Simultaneous Dempster-Shafer clustering and gradual determination of number of clusters using a neural network structure

In this paper we extend an earlier result within Dempster-Shafer theory ["Fast Dempster-Shafer Clustering Using a Neural Network Structure," in Proc. Seventh Int. Conf. Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU'98)] where several pieces of evidence were clustered into a fixed number of clusters using a neural structure. This was done by minimizing a metaconflict function. We now develop a method for simultaneous clustering and determination of number of clusters during iteration in the neural structure. We let the output signals of neurons represent the degree to which a pieces of evidence belong to a corresponding cluster. From these we derive a probability distribution regarding the number of clusters, which gradually during the iteration is transformed into a determination of number of clusters. This gradual determination is fed back into the neural structure at each iteration to influence the clustering process.Comment: 6 pages, 10 figure

Specifying nonspecific evidence

In an earlier article [J. Schubert, On nonspecific evidence, Int. J. Intell. Syst. 8(6), 711-725 (1993)] we established within Dempster-Shafer theory a criterion function called the metaconflict function. With this criterion we can partition into subsets a set of several pieces of evidence with propositions that are weakly specified in the sense that it may be uncertain to which event a proposition is referring. Each subset in the partitioning is representing a separate event. The metaconflict function was derived as the plausibility that the partitioning is correct when viewing the conflict in Dempster's rule within each subset as a newly constructed piece of metalevel evidence with a proposition giving support against the entire partitioning. In this article we extend the results of the previous article. We will not only find the most plausible subset for each piece of evidence as was done in the earlier article. In addition we will specify each piece of nonspecific evidence, in the sense that we find to which events the proposition might be referring, by finding the plausibility for every subset that this piece of evidence belong to the subset. In doing this we will automatically receive indication that some evidence might be false. We will then develop a new methodology to exploit these newly specified pieces of evidence in a subsequent reasoning process. This will include methods to discount evidence based on their degree of falsity and on their degree of credibility due to a partial specification of affiliation, as well as a refined method to infer the event of each subset.Comment: 39 pages, 2 figure

Finding a posterior domain probability distribution by specifying nonspecific evidence

This article is an extension of the results of two earlier articles. In [J. Schubert, “On nonspecific evidence”, Int. J. Intell. Syst. 8 (1993) 711-725] we established within Dempster-Shafer theory a criterion function called the metaconflict function. With this criterion we can partition into subsets a set of several pieces of evidence with propositions that are weakly specified in the sense that it may be uncertain to which event a proposition is referring. In a second article [J. Schubert, “Specifying nonspecific evidence”, in “Cluster-based specification techniques in Dempster-Shafer theory for an evidential intelligence analysis of multiple target tracks”, Ph.D. Thesis, TRITA-NA-9410, Royal Institute of Technology, Stockholm, 1994, ISBN 91-7170-801-4] we not only found the most plausible subset for each piece of evidence, we also found the plausibility for every subset that this piece of evidence belongs to the subset. In this article we aim to find a posterior probability distribution regarding the number of subsets. We use the idea that each piece of evidence in a subset supports the existence of that subset to the degree that this piece of evidence supports anything at all. From this we can derive a bpa that is concerned with the question of how many subsets we have. That bpa can then be combined with a given prior domain probability distribution in order to obtain the sought-after posterior domain distribution. Keywords: belief functions, Dempster-Shafer theory, evidential reasoning, evidence correlation, cluster analysis, posterior distribution

Use of Evidence theory for the fusion and the estimation of relevance of data sources : application to an alcoholic bioprocess

In this paper, we present an application of the evidence theory for the classification of physiological states in a bioprocess. We are particularly interested by the relevance of the data sources which are here biochemical parameters measured during the bioprocess. The evidence theory, and more particularly the notion of conflict is used to evaluate the relevance of each data source. An other measure of conflict, based on a distance, is also used, and provides in some cases, better results than the classical notion of conflict of the evidence theory. Results are presented for two kinds of bioprocesses : batch process (which corresponds to a supervised classification) and fed-batch process (which corresponds to an unsupervised classification).Dans cet article, nous présentons une application de la théorie des fonctions de croyance pour la classification d’états physiologiques dans un bioprocédé. Nous nous intéressons surtout à la pertinence des sources d’informations qui sont ici des paramètres biochimiques mesurés durant le procédé. La théorie des fonctions de croyance, et plus particulièrement la notion de conflit est utilisée pour évaluer la pertinence de chaque source d’information. Une autre mesure du conflit, basée sur une distance, est utilisée comme alternative, et fournit dans certains cas, des résultats plus cohérents qu’avec le conflit défini dans la théorie de Demspter et Shafer. Les résultats concernant deux types de bioprocédés (procédé batch correspondant à une classification supervisée, et procédé fed-batch correspondant à une classification non supervisée) sont présentés