Given a database, structure mining algorithms search for substructures that satisfy constraints such as minimum frequency, minimum confidence, minimum interest and maximum frequency. Examples of substructures include graphs, trees and paths. For these substructures many mining algorithms have been proposed. In order to make graph mining more efficient, we investigate the use of the "quickstart principle", which is based on the fact that these classes of structures are contained in each other, thus allowing for the development of structure mining algorithms that split the search into steps of increasing complexity. We introduce the GrAph/Sequence/Tree extractiON (Gaston) algorithm that implements this idea by searching first for frequent paths, then frequent free trees and finally cyclic graphs. We investigate two alternatives for computing the frequency of structures and present experimental results to relate these alternatives.

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The field of data mining has become accustomed to specifying constraints on patterns of interest. A large number of systems and techniques has been developed for solving such constraint-based mining problems, especially for mining itemsets. The approach taken in the field of data mining contrasts with the constraint programming principles developed within the artificial intelligence community. While most data mining research focuses on algorithmic issues and aims at developing highly optimized and scalable implementations that are tailored towards specific tasks, constraint programming employs a more declarative approach. The emphasis lies on developing high-level modeling languages and general solvers that specify what the problem is, rather than outlining how a solution should be computed, yet are powerful enough to be used across a wide variety of applications and application domains.This paper contributes a declarative constraint programming approach to data mining. More specifically, we show that it is possible to employ off-the-shelf constraint programming techniques for modeling and solving a wide variety of constraint-based itemset mining tasks, such as frequent, closed, discriminative, and cost-based itemset mining. In particular, we develop a basic constraint programming model for specifying frequent itemsets and show that this model can easily be extended to realize the other settings. This contrasts with typical procedural data mining systems where the underlying procedures need to be modified in order to accommodate new types of constraint, or novel combinations thereof. Even though the performance of state-of-the-art data mining systems outperforms that of the constraint programming approach on some standard tasks, we also show that there exist problems where the constraint programming approach leads to significant performance improvements over state-of-the-art methods in data mining and as well as to new insights into the underlying data mining problems. Many such insights can be obtained by relating the underlying search algorithms of data mining and constraint programming systems to one another. We discuss a number of interesting new research questions and challenges raised by the declarative constraint programming approach to data mining.

The relationship between constraint-based mining and constraint programming is explored by showing how the typical constraints used in pattern mining can be formulated for use in constraint programming environments. The resulting framework is surprisingly flexible and allows us to combine a wide range of mining constraints in different ways. We implement this approach in off-the-shelf constraint programming systems and evaluate it empirically. The results show that the approach is not only very expressive, but also works well on complex benchmark problems.

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We introduce the k-pattern set mining problem, which is concerned with finding sets of k patterns that satisfy constraints. We formulate a number of such constraints, both at the local level, that is, on individual patterns, and more importantly, also on the global level, that is, on the overall pattern set. The resulting framework is flexible and generic in the sense that it can be instantiated to a wide variety of well-known mining tasks including concept-learning, rule-learning, redescription mining, conceptual clustering and tiling. We present a solution method based on constraint programming and discuss how many problems can been modelled in a constraint programming system. Finally, a number of experiments show the promise and generality of the approach.

Substructure mining algorithms are important drug discovery tools since they can find substructures that affect physicochemical and biological properties. Current methods, however, only consider a part of all chemical information that is present within a data set of compounds. Therefore, the overall aim of our study was to enable more exhaustive data mining by designing methods that detect all substructures of any size, shape, and level of chemical detail. A means of chemical representation was developed that uses atomic hierarchies, thus enabling substructure mining to consider general and/or highly specific features. As a proof-of-concept, the efficient, multipurpose graph mining system Gaston learned substructures of any size and shape from a mutagenicity data set that was represented in this manner. From these substructures, we extracted a set of only six nonredundant, discriminative substructures that represent relevant biochemical knowledge. Our results demonstrate the individual and synergistic importance of elaborate chemical representation and mining for nonlinear substructures. We conclude that the combination of elaborate chemical representation and Gaston provides an excellent method for 2D substructure mining as this recipe systematically explores all substructures in different levels of chemical detail.

Abstract. This paper investigates the trade-off between the expressiveness of the pattern language and the performance of the pattern miner in structured data mining. This trade-off is investigated in the context of correlated pattern mining, which is concerned with finding the k-best patterns according to a convex criterion, for the pattern languages of itemsets, multi-itemsets, sequences, trees and graphs. The criteria used in our investigation are the typical ones in data mining: computational cost and predictive accuracy and the domain is that of mining molecular graph databases. More specifically, we provide empirical answers to the following questions: how does the expressive power of the language affect the computational cost? and what is the trade-off between expressiveness of the pattern language and the predictive accuracy of the learned model? While answering the first question, we also introduce a novel stepwise approach to correlated pattern mining in which the results of mining a simpler pattern language are employed as a starting point for mining in a more complex one. This stepwise approach typically leads to significant speed-ups (up to a factor 1000) for mining graphs.