EGMM: an Evidential Version of the Gaussian Mixture Model for Clustering

The Gaussian mixture model (GMM) provides a convenient yet principled framework for clustering, with properties suitable for statistical inference. In this paper, we propose a new model-based clustering algorithm, called EGMM (evidential GMM), in the theoretical framework of belief functions to better characterize cluster-membership uncertainty. With a mass function representing the cluster membership of each object, the evidential Gaussian mixture distribution composed of the components over the powerset of the desired clusters is proposed to model the entire dataset. The parameters in EGMM are estimated by a specially designed Expectation-Maximization (EM) algorithm. A validity index allowing automatic determination of the proper number of clusters is also provided. The proposed EGMM is as convenient as the classical GMM, but can generate a more informative evidential partition for the considered dataset. Experiments with synthetic and real datasets demonstrate the good performance of the proposed method as compared with some other prototype-based and model-based clustering techniques

For True Conditionalizers Weisberg’s Paradox is a False Alarm

Weisberg (2009) introduces a phenomenon he terms perceptual undermining. He argues that it poses a problem for Jeffrey conditionalization (Jeffrey 1983), and Bayesian epistemology in general. This is Weisberg’s paradox. Weisberg (2014) argues that perceptual undermining also poses a problem for ranking theory (Spohn 2012) and for Dempster-Shafer theory (Shafer 1976). In this note I argue that perceptual undermining does not pose a problem for any of these theories: for true conditionalizers Weisberg’s paradox is a false alarm

Evidential Clustering: A Review

International audienceIn evidential clustering, uncertainty about the assignment of objects to clusters is represented by Dempster-Shafer mass functions. The resulting clustering structure, called a credal partition, is shown to be more general than hard, fuzzy, possibilistic and rough partitions, which are recovered as special cases. Three algorithms to generate a credal partition are reviewed. Each of these algorithms is shown to implement a decision-directed clustering strategy. Their relative merits are discussed

Combining clusterings in the belief function framework

International audienceIn this paper, we propose a clustering ensemble method based on Dempster-Shafer Theory. In the first step, base partitions are generated by evidential clustering algorithms such as the evidential c-means or EVCLUS. Base credal partitions are then converted to their relational representations, which are combined by averaging. The combined relational representation is then made transitive using the theory of intuitionistic fuzzy relations. Finally, the consensus solution is obtained by minimizing an error function. Experiments with simulated and real datasets show the good performances of this method

Evidential Evolving Gustafson-Kessel Algortithm (E2GK) and its application to PRONOSTIA's Data Streams Partitioning.

International audienceCondition-based maintenance (CBM) appears to be a key element in modern maintenance practice. Research in diagnosis and prognosis, two important aspects of a CBM program, is growing rapidly and many studies are conducted in research laboratories to develop models, algorithms and technologies for data processing. In this context, we present a new evolving clustering algorithm developed for prognostics perspectives. E2GK (Evidential Evolving Gustafson-Kessel) is an online clustering method in the theoretical framework of belief functions. The algorithm enables an online partitioning of data streams based on two existing and efficient algorithms: Evidantial c-Means (ECM) and Evolving Gustafson-Kessel (EGK). To validate and illustrate the results of E2GK, we use a dataset provided by an original platform called PRONOSTIA dedicated to prognostics applications

Evidential Evolving Gustafson-Kessel Algorithm (E2GK) and its application to PRONOSTIA's Data Streams Partitioning.

International audienceCondition-based maintenance (CBM) appears to be a key element in modern maintenance practice. Research in diagnosis and prognosis, two important aspects of a CBM program, is growing rapidly and many studies are conducted in research laboratories to develop models, algorithms and technologies for data processing. In this context, we present a new evolving clustering algorithm developed for prognostics perspectives. E2GK (Evidential Evolving Gustafson-Kessel) is an online clustering method in the theoretical framework of belief functions. The algorithm enables an online partitioning of data streams based on two existing and efficient algorithms: Evidantial c-Means (ECM) and Evolving Gustafson-Kessel (EGK). To validate and illustrate the results of E2GK, we use a dataset provided by an original platform called PRONOSTIA dedicated to prognostics applications

Distention for Sets of Probabilities

A prominent pillar of Bayesian philosophy is that, relative to just a few constraints, priors “wash out” in the limit. Bayesians often appeal to such asymptotic results as a defense against charges of excessive subjectivity. But, as Seidenfeld and coauthors observe, what happens in the short run is often of greater interest than what happens in the limit. They use this point as one motivation for investigating the counterintuitive short run phenomenon of dilation since, it is alleged, “dilation contrasts with the asymptotic merging of posterior probabilities reported by Savage (1954) and by Blackwell and Dubins (1962)” (Herron et al., 1994). A partition dilates an event if, relative to every cell of the partition, uncertainty concerning that event increases. The measure of uncertainty relevant for dilation, however, is not the same measure that is relevant in the context of results concerning whether priors wash out or “opinions merge.” Here, we explicitly investigate the short run behavior of the metric relevant to merging of opinions. As with dilation, it is possible for uncertainty (as gauged by this metric) to increase relative to every cell of a partition. We call this phenomenon distention. It turns out that dilation and distention are orthogonal phenomena