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Can Confirmation Measures Reflect Statistically Sound Dependencies in Data? The Concordance-based Assessment

Susmaga R., Szczęch I.

Foundations of Computing and Decision Sciences

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2018

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Vol. 43, No. 1

41--66

EN

The paper considers particular interestingness measures, called confirmation measures (also known as Bayesian confirmation measures), used for the evaluation of “if evidence, then hypothesis” rules. The agreement of such measures with a statistically sound (significant) dependency between the evidence and the hypothesis in data is thoroughly investigated. The popular confirmation measures were not defined to possess such form of agreement. However, in error-prone environments, potential lack of agreement may lead to undesired effects, e.g. when a measure indicates either strong confirmation or strong disconfirmation, while in fact there is only weak dependency between the evidence and the hypothesis. In order to detect and prevent such situations, the paper employs a coefficient allowing to assess the level of dependency between the evidence and the hypothesis in data, and introduces a method of quantifying the level of agreement (referred to as a concordance) between this coefficient and the measure being analysed. The concordance is characterized and visualised using specialized histograms, scatter-plots, etc. Moreover, risk-related interpretations of the concordance are introduced. Using a set of 12 confirmation measures, the paper presents experiments designed to establish the actual concordance as well as other useful characteristics of the measures.

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Can interestingness measures be usefully visualized?

Susmaga R., Szczęch I.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 2

323--336

EN

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 data may be effectively represented in three dimensions using a tetrahedron-based barycentric coordinate system. At the same time, an additional, scalar function of the data (referred to as the operational function, e.g., any interestingness measure) may be rendered using colour. Throughout the paper a particular group of interestingness measures, known as confirmation measures, is used to demonstrate the capabilities of the visualization techniques. They cover a wide spectrum of possibilities, ranging from the determination of specific values (extremes, zeros, etc.) of a single measure, to the localization of pre-defined regions of interest, e.g., such domain areas for which two or more measures do not differ at all or differ the most.

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Visualization support for the analysis of properties of interestingness measures

Susmaga R., Szczęch I.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2015

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Vol. 63, nr 1

315--327

EN

The paper considers a particular group of rule interestingness measures, called Bayesian confirmation measures, which have become the subject of numerous, but often exclusively theoretical studies. To assist and enhance their analysis in real-life situations, where time constraints may impede conducting such time consuming procedures, a visual technique has been introduced and described in this paper. It starts with an exhaustive and non-redundant set of contingency tables, which consists of all possible tables having the same number of observations. These data, originally 4-dimensional, may, owing to an inherent constraint, be effectively represented as a 3-dimensional tetrahedron, while an additional, scalar function of the data (e.g. a confirmation measure) may be rendered using colour. Dedicated analyses of particular colour patterns on this tetrahedron allow to promptly perceive particular properties of the visualized measures. To illustrate the introduced technique, a set of 12 popular confirmation measures has been selected and visualized. Additionally, a set of 9 popular properties has been chosen and the visual interpretations of the measures in terms of the properties have been presented.

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Application of Rough Set Theory to Prediction of Antimicrobial Activity of Bis-Quaternary Imidazolium Chlorides

Pałkowski Ł., Krysiński J., Błaszczyński J., Słowiński R., Skrzypczak A., Błaszczak J., Gospodarek E., Wróblewska J.

Fundamenta Informaticae

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2014

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Vol. 132, nr 3

315--330

EN

The paper investigates relationships between chemical structure, surface active properties and antibacterial activity of 70 bis-quaternary imidazolium chlorides. Chemical structure and properties of imidazolium chlorides were described by 7 condition attributes and antimicrobial properties were mapped by a decision attribute. Dominance-based Rough Set Approach (DRSA) was applied to discover a priori unknown rules exhibiting monotonicity relationships in the data, which hold in some parts of the evaluation space. Strong decision rules discovered in this way may enable creating prognostic models of new compounds with favorable antimicrobial properties. Moreover, relevance of the attributes estimated from the discovered rules allows to distinguish which of the structure and surface active properties describe compounds that have the most preferable and the least preferable antimicrobial properties.