Marie-Jeanne Lesot

Data analysis with fuzzy clustering methods

An encompassing, self-contained introduction to the foundations of the broad field of fuzzy clustering is presented. The fuzzy cluster partitions are introduced with special emphasis on the interpretation of the two most encountered types of gradual cluster assignments: the fuzzy and the possibilistic membership degrees. A systematic overview of present fuzzy clustering methods is provided, highlighting the underlying ideas of the different approaches. The class of objective function-based methods, the family of alternating cluster estimation algorithms, and the fuzzy maximum likelihood estimation scheme are discussed. The latter is a fuzzy relative of the well-known expectation maximization algorithm and it is compared to its counterpart in statistical clustering. Related issues are considered, concluding with references to selected developments in the area.

Similarity measures for binary and numerical data: a survey

Similarity measures aim at quantifying the extent to which objects resemble each other. Many techniques in data mining, data analysis or information retrieval require a similarity measure, and selecting an appropriate measure for a given problem is a difficult task. In this paper, the diverse forms similarity measures can take are examined, as well as their relationships and respective properties. Their semantic differences are highlighted and numerical tools to quantify these differences are proposed, considering several points of view and including global and local comparisons, order-based and value-based comparisons, and mathematical properties such as derivability. The paper studies similarity measures for two types of data: binary and numerical data, i.e., set data represented by the presence or absence of characteristics and data represented by real vectors.

Fuzzy Prototypes Based on Typicality Degrees

This paper considers the task of constructing fuzzy prototypes for numerical data in order to characterize the data subgroups obtained after a clustering step. The proposed solution is motivated by the will of describing prototypes with a richer representation than point-based methods, and also to provide a characterization of the groups that catches not only the common features of the data pertaining to a group, but also their specificity. It transposes a method that has been designed for fuzzy data to numerical data, based on a prior computation of typicality degrees that are defined according to concepts used in cognitive science and psychology. The paper discusses the construction of prototypes and how their desirable semantics and properties can guide the selection of the various operators involved in the construction process.

Fuzzy Prototypes: From a Cognitive View to a Machine Learning Principle

Cognitive psychology works have shown that the cognitive representation of categories is based on a typicality notion: all objects of a category do not have the same representativeness, some are more characteristic or more typical than others, and better exemplify their category. Categories are then defined in terms of prototypes, i.e. in terms of their most typical elements. Furthermore, these works showed that an object is all the more typical of its category as it shares many features with the other members of the category and few features with the members of other categories.

Real-World Fuzzy Logic Applications in Data Mining and Information Retrieval

This chapter focuses on real-world applications of fuzzy techniques for information retrieval and data mining. It gives a presentation of the theoretical background common to all applications, lying on two main elements: the concept of similarity and the fuzzy machine learning framework. It then describes a panel of real-world applications covering several domains namely medical, educational, chemical and multimedia.

Linguistic summaries for periodicity detection based on mathematical morphology

The paper presents a methodology to evaluate the periodicity of a temporal data series, neither relying on assumption about the series form nor requiring expert knowledge to set parameters. It exploits tools from mathematical morphology to compute a periodicity degree and a candidate period, as well as the fuzzy set theory to generate a natural language sentence, improving the result interpretability. Experiments on both artificial and real data illustrate the relevance of the proposed approach.

Modelling and management of subjective information in a fuzzy setting

Subjective information is very natural for human beings. It is an issue at the crossroad of cognition, semiotics, linguistics, and psycho-physiology. Its management requires dedicated methods, among which we point out the usefulness of fuzzy and possibilistic approaches and related methods, such as evidence theory. We distinguish three aspects of subjectivity: the first deals with perception and sensory information, including the elicitation of quality assessment and the establishment of a link between physical and perceived properties; the second is related to emotions, their fuzzy nature, and their identification; and the last aspect stems from natural language and takes into account information quality and reliability of information.

Scalable Fuzzy Algorithms for Data Management and Analysis: Methods and Design

Today, fuzzy methods are of common use as they provide tools to handle data sets in a relevant, robust, and interpretable way, making it possible to cope with both imprecision and uncertainties. Scalable Fuzzy Algorithms for Data Management and Analysis: Methods and Design presents up-to-date techniques for addressing data management problems with logic and memory use. This critical mass of the most sought after findings covers a wide scope of research areas from both a theoretical and experimental point of view.

Descriptive concept extraction with exceptions by hybrid clustering

Natural concept modelling aims at representing numerically semantic knowledge; generally, experts are asked to provide examples of linguistic terms associated with numerical data descriptions. We propose to exploit directly non labelled databases to extract the concepts that enable a semantic description of the data. Our method consists in identifying the subgroups corresponding to the concepts and then representing them as fuzzy subsets. For the identification step, we propose an algorithm based on a conjugate iterative use of the single linkage hierarchical clustering algorithm and the fuzzy c-means, that explicitly takes into account both a separability objective and a compactness aim; the description step builds membership functions as generalized Gaussians. The adequacy of the results with spontaneous descriptions is illustrated on artificial and real databases.

Formalising Information Scoring in a Multivalued Logic Framework

This paper addresses the task of information scoring seen as measuring the degree of trust that can be invested in a piece of information. To this end, it proposes to model the trust building process as the sequential integration of relevant dimensions. It also proposes to formalise both the degree of trust and the process in an extended multivalued logic framework that distinguishes between an indifferent level and the actual impossibility to measure. To formalise the process, it proposes multivalued combination operators matching the desired behaviours.