Observational Calculi and Association Rules

Rauch, Jan

doi:10.1007/978-3-642-11737-4

Cited by 33 publications

(31 citation statements)

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“…More precisely, the patterns the LISp-Miner deals with contain several derived Boolean attributes (from two in the 4ft-Miner to five in the SD4ft-Miner). Moreover, the procedures described in Section 14.9 in [6] deal also with categorical attributes not transformed into Boolean ones. However, we have not used these latter procedures in this study.…”

Section: Discussionmentioning

confidence: 99%

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Using GUHA Data Mining Method in Analyzing Road Traffic Accidents Occurred in the Years 2004–2008 in Finland

Turunen

2017

Data Sci. Eng.

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The suitability of the GUHA data mining method in analyzing a big data matrix is studied in this report in general, and, in particular, a data matrix containing more than 80,000 road traffic accidents occurred in Finland in 2004-2008 is examined by LISp-Miner, a software implementation of GUHA. The general principles of GUHA are first outlined, and then, the road accident data is analyzed. As a result, more than 10,000 associations and dependencies, called hypothesis in the GUHA language, were found; some easily understandable of them are presented here. Our conclusion is that the GUHA method is useful, in particular when one wants to explore relatively small size, but still significant dependencies in a given large data matrix.

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Section: Discussionmentioning

confidence: 99%

“…At present there are 21 quantifiers implemented to LISpMiner [6]. In general, there are various types of generalized quantifiers in GUHA theory formalizing various kinds of associations:…”

Section: Introductionmentioning

confidence: 99%

Using GUHA Data Mining Method in Analyzing Road Traffic Accidents Occurred in the Years 2004–2008 in Finland

Turunen

2017

Data Sci. Eng.

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“…O NE of the main directions in data mining is extracting various kinds of logical rules, such as classification rules, association rules or fuzzy rules, from the available data [1]- [4]. Logical rules, especially the Boolean IF .…”

Section: Introductionmentioning

confidence: 99%

“…During the last 10-15 years, however, quantifiers based on other data analysis methods emerged, in particular, general contingency tables, estimates of joint distributions of multivariate discrete variables, searching for exceptionally high values of some interestingness measures, checking a state change of an object by time series analysis of its attributes (action rules), and fuzzy hypotheses testing [7]- [12]. A survey can be found in [13], whereas much of the underlying theoretical developments of observational calculus has been presented in the recent monograph [4].…”

Section: Introductionmentioning

confidence: 99%

Using Copulas in Data Mining Based on the Observational Calculus

Holeňa

Bajer

Scavnicky

2015

IEEE Trans. Knowl. Data Eng.

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The objective of the paper is a contribution to data mining within the framework of the observational calculus, through introducingǵeneralized quantifiers related to copulas. Fitting copulas to multidimensional data is an increasingly important method for analyzing dependencies, and the proposed quantifiers of observational calculus assess the results of estimating the structure of joint distributions of continuous variables by means of hierarchical Archimedean copulas. To this end, the existing theory of hierarchical Archimedean copulas has been slightly extended in the paper: It has been proven that sufficient conditions for the function defining a hierarchical Archimedean copula to be indeed a copula, which have so far been rigorously established only for the special case of fully nested Archimedean copulas, hold in general. These conditions allow to define three new generalized quantifiers, which are then thoroughly validated on four benchmark data sets and one data set from a real-world application The paper concludes by comparing the proposed quantifiers to a more traditional approach -maximum weight spanning trees.

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“…Examples of 4ft-quantifiers and their associated functions F ≈ are given in section 2.3. There are about forty 4ft-quantifiers defined and studied in [23]. Associated functions of some of them are defined such that suitable thresholds are used for various measures of interestingness of association rules as defined e.g.…”

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Formal Framework for Data Mining with Association Rules and Domain Knowledge – Overview of an Approach

Rauch

2015

Fundamenta Informaticae

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A formal framework for data mining with association rules is introduced. The framework is based on a logical calculus of association rules which is enhanced by several formal tools. The enhancement allows the description of the whole data mining process, including formulation of analytical questions, application of an analytical procedure and interpretation of its results. The role of formalized domain knowledge is discussed.We deal with association rules ϕ ≈ ψ where ϕ and ψ are general Boolean attributes derived from columns of analysed data matrices. Data matrices are results of observation of a finite number of objects. Rows of a data matrix correspond to observed objects, columns correspond to observed attributes. There is a finite number of possible values (i.e. categories) of each attribute. Principles of our approach to association rules and calculi of association rules are informally introduced in sections 2.1.1 -2.1.3. Let us note that detailed description of logical calculi of association rules is provided in [23]. Boolean AttributesBasic Boolean attributes are defined first. Basic Boolean attribute is an expression A(α) where A is an attribute and α is a subset of its categories. Expressions Sex(F ) and Education(secondary, university) are examples of basic Boolean attributes, see logical calculus ST of association rules inspired by a real data set introduced in section 2. Basic Boolean attributea value of the column of M corresponding to the attribute A in the row o. Each basic Boolean attribute is a Boolean attribute. If κ and λ are Boolean attributes then ¬κ, κ ∧ λ, and κ ∨ λ are Boolean attributes. Expression Sex(F) ∧ Education(secondary, university) and Diabetes(yes) ∨ Infarction(yes) are examples of Boolean attributes, see also section 2.2. Truthfulness of Boolean attributes ¬κ, κ ∧ λ, and κ ∨ λ is defined in a usual way. This means that ¬κ is true in a row o of a data matrix M if and only if κ is false in o, κ ∧ λ is true in o if and only if both κ and λ are true in o, and κ ∨ λ is true in o if and only if κ or λ are true in o.The symbol ≈ used in ϕ ≈ ψ is called 4ft-quantifier. A function F ≈ mapping a set of all quadruples a, b, c, d of non-negative integer numbers satisfying a + b + c + d > 0 into the set {0, 1} is associated to each 4ft-quantifier ≈. Examples of 4ft-quantifiers and their associated functions F ≈ are given in section 2.3. There are about forty 4ft-quantifiers defined and studied in [23]. Associated functions of some of them are defined such that suitable thresholds are used for various measures of interestingness of association rules as defined e.g. in [5]. The additional 4ft-quantifiers correspond to statistical hypotheses tests. The association rule ϕ ≈ ψ is true in a data matrix M if and only if it is F ≈ (a, b, c, d) = 1 where a, b, c, d = 4f t(ϕ,ψ, M) and F ≈ is the associated function of ≈. J. Rauch / Formal Framework for Data Mining with Association Rules and Domain Knowledge -Overview 175 2.1.3 . Calculus of Association RulesDeduction rules of the form ϕ≈ψ ϕ ≈ψ where ...

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Observational Calculi and Association Rules

Cited by 33 publications

References 0 publications

Using GUHA Data Mining Method in Analyzing Road Traffic Accidents Occurred in the Years 2004–2008 in Finland

Using GUHA Data Mining Method in Analyzing Road Traffic Accidents Occurred in the Years 2004–2008 in Finland

Using Copulas in Data Mining Based on the Observational Calculus

Formal Framework for Data Mining with Association Rules and Domain Knowledge – Overview of an Approach

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