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Cluster-based specification techniques in Dempster-Shafer theory
- SYMBOLIC AND QUANTITATIVE APPROACHES TO REASONING AND UNCERTAINTY, C. FROIDEVAUX, AND J. KOLAS, EDS., PROCEEDINGS OF THE EUROPEAN CONFERENCE (ECSQARU'95)
, 1995
"... When reasoning with uncertainty there are many situations where evidences are not only uncertain but their propositions may also be weakly specified in the sense that it may not be certain to which event a proposition is referring. It is then crucial not to combine such evidences in the mistaken bel ..."
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Cited by 25 (12 self)
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When reasoning with uncertainty there are many situations where evidences are not only uncertain but their propositions may also be weakly specified in the sense that it may not be certain to which event a proposition is referring. It is then crucial not to combine such evidences in the mistaken belief that they are referring to the same event. This situation would become manageable if the evidences could be clustered into subsets representing events that should be handled separately. In an earlier article we established within Dempster-Shafer theory a criterion function called the metaconflict function. With this criterion we can partition a set of evidences into subsets. Each subset representing a separate event. In this article we will not only find the most plausible subset for each piece of evidence, we will also find the plausibility for every subset that the evidence belongs to the subset. Also, when the number of subsets are uncertain we aim to find a posterior probability distribution regarding the number of subsets.
Clustering belief functions based on attracting and conflicting metalevel evidence
- Intelligent Systems for Information Processing: From Representation to Applications, B. Bouchon-Meunier, L. Foulloy and R.R. Yager (Eds.)
, 2003
"... In this paper we develop a method for clustering belief functions based on attracting and conflicting metalevel evidence. Such clustering is done when the belief functions concern multiple events, and all belief functions are mixed up. The clustering process is used as the means for separating the b ..."
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Cited by 25 (16 self)
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In this paper we develop a method for clustering belief functions based on attracting and conflicting metalevel evidence. Such clustering is done when the belief functions concern multiple events, and all belief functions are mixed up. The clustering process is used as the means for separating the belief functions into subsets that should be handled independently. While the conflicting metalevel evidence is generated internally from pairwise conflicts of all belief functions, the attracting metalevel evidence is assumed given by some external source.
Dempster-Shafer clustering using Potts spin mean field theory
- Soft Computing
, 2001
"... In this article we investigate a problem within Dempster-Shafer theory where 2^q - 1 pieces of evidence are clustered into q clusters by minimizing a metaconflict function, or equivalently, by minimizing the sum of weight of conflict over all dusters. Previously one of us developed a method based on ..."
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Cited by 18 (14 self)
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In this article we investigate a problem within Dempster-Shafer theory where 2^q - 1 pieces of evidence are clustered into q clusters by minimizing a metaconflict function, or equivalently, by minimizing the sum of weight of conflict over all dusters. Previously one of us developed a method based on a Hopfield and Tank model. However, for very large problems we need a method with lower computational complexity. We demonstrate that the weight of conflict of evidence can, as an approximation, be linearized and mapped to an antiferromagnetic Potts spin model. This facilitates efficient numerical solution, even for large problem sizes. Optimal or nearly optimal solutions are found for Dempster-Shafer clustering benchmark tests with a time complexity of approximately O(N^2 log^2 N). Furthermore, an isomorphism between the antiferromagnetic Potts spin model and a graph optimization problem is shown. The graph model has dynamic variables living on the links, which have a priori probabilities that are directly related to the pairwise conflict between pieces of evidence. Hence, the relations between three different models are shown.
Conflict-based Force Aggregation
- Proceedings of the Sixth International Command and Control Research and Technology Symposium (6th ICCRTS)
, 2001
"... In this paper we present an application where we put together two methods for clustering and classification into a force aggregation method. Both methods are based on conflicts between elements. These methods work with different type of elements (intelligence reports, vehicles, military units) on di ..."
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Cited by 18 (7 self)
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In this paper we present an application where we put together two methods for clustering and classification into a force aggregation method. Both methods are based on conflicts between elements. These methods work with different type of elements (intelligence reports, vehicles, military units) on different hierarchical levels using specific conflict assessment methods on each level. We use Dempster-Shafer theory for conflict calculation between elements, Dempster-Shafer clustering for clustering these elements, and templates for classification. The result of these processes is a complete force aggregation on all levels handled.
Conflict Management in Dempster-Shafer Theory by Sequential Discounting Using the Degree of Falsity
, 2008
"... In this paper we develop a method for conflict management within Dempster-Shafer theory. The idea is that each piece of evidence is discounted in proportion to the degree that it contributes to the conflict. This way the contributors of conflict are managed on a case−by−case basis in relation to the ..."
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Cited by 16 (5 self)
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In this paper we develop a method for conflict management within Dempster-Shafer theory. The idea is that each piece of evidence is discounted in proportion to the degree that it contributes to the conflict. This way the contributors of conflict are managed on a case−by−case basis in relation to the problem they cause. Discounting is performed in a sequence of incremental steps, with conflict updated at each step, until the overall conflict is brought down exactly to a predefined acceptable level.
Dempster's rule for evidence ordered in a complete directed acyclic graph
- International Journal of Approximate Reasoning
, 1993
"... For the case of evidence ordered in a complete directed acyclic graph this paper presents a new algorithm with lower computational complexity for Dempster's rule than that of step-by-step application of Dempster's rule. In this problem, every original pair of evidences, has a corresponding ..."
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Cited by 15 (7 self)
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For the case of evidence ordered in a complete directed acyclic graph this paper presents a new algorithm with lower computational complexity for Dempster's rule than that of step-by-step application of Dempster's rule. In this problem, every original pair of evidences, has a corresponding evidence against the simultaneous belief in both propositions. In this case, it is uncertain whether the propositions of any two evidences are in logical conflict. The original evidences are associated with the vertices and the additional evidences are associated with the edges. The original evidences are ordered, i.e., for every pair of evidences it is determinable which of the two evidences is the earlier one. We are interested in finding the most probable completely specified path through the graph, where transitions are possible only from lower- to higher-ranked vertices. The path is here a representation for a sequence of states, for instance a sequence of snapshots of a physical object's track. A completely specified path means that the path includes no other vertices than those stated in the path representation, as opposed to an incompletely specified path that may also include other vertices than those stated. In a hierarchical network of all subsets of the frame, i.e., of all incompletely specified paths, the original and additional evidences support subsets that are not disjoint, thus it is not possible to prune the network to a tree. Instead of propagating belief, the new algorithm reasons about the logical conditions of a completely specified path through the graph. The new algorithm is O(|Θ| log |Θ|), compared to O(|Θ|^log |Θ|) of the classic brute force algorithm. After a detailed presentation of the reasoning behind the new algorithm we conclude that it is feasible to reason without approximation about completely specified paths through a complete directed acyclic graph.
Fast Dempster-Shafer clustering using a neural network structure
- Proceedings of the Seventh International Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU´'98)
, 1998
"... In this paper we study a problem within Dempster-Shafer theory where 2^n − 1 pieces of evidence are clustered by a neural structure into n clusters. The clustering is done by minimizing a metaconflict function. Previously we developed a method based on iterative optimization. However, for large scal ..."
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Cited by 12 (10 self)
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In this paper we study a problem within Dempster-Shafer theory where 2^n − 1 pieces of evidence are clustered by a neural structure into n clusters. The clustering is done by minimizing a metaconflict function. Previously we developed a method based on iterative optimization. However, for large scale problems we need a method with lower computational complexity. The neural structure was found to be effective and much faster than iterative optimization for larger problems. While the growth in metaconflict was faster for the neural structure compared with iterative optimization in medium sized problems, the metaconflict per cluster and evidence was moderate. The neural structure was able to find a global minimum over ten runs for problem sizes up to six clusters.
Applying data mining and machine learning techniques to submarine intelligence analysis
- Proceedings of the Third International Conference on Knowledge Discovery and Data Mining (KDD'97)
, 1997
"... We describe how specialized database technology and data analysis methods were applied by the Swedish defense to help deal with the violation of Swedish marine territory by foreign submarine intruders during the Eighties and early Nineties. Among several approaches tried some yielded interesting inf ..."
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Cited by 12 (6 self)
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We describe how specialized database technology and data analysis methods were applied by the Swedish defense to help deal with the violation of Swedish marine territory by foreign submarine intruders during the Eighties and early Nineties. Among several approaches tried some yielded interesting information, although most of the key questions remain unanswered. We conclude with a survey of belieffunction- and genetic-algorithm-based methods which were proposed to support interpretation of intelligence reports and prediction of future submarine positions, respectively.
Finding a posterior domain probability distribution by specifying nonspecific evidence
- International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
, 1995
"... 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 ..."
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Cited by 11 (11 self)
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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 DempsterShafer 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.
Sequential clustering with particle filters: Extimating the number of clusters from data
- 7th International Conference on Information Fusion (FUSION
, 2005
"... Abstract- In this paper we develop a particle filtering approach for grouping observations into an unspecified number of clusters. Each cluster corresponds to a potential target from which the observations originate. A potential clustering with a specified number of clusters is represented by an ass ..."
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Cited by 11 (6 self)
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Abstract- In this paper we develop a particle filtering approach for grouping observations into an unspecified number of clusters. Each cluster corresponds to a potential target from which the observations originate. A potential clustering with a specified number of clusters is represented by an association hypothesis. Whenever a new report arrives, a posterior distribution over all hypotheses is iteratively calculated from a prior distribution, an update model and a likelihood function. The update model is based on an association probability for clusters given the probability of false detection and a derived probability of an unobserved target. The likelihood of each hypothesis is derived from a cost value of associating the current report with its corresponding cluster according to the hypothesis. A set of hypotheses is maintained by Monte Carlo sampling. In this case, the state-space, i.e., the space of all hypotheses, is discrete with a linearly growing dimensionality over time. To lower the complexity further, hypotheses are combined if their clusters are close to each other in the observation space. Finally, for each time-step, the posterior distribution is projected into a distribution over the number of clusters. Compared to earlier information theoretic approaches for finding the number of clusters this approach does not require a large number of trial clusterings, since it maintains an estimate of the number of clusters along with the cluster configuration.
