequency, closedness, size, etc). In the context of sequential pattern mining, a large number of devoted techniques have been developed for solving particular classes of constraints. The aim of this paper is to investigate the use of Constraint Programming (CP) to model and mine sequential patterns in a sequence database. Our CP approach offers a natural way to simultaneously combine in a same framework a large set of constraints coming from various origins. Experiments show the feasibility and the interest of our approach.
Discovering pattern sets or global patterns is an attractive issue from the pattern mining community in order to provide useful information. By combining local patterns satisfying a joint meaning, this approach produces patterns of higher level and thus more useful for the data analyst than the usual local patterns, while reducing the number of patterns. In parallel, recent works investigating relationships between data mining and constraint programming (CP) show that the CP paradigm is a nice framework to model and mine such patterns in a declarative and generic way. We present a constraint-based language which enables us to define queries addressing patterns sets and global patterns. The usefulness of such a declarative approach is highlighted by several examples coming from the clustering based on associations. This language has been implemented in the CP framework.