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The paper presents visualization techniques for interestingness measures. The process of measure visualization provides useful insights into different domain areas of the visualized measures and thus effectively assists their comprehension and selection for different knowledge discovery tasks. Assuming a common domain form of the visualized measures, a set of contingency tables, which consists of all possible tables having the same total number of observations, is constructed. These originally four-dimensional...
In this paper we present an overview of mathematical models for handling partial entailments and their extensions in a probabilistic frame.
The formal concept analysis gives a mathematical definition of a formal concept. However, in many real-life applications, the problem under investigation cannot be described by formal concepts. Such concepts are called the non-definable concepts (Saquer and Deogun, 2000a). The process of finding formal concepts that best describe non-definable concepts is called the concept approximation. In this paper, we present two different approaches to the concept approximation. The first approach is based...
This paper introduces an encoding of knowledge representation statements
as regular languages and proposes a two-phase approach to
processing of explicitly declared conceptual information. The idea is presented
for the simple conceptual graphs where conceptual pattern search is
implemented by the so called projection operation. Projection calculations
are organised into off-line preprocessing and run-time computations. This
enables fast run-time treatment of NP-complete problems, given that the
intermediate...
Marginal problem (see [Kel]) consists in finding a joint distribution whose marginals are equal to the given less-dimensional distributions. Let’s generalize the problem so that there are given not only less-dimensional distributions but also conditional probabilities. It is necessary to distinguish between objective (Kolmogorov) probability and subjective (de Finetti) approach ([Col,Sco]). In the latter, the coherence problem incorporates both probabilities and conditional probabilities in a unified...
An overview is given of results achieved by F. Matúš on probabilistic conditional independence (CI). First, his axiomatic characterizations of stochastic functional dependence and unconditional independence are recalled. Then his elegant proof of discrete probabilistic representability of a matroid based on its linear representability over a finite field is recalled. It is explained that this result was a basis of his methodology for constructing a probabilistic representation of a given abstract...
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