Weighting by Tying: A New Approach to Weighted Rank Correlation

Measures of rank correlation are commonly used in statistics to capture the degree of concordance between two orderings of the same set of items. Standard measures like Kendall's tau and Spearman's rho coefficient put equal emphasis on each position of a ranking. Yet, motivated by applications in which some of the positions (typically those on the top) are more important than others, a few weighted variants of these measures have been proposed. Most of these generalizations fail to meet desirable formal properties, however. Besides, they are often quite inflexible in the sense of committing to a fixed weighing scheme. In this paper, we propose a weighted rank correlation measure on the basis of fuzzy order relations. Our measure, called scaled gamma, is related to Goodman and Kruskal's gamma rank correlation. It is parametrized by a fuzzy equivalence relation on the rank positions, which in turn is specified conveniently by a so-called scaling function. This approach combines soundness with flexibility: it has a sound formal foundation and allows for weighing rank positions in a flexible way.Comment: 15 page

Rule Chains for Visualizing Evolving Fuzzy Rule-Based Systems

Abstract Evolving fuzzy systems are data-driven fuzzy (rule-based) systems supporting an incremental model adaptation in dynamically changing environments; typically, such models are learned on a continuous stream of data in an online manner. This paper advocates the use of visualization techniques in order to help a user gain insight into the process of model evolution. More specifically, rule chains are introduced as a novel visualization technique for theinspectionofevolvingTakagi-Sugeno-Kang(TSK)fuzzysystems.Toshow the usefulness of this techniques, we illustrate its application in the context of learning from data streams with temporal concept drift.

Comparing Fuzzy Partitions: A Generalization of the Rand Index and Related Measures

International audienceIn this paper, we introduce a fuzzy extension of a class of measures to compare clustering structures, namely, measures that are based on the number of concordant and the number of discordant pairs of data points. This class includes the well-known Rand index but also commonly used alternatives, such as the Jaccard measure. In contrast with previous proposals, our extension exhibits desirable metrical properties. Apart from elaborating on formal properties of this kind, we present an experimental study in which we compare different fuzzy extensions of the Rand index and the Jaccard measure