RCA-Seq: an Original Approach for Enhancing the Analysis of Sequential Data Based on Hierarchies of Multilevel Closed Partially-Ordered Patterns

International audienceMethods for analysing sequential data generally produce a huge number of sequential patterns that have then to be evaluated and interpreted by domain experts. To diminish this number and thus the difficulty of the interpretation task, methods that directly extract a more compact representation of sequential patterns, namely closed partially-ordered patterns (CPO-patterns), were introduced. In spite of the fewer number of obtained CPO-patterns, their analysis is still a challenging task for experts since they are unorgan-ised and besides, do not provide a global view of the discovered regularities. To address these problems, we present and formalise an original approach within the framework of Relational Concept Analysis (RCA), referred to as RCA-Seq, that focuses on facilitating the interpretation task of experts. The hierarchical RCA result allows to directly obtain and organize the relationships between the extracted CPO-patterns. Moreover, a generalisation order on items is also revealed, and multilevel CPO-patterns are obtained. Therefore, a hierarchy of such CPO-patterns guides the interpretation task, helps experts in better understanding the extracted patterns, and minimises the chance of overlooking interesting CPO-patterns. RCA-Seq is compared with another approach that relies on pattern structures. In addition, we highlight the adaptability of RCA-Seq by integrating a user-defined tax-* onomy over the items, and by considering user-specified constraints on the order relations on itemsets

Mining frequent closed rooted trees

Many knowledge representation mechanisms are based on tree-like structures, thus symbolizing the fact that certain pieces of information are related in one sense or another. There exists a well-studied process of closure-based data mining in the itemset framework: we consider the extension of this process into trees. We focus mostly on the case where labels on the nodes are nonexistent or unreliable, and discuss algorithms for closurebased mining that only rely on the root of the tree and the link structure. We provide a notion of intersection that leads to a deeper understanding of the notion of support-based closure, in terms of an actual closure operator. We describe combinatorial characterizations and some properties of ordered trees, discuss their applicability to unordered trees, and rely on them to design efficient algorithms for mining frequent closed subtrees both in the ordered and the unordered settings. Empirical validations and comparisons with alternative algorithms are provided.Postprint (author’s final draft

Reasoning with imprecise trade-offs in decision making under certainty and uncertainty

In many real world situations, we make decisions in the presence of multiple, often conflicting and non-commensurate objectives. The process of optimizing systematically and simultaneously over a set of objective functions is known as multi-objective optimization. In multi-objective optimization, we have a (possibly exponentially large) set of decisions and each decision has a set of alternatives. Each alternative depends on the state of the world, and is evaluated with respect to a number of criteria. In this thesis, we consider the decision making problems in two scenarios. In the first scenario, the current state of the world, under which the decisions are to be made, is known in advance. In the second scenario, the current state of the world is unknown at the time of making decisions. For decision making under certainty, we consider the framework of multiobjective constraint optimization and focus on extending the algorithms to solve these models to the case where there are additional trade-offs. We focus especially on branch-and-bound algorithms that use a mini-buckets algorithm for generating the upper bound at each node of the search tree (in the context of maximizing values of objectives). Since the size of the guiding upper bound sets can become very large during the search, we introduce efficient methods for reducing these sets, yet still maintaining the upper bound property. We define a formalism for imprecise trade-offs, which allows the decision maker during the elicitation stage, to specify a preference for one multi-objective utility vector over another, and use such preferences to infer other preferences. The induced preference relation then is used to eliminate the dominated utility vectors during the computation. For testing the dominance between multi-objective utility vectors, we present three different approaches. The first is based on a linear programming approach, the second is by use of distance-based algorithm (which uses a measure of the distance between a point and a convex cone); the third approach makes use of a matrix multiplication, which results in much faster dominance checks with respect to the preference relation induced by the trade-offs. Furthermore, we show that our trade-offs approach, which is based on a preference inference technique, can also be given an alternative semantics based on the well known Multi-Attribute Utility Theory. Our comprehensive experimental results on common multi-objective constraint optimization benchmarks demonstrate that the proposed enhancements allow the algorithms to scale up to much larger problems than before. For decision making problems under uncertainty, we describe multi-objective influence diagrams, based on a set of p objectives, where utility values are vectors in Rp, and are typically only partially ordered. These can be solved by a variable elimination algorithm, leading to a set of maximal values of expected utility. If the Pareto ordering is used this set can often be prohibitively large. We consider approximate representations of the Pareto set based on ϵ-coverings, allowing much larger problems to be solved. In addition, we define a method for incorporating user trade-offs, which also greatly improves the efficiency