Semantics-Based Classification of Rule Interestingness Measures

Semantics-Based Classification of Rule Interestingness Measures

Julien Blanchard (Polytechnic School of Nantes University, France), Fabrice Guillet (Polytechnic School of Nantes University, France) and Pascale Kuntz (Polytechnic School of Nantes University, France)
DOI: 10.4018/978-1-60566-404-0.ch004
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Abstract

Assessing rules with interestingness measures is the cornerstone of successful applications of association rule discovery. However, as numerous measures may be found in the literature, choosing the measures to be applied for a given application is a difficult task. In this chapter, the authors present a novel and useful classification of interestingness measures according to three criteria: the subject, the scope, and the nature of the measure. These criteria seem essential to grasp the meaning of the measures, and therefore to help the user to choose the ones (s)he wants to apply. Moreover, the classification allows one to compare the rules to closely related concepts such as similarities, implications, and equivalences. Finally, the classification shows that some interesting combinations of the criteria are not satisfied by any index.
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Introduction

Most of association rule mining algorithms are unsupervised algorithms, i.e. they do not need any endogenous variable but search all the valid associations existing in the data. This makes the main interest of association rules, since the algorithms can discover relevant rules that the user didn’t even think of beforehand. However, the unsupervised nature of association rules causes their principal drawback too: the number of rules generated increases exponentially with the number of variables. Then a very high number of rules can be extracted even from small datasets.

To help the user to find relevant knowledge in this mass of information, many Rule Interestingness Measures (RIM) have been proposed in the literature. RIMs allow one to assess, sort, and filter the rules according to various points of view. They are often classified into two categories: the subjective (user-oriented) ones and the objective (data-oriented) ones. Subjective RIMs take into account the user’s goals and user’s beliefs of the data domain (Silberschatz & Tuzhilin, 1996; Padmanabhan & Tuzhilin, 1999; Liu et al., 2000). On the other hand, the objective RIMs do not depend on the user but only on objective criteria such as data cardinalities or rule complexity. In this chapter, we are interested in the objective RIMs. This category is very heterogeneous: one can find both elementary measures based on frequency and sophisticated measures based on probabilistic models, as well as information-theoretic measures or statistical similarity measures. In practice, the use of RIMs is problematic since:

  • The RIMs are too numerous, and sometimes redundant (Bayardo & Agrawal, 1999; Tan et al., 2004; Blanchard et al., 2005a; Huynh et al., 2006; Lenca et al., 2007).

  • The meanings of the RIMs are often unclear, so that it is hard to know precicely what is measured.

  • Finally, choosing the RIMs to apply for a given study remains a difficult task for the user.

The main contribution of this chapter is to present a novel and useful classification of RIMs according to three criteria: the subject, the scope, and the nature of the measure. These criteria seem to us essential to grasp the meaning of the RIMs, and therefore to help the user to choose the ones (s)he wants to apply. Moreover, the classification allows one to compare the rules to closely related concepts such as similarities, implications, and equivalences. Finally, the classification shows that some interesting combinations of the criteria are not satisfied by any index.

The remainder of the chapter is organized as follows. In the next section, after introducing the notations, we formalize the concepts of rule and interestingness measure, and then take inventory of numerous measures traditionally used to assess rules. Section 3 defines the three classification criteria, presents our classification of rule interestingness measures, and describes two original measures that we specifically developed to complement the classification. Section 4 discusses the related works. Finally, we give our conclusion in section 5.

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Rules And Interestingness Measures

Notations

We consider a set O of n objects described by boolean variables. In the association rule terminology, the objects are transactions stored in a database, the variables are called items, and the conjunctions of variables are called itemsets.

Let a be a boolean variable which is either an itemset, or the negation of an itemset1. The variable a* is the negation of a. We note A the set of objects that verify a, and na the cardinality of A. The complementary set of A in O is the set A* with cardinality na*. The probability of the event “a is true” is noted P(a). It is estimated by the empirical frequency: P(a)=na/n.

In the following, we study two boolean variables a and b. The repartition of the n objects in O with regard to a and b is given by the contingency Figure 1, where the value nab is the number of objects that verify both a and b.

Figure 1.

Contingency table for two boolean variables a and b. 0 and 1 refer to true and false

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Table of Contents
Foreword
David Bell
Acknowledgment
Yanchang Zhao, Chengqi Zhang, Longbing Cao
Chapter 1
Paul D. McNicholas, Yanchang Zhao
Association rules present one of the most versatile techniques for the analysis of binary data, with applications in areas as diverse as retail... Sample PDF
Association Rules: An Overview
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Chapter 2
Mirko Boettcher, Georg Ruß, Detlef Nauck, Rudolf Kruse
Association rule mining typically produces large numbers of rules, thereby creating a second-order data mining problem: which of the generated rules... Sample PDF
From Change Mining to Relevance Feedback: A Unified View on Assessing Rule Interestingness
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Chapter 3
Solange Oliveira Rezende, Edson Augusto Melanda, Magaly Lika Fujimoto, Roberta Akemi Sinoara, Veronica Oliveira de Carvalho
Association rule mining is a data mining task that is applied in several real problems. However, due to the huge number of association rules that... Sample PDF
Combining Data-Driven and User-Driven Evaluation Measures to Identify Interesting Rules
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Chapter 4
Julien Blanchard, Fabrice Guillet, Pascale Kuntz
Assessing rules with interestingness measures is the cornerstone of successful applications of association rule discovery. However, as numerous... Sample PDF
Semantics-Based Classification of Rule Interestingness Measures
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Chapter 5
Huawen Liu, Jigui Sun, Huijie Zhang
In data mining, rule management is getting more and more important. Usually, a large number of rules will be induced from large databases in many... Sample PDF
Post-Processing for Rule Reduction Using Closed Set
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Chapter 6
Hacène Cherfi, Amedeo Napoli, Yannick Toussaint
A text mining process using association rules generates a very large number of rules. According to experts of the domain, most of these rules... Sample PDF
A Conformity Measure Using Background Knowledge for Association Rules: Application to Text Mining
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Chapter 7
Hetal Thakkar, Barzan Mozafari, Carlo Zaniolo
The real-time (or just-on-time) requirement associated with online association rule mining implies the need to expedite the analysis and validation... Sample PDF
Continuous Post-Mining of Association Rules in a Data Stream Management System
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Chapter 8
Ronaldo Cristiano Prati
Receiver Operating Characteristics (ROC) graph is a popular way of assessing the performance of classification rules. However, as such graphs are... Sample PDF
QROC: A Variation of ROC Space to Analyze Item Set Costs/Benefits in Association Rules
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Chapter 9
Maria-Luiza Antonie, David Chodos, Osmar Zaïane
The chapter introduces the associative classifier, a classification model based on association rules, and describes the three phases of the model... Sample PDF
Variations on Associative Classifiers and Classification Results Analyses
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Chapter 10
Silvia Chiusano, Paolo Garza
In this chapter the authors make a comparative study of five well-known classification rule pruning methods with the aim of understanding their... Sample PDF
Selection of High Quality Rules in Associative Classification
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Chapter 11
Sadok Ben Yahia, Olivier Couturier, Tarek Hamrouni, Engelbert Mephu Nguifo
Providing efficient and easy-to-use graphical tools to users is a promising challenge of data mining, especially in the case of association rules.... Sample PDF
Meta-Knowledge Based Approach for an Interactive Visualization of Large Amounts of Association Rules
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Chapter 12
Claudio Haruo Yamamoto, Maria Cristina Ferreira de Oliveira, Solange Oliveira Rezende
Miners face many challenges when dealing with association rule mining tasks, such as defining proper parameters for the algorithm, handling sets of... Sample PDF
Visualization to Assist the Generation and Exploration of Association Rules
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Chapter 13
Nicolas Pasquier
After more than one decade of researches on association rule mining, efficient and scalable techniques for the discovery of relevant association... Sample PDF
Frequent Closed Itemsets Based Condensed Representations for Association Rules
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Chapter 14
Mengling Feng, Jinyan Li, Guozhu Dong, Limsoon Wong
This chapter surveys the maintenance of frequent patterns in transaction datasets. It is written to be accessible to researchers familiar with the... Sample PDF
Maintenance of Frequent Patterns: A Survey
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Chapter 15
Guozhu Dong, Jinyan Li, Guimei Liu, Limsoon Wong
This chapter considers the problem of “conditional contrast pattern mining.” It is related to contrast mining, where one considers the mining of... Sample PDF
Mining Conditional Contrast Patterns
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Chapter 16
Qinrong Feng, Duoqian Miao, Ruizhi Wang
Decision rules mining is an important technique in machine learning and data mining, it has been studied intensively during the past few years.... Sample PDF
Multidimensional Model-Based Decision Rules Mining
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About the Contributors