A method of classification for multisource data in remote sensing based on interval-valued probabilities

An axiomatic approach to intervalued (IV) probabilities is presented, where the IV probability is defined by a pair of set-theoretic functions which satisfy some pre-specified axioms. On the basis of this approach representation of statistical evidence and combination of multiple bodies of evidence are emphasized. Although IV probabilities provide an innovative means for the representation and combination of evidential information, they make the decision process rather complicated. It entails more intelligent strategies for making decisions. The development of decision rules over IV probabilities is discussed from the viewpoint of statistical pattern recognition. The proposed method, so called evidential reasoning method, is applied to the ground-cover classification of a multisource data set consisting of Multispectral Scanner (MSS) data, Synthetic Aperture Radar (SAR) data, and digital terrain data such as elevation, slope, and aspect. By treating the data sources separately, the method is able to capture both parametric and nonparametric information and to combine them. Then the method is applied to two separate cases of classifying multiband data obtained by a single sensor. In each case a set of multiple sources is obtained by dividing the dimensionally huge data into smaller and more manageable pieces based on the global statistical correlation information. By a divide-and-combine process, the method is able to utilize more features than the conventional maximum likelihood method

Rejoinder to comments on “reasoning with belief functions: An analysis of compatibility”

AbstractAn earlier position paper has examined the applicability of belief-functions methodology in three reasoning tasks: (1) representation of incomplete knowledge, (2) belief-updating, and (3) evidence pooling. My conclusions were that the use of belief functions encounters basic difficulties along all three tasks, and that extensive experimental and theoretical studies should be undertaken before belief functions could be applied safely. This article responds to the discussion, in this issue, of my conclusions and the degree to which they affect the applicability of belief functions in automated reasoning tasks

ON THE USE OF THE DEMPSTER SHAFER MODEL IN INFORMATION INDEXING AND RETRIEVAL APPLICATIONS

The Dempster Shafer theory of evidence concerns the elicitation and manipulation of degrees of belief rendered by multiple sources of evidence to a common set of propositions. Information indexing and retrieval applications use a variety of quantitative means - both probabilistic and quasi-probabilistic - to represent and manipulate relevance numbers and index vectors. Recently, several proposals were made to use the Dempster Shafes model as a relevance calculus in such applications. The paper provides a critical review of these proposals, pointing at several theoretical caveats and suggesting ways to resolve them. The methodology is based on expounding a canonical indexing model whose relevance measures and combination mechanisms are shown to be isomorphic to Shafer's belief functions and to Dempster's rule, respectively. Hence, the paper has two objectives: (i) to describe and resolve some caveats in the way the Dempster Shafer theory is applied to information indexing and retrieval, and (ii) to provide an intuitive interpretation of the Dempster Shafer theory, as it unfolds in the simple context of a canonical indexing model.Information Systems Working Papers Serie

AN INTUITIVE INTERPRETATION OF THE THEORY OF EVIDENCE IN THE CONTEXT OF BIBLIOGRAPHICAL INDEXING

Models of bibliographical Indexing concern the construction of effective keyword taxonomies and the representation of relevance between document s and keywords. The theory of evidence concerns the elicitation and manipulation of degrees of belief rendered by multiple sources of evidence to a common set of propositions. The paper presents a formal framework in which adaptive taxonomies and probabilistic indexing are induced dynamically by the relevance opinions of the library's patrons. Different measures of relevance and mechanisms for combining them are presented and shown to be isomorphic to the belief functions and combination rules of the theory of evidence. The paper thus has two objectives: (i) to treat formally slippery concepts like probabilistic indexing and average relevance, and (ii) to provide an intuitive justification to the Dempster Shafer theory of evidence, using bibliographical indexing as a canonical example.Information Systems Working Papers Serie

MULTI-PLAYER BELIEF CALCULI: MODELS AND APPLICATIONS

In developing methods for dealing with uncertainty in reasoning systems, it is important to consider the needs of the target applications. In particular, when the source of inferential uncertainty can be tracked to distributions of expert opinions, there might be different ways to model the representation and combination of these opinions. In this paper we present the notion of multiplayer belief calculi - a framework that takes into consideration not only the 'regular' type of evidential uncertainty, but also the diversity of expert opinions when the evidence is held fixed. Using several applied examples, we show how the basic framework can be naturally extended to support different application needs and different sets of assumptions about the nature of the inference process.Information Systems Working Papers Serie