Régis Gras

Using information-theoretic measures to assess association rule interestingness

Assessing rules with interestingness measures is the cornerstone of successful applications of association rule discovery. However, there exists no information-theoretic measure which is adapted to the semantics of association rules. In this article, we present the directed information ratio (DIE), a new rule interestingness measure which is based on information theory. DIR is specially designed for association rules, and in particular it differentiates two opposite rules a /spl rarr/ b and a /spl rarr/ b~. Moreover, to our knowledge, DIR is the only rule interestingness measure which rejects both independence and (what we call) equilibrium, i.e. it discards both the rules whose antecedent and consequent are negatively correlated, and the rules which have more counter-examples than examples. Experimental studies show that DIR is a very filtering measure, which is useful for association rule post-processing.

A Graph-based Clustering Approach to Evaluate Interestingness Measures: A Tool and a Comparative Study

Finding interestingness measures to evaluate association rules has become an important knowledge quality issue in KDD. Many interestingness measures may be found in the literature, and many authors have discussed and compared interestingness properties in order to improve the choice of the most suitable measures for a given application. As interestingness depends both on the data structure and on the decision-makers goals, some measures may be relevant in some context, but not in others. Therefore, it is necessary to design new contextual approaches in order to help the decision-maker select the most suitable interestingness measures. In this paper, we present a new approach implemented by a new tool, ARQAT, for making comparisons. The approach is based on the analysis of a correlation graph presenting the clustering of objective interestingness measures and reflecting the post-processing of association rules. This graph-based clustering approach is used to compare and discuss the behavior of thirty-six interestingness measures on two prototypical and opposite datasets: a highly correlated one and a lowly correlated one. We focus on the discovery of the stable clusters obtained from the data analyzed between these thirty-six measures.

Implicative statistical analysis

Implicative analysis, due to a problem of evaluation in education, allows us to treat a table crossing subjects or objects and variables according to a nonsymmetrical point of view. In term of method of data analysis, it structures the set of variables, leads to tree and hierarchical structures and leads to the calculation of the objects contribution to the structure of the variables. Furthermore, it appears to be an effective tool in artificial intelligence to explain a base of rules in a set of knowledge. An example of the treatment of a big corpus of human behaviours is presented. The results, given by the method, have been validated a posteriori by the expert (psychologist).

An overview of the Statistical Implicative Analysis (SIA) development

Summary. This paper presents an overview of the Statistical Implicative Analysis which is a data analysis method devoted to the extraction and the structuration of quasi-implications. Originally developed by Gras [11] for applications in the didactics of mathematics, it has considerably evolved and has been applied to a wide range of data, in particular in data mining. This paper is a synthesis which both briefly presents the basic statistical framework of the approach and details recent developments.

Discovering R-rules with a directed hierarchy

In this paper, we extend the classical notion of quasi-implication (“when ai is present then usually aj is also present”) to R-rules (rules of rules), the premisses and the conclusions of which can be rules themselves. A new statistical measure, based on the implicative intensity defined by Gras for quasi-implications, is defined to assess the significance of R-rules on a data set. We show how to organize R-rules in a new combinatorial structure, the directed hierarchy, which is inspired by the classical hierarchical classification. An incremental algorithm is developed to find the most significant R-rule “amalgamation”. An illustration is presented on a real data set stemming from a recent survey of the French Public Education Mathematical Teacher Society on the level in mathematics of pupils in the final year of secondary education and the perception of this subject.

Reducing the Number of Variables Using Implicative Analysis

The interpretation of complex data with data mining techniques is often a difficult task. Nevertheless, this task may be simplified by reducing the variables which could be considered as equivalent. The aim of this paper is to describe a new method for reducing the number of variables in a large set of data. Implicative analysis, which builds association rules with a measure more powerful than conditional probability, is used to detect quasi-equivalent variables. This technique has some advantages over traditional similarity analysis.

A new approach in Zadeh's classification: Fuzzy implication through statistic implication

In relationship to the classification of the various approaches to the fuzzy logic of Zadeh (possibilistic, probabilistic, veristic) [14] the implication according to Gras is introduced as a new approach with its own characteristics. The notion of statistical implication is based on the statistical comparison between the inclusion of sets observed in a population and one that would have comparable sets, but chosen casually in the same population. Such an approach has to do with, in particular, variables-intervals. Therefore, it is suitable for representing fuzzy implication. The experimental comparison with classic fuzzy implications (Reichenbach and Lukasievicz) confirms a better semantic adequacy. The implicative methods are implemented in the statistic software (CHIC 3.1). The new epistemological perspective opens interesting application perspectives. The implication of variables of interval of Gras is neither completely descriptive nor completely inferential. We are in the presence of a new epistemological approach to fuzzy implication. The implication of Gras keeps in mind richer semantics when it is experimentally compared with other classical implications such as that of Reichenbach and Lukasiewicz. This type of implication can perhaps have some more interesting results in the applications of the Artificial Intelligence.

Assessing the interestingness of temporal rules with Sequential Implication Intensity

In this article, we study the assessment of the interestingness of sequential rules (generally temporal rules). This is a crucial problem in sequence analysis since the frequent pattern mining algorithms are unsupervised and can produce huge amounts of rules. While association rule interestingness has been widely studied in the literature, there are few measures dedicated to sequential rules. Continuing with our work on the adaptation of implication intensity to sequential rules, we propose an original statistical measure for assessing sequential rule interestingness. More precisely, this measure named Sequential Implication Intensity (SII) evaluates the statistical significance of the rules in comparison with a probabilistic model. Numerical simulations show that SII has unique features for a sequential rule interestingness measure.

On the use of Implication Intensity for matching ontologies and textual taxonomies

data algorithm analysis artificial intelligence computer science database system image processing computer architecture computer programming A1

Using the Statistical Implicative Analysis for Elaborating Behavioral Referentials

Various informatic assessment tools have been created to help human resources managers in evaluating the behavioral profile of a person. The psychological basis of those tools have all been validated, but very few of them have follow a deep statistical analysis. The PerformanSe Echo assessment tool is one of them. It gives the behavioral profile of a person along 10 bipolar dimensions. It has been validated on a population of 4538 subjects in 2004. We are now interested in building a set of psychological indicators based on Echo on a population of 613 experienced executives who are 45 years old and more, and seeking a job. Our goal is twofold: first to confirm the previous validation study, then to build a relevant behavioral referential on this population. The final goal is to have relevant indicators helping to understand the link between some behavioral characteristics and current profiles that can be categorized in the population. In the end, it may provide the foundation for a decision support tool intended for consultants specialized in coaching and outplacement.