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Geometric Analysis of Belief Space and Conditional Subspaces
, 2001
"... In this paper the geometric structure of the space S of the belief functions dened over a discrete set (be lief space) is analyzed. Using the Moebius inversion lemma we prove the recursive bundle structure of the belief space and show how an arbitrary belief function can be uniquely represented ..."
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Cited by 19 (18 self)
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In this paper the geometric structure of the space S of the belief functions dened over a discrete set (be lief space) is analyzed. Using the Moebius inversion lemma we prove the recursive bundle structure of the belief space and show how an arbitrary belief function can be uniquely represented as a convex combination of certain elements of the bers, giving S the form of a simplex. The commutativity of orthogonal sum and convex closure operator is proved and used to depict the geometric structure of conditional subspaces, i.e. sets of belief functions conditioned by a given function s. Future applications of these geometric methods to classical problems like probabilistic approximation and canonical decomposition are outlined.
Lattice Structure of the Families of Compatible Frames of Discernment
, 2001
"... One of the central ideas in Shafer's mathematical theory of evidence is the concept of different level of knowledge of a given phenomenon, embodied into the notion of compatible frames of discernment. In this work we are going to analyze the concept of family of frames from an algebraic point o ..."
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Cited by 7 (7 self)
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One of the central ideas in Shafer's mathematical theory of evidence is the concept of different level of knowledge of a given phenomenon, embodied into the notion of compatible frames of discernment. In this work we are going to analyze the concept of family of frames from an algebraic point of view, distinguish among finite and general families and introduce the internal operation of maximal coarsening, originating the structure of semimodular lattice. We will show the equivalence between the classical independence of frames and the independence of frames as elements of a locally finite Birkhoff lattice, eventually prefiguring a solution to the conflict problem based on a pseudo GramSchmidt algorithm.
Integrating Feature Spaces for Object Tracking
 PROC. OF MTNS2000
, 2000
"... Object tracking is an interesting field of computer vision whose difficult problems stimulate the search for new viewpoints and suitable mathematical tools. It consists on reconstructing the actual pose a moving object by processing the sequence of images taken during the movement. We are looking fo ..."
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Cited by 1 (1 self)
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Object tracking is an interesting field of computer vision whose difficult problems stimulate the search for new viewpoints and suitable mathematical tools. It consists on reconstructing the actual pose a moving object by processing the sequence of images taken during the movement. We are looking for a tracking system which rests on information about images as complete as possible. It should integrate different descriptions to increase the estimation robustness and overcome singlefeature drawbacks. It should also measure the consistency of the acquired data and compute the estimate from the most coherent set of measurements. It must be pointed out that it is often impossible to write analytic relations between different features for they can concern completely unrelated aspects of the images. The theory of evidence 4 has been introduced in the late Seventies by Glenn Shafer as a way of representing epistemic knowledge, starting from the seminal work 2 of Arthur Dempster. In this formalism the best representation of chance is a belief function (b.f.) rather than a Bayesian mass distribution. They assign probability values to sets of possibilities rather than single events so they naturally encode evidence in favor to propositions. Following Shafer, 4 if we will call the finite set of possibilities frame of discernment (FOD)
Adaptive User Modeling for Filtering Electronic News
"... A prototype system for the finegrained filtering of news items has been developed and a pilot test has been conducted. The system is based on an adaptive user model that integrates stereotypes and artificial neural networks. The stereotypes are based on newspaper sections and subsections, along wi ..."
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A prototype system for the finegrained filtering of news items has been developed and a pilot test has been conducted. The system is based on an adaptive user model that integrates stereotypes and artificial neural networks. The stereotypes are based on newspaper sections and subsections, along with editor specified and user specified keywords. Eight subjects trained the system over six days of news papers (986 news items) and then tested the system on a seventh day (171 news items). Five users were simply asked to ‘read the news ’ while three users developed ‘corporate ’ profiles with explicit information needs. The evaluations suggests that such an integrated adaptive user model did, in fact, reflect the difference between the two different types of task. In both cases, the results also reflect the quality of the training of the adaptive neural network by the user in creating the user profile.
Adaptive User Modeling for Filtering Electronic News
"... A prototype system for the finegrained filtering of news items has been developed and a pilot test has been conducted. The system is based on an adaptive user model that integrates stereotypes and artificial neural networks. The stereotypes are based on newspaper sections and subsections, along wi ..."
Abstract
 Add to MetaCart
(Show Context)
A prototype system for the finegrained filtering of news items has been developed and a pilot test has been conducted. The system is based on an adaptive user model that integrates stereotypes and artificial neural networks. The stereotypes are based on newspaper sections and subsections, along with editor specified and user specified keywords. Eight subjects trained the system over six days of news papers (986 news items) and then tested the system on a seventh day (171 news items). Five users were simply asked to ‘read the news ’ while three users developed ‘corporate ’ profiles with explicit information needs. The evaluations suggests that such an integrated adaptive user model did, in fact, reflect the difference between the two different types of task. In both cases, the results also reflect the quality of the training of the adaptive neural network by the user in creating the user profile.