text: The use of Association Rule Mining techniques in diverse contexts and domains has resulted in the creation of numerous interestingness measures. This, in turn, has motivated researchers to come up with various classification schemes for these measures. One popular approach to classify the objective measures is to assess the set of mathematical properties they satisfy in order to help practitioners select the right measure for a given problem. In this research, we discuss the insufficiency of the existing properties in literature to capture certain behaviors of interestingness measures. This motivates us to present a novel approach to analyze and classify measures. We refer to this as a rate of change analysis (RCA). In this analysis a measure is described by how it varies if there is a unit change in the frequency count @math , for different pre-existing states of the frequency counts. More formally, we look at the first partial derivative of the measure with respect to the various frequency count variables. We then use this analysis to define two new properties, Unit-Null Asymptotic Invariance (UNAI) and Unit-Null Zero Rate (UNZR). UNAI looks at the asymptotic effect of adding frequency patterns, while UNZR looks at the initial effect of adding frequency patterns when they do not pre-exist in the dataset. We present a comprehensive analysis of 50 interestingness measures and classify them in accordance with the two properties. We also present empirical studies, involving both synthetic and real-world datasets, which are used to cluster various measures according to the rule ranking patterns of the measures. The study concludes with the observation that classification of measures using the empirical clusters share significant similarities to the classification of measures done through the properties presented in this research.
  @cite_13: Finding interesting association rules is an important and active research field in data mining. The algorithms of the Apriori family are based on two rule extraction measures, support and confidence. Although these two measures have the virtue of being algorithmically fast, they generate a prohibitive number of rules most of which are redundant and irrelevant. It is therefore necessary to use further measures which filter uninteresting rules. Many synthesis studies were then realized on the interestingness measures according to several points of view. Different reported studies have been carried out to identify "good" properties of rule extraction measures and these properties have been assessed on 61 measures. The purpose of this paper is twofold. First to extend the number of the measures and properties to be studied, in addition to the formalization of the properties proposed in the literature. Second, in the light of this formal study, to categorize the studied measures. This paper leads then to identify categories of measures in order to help the users to efficiently select an appropriate measure by choosing one or more measure(s) during the knowledge extraction process. The properties evaluation on the 61 measures has enabled us to identify 7 classes of measures, classes that we obtained using two different clustering techniques.
  @cite_14: When mining a large database, the number of patterns discovered can easily exceed the capabilities of a human user to identify interesting results. To address this problem, various techniques have been suggested to reduce and or order the patterns prior to presenting them to the user. In this paper, our focus is on ranking summaries generated from a single dataset, where attributes can be generalized in many different ways and to many levels of granularity according to taxonomic hierarchies. We theoretically and empirically evaluate thirteen diversity measures used as heuristic measures of interestingness for ranking summaries generated from databases. The thirteen diversity measures have previously been utilized in various disciplines, such as information theory, statistics, ecology, and economics. We describe five principles that any measure must satisfy to be considered useful for ranking summaries. Theoretical results show that only four of the thirteen diversity measures satisfy all of the principles. We then analyze the distribution of the index values generated by each of the thirteen diversity measures. Empirical results, obtained using synthetic data, show that the distribution of index values generated tend to be highly skewed about the mean, median, and middle index values. The objective of this work is to gain some insight into the behaviour that can be expected from each of the measures in practice.
  @cite_7: Many techniques for association rule mining and feature selection require a suitable metric to capture the dependencies among variables in a data set. For example, metrics such as support, confidence, lift, correlation, and collective strength are often used to determine the interestingness of association patterns. However, many such measures provide conflicting information about the interestingness of a pattern, and the best metric to use for a given application domain is rarely known. In this paper, we present an overview of various measures proposed in the statistics, machine learning and data mining literature. We describe several key properties one should examine in order to select the right measure for a given application domain. A comparative study of these properties is made using twenty one of the existing measures. We show that each measure has different properties which make them useful for some application domains, but not for others. We also present two scenarios in which most of the existing measures agree with each other, namely, support-based pruning and table standardization. Finally, we present an algorithm to select a small set of tables such that an expert can select a desirable measure by looking at just this small set of tables.
  @cite_9: Objective measures such as support, confidence, interest factor, correlation, and entropy are often used to evaluate the interestingness of association patterns. However, in many situations, these measures may provide conflicting information about the interestingness of a pattern. Data mining practitioners also tend to apply an objective measure without realizing that there may be better alternatives available for their application. In this paper, we describe several key properties one should examine in order to select the right measure for a given application. A comparative study of these properties is made using twenty-one measures that were originally developed in diverse fields such as statistics, social science, machine learning, and data mining. We show that depending on its properties, each measure is useful for some application, but not for others. We also demonstrate two scenarios in which many existing measures become consistent with each other, namely, when support-based pruning and a technique known as table standardization are applied. Finally, we present an algorithm for selecting a small set of patterns such that domain experts can find a measure that best fits their requirements by ranking this small set of patterns.
  @cite_1: 
  @cite_3: An arc quenching composition suitable for deionizing and extinguishing a high voltage electrical arc comprising an effective proportion of hexamethylenetetramine. Depending on the application in which the arc extinguishing composition is employed, the hexamethylenetetramine may be utilized alone, admixed with a suitable binder, or used to impregnate another material.
  @cite_5: 
  @cite_10: This paper discusses several factors influencing the evaluation of the degree of interestingness of rules discovered by a data mining algorithm. This article aims at: (1) drawing attention to several factors related to rule interestingness that have been somewhat neglected in the literature; (2) showing some ways of modifying rule interestingness measures to take these factors into account; (3) introducing a new criterion to measure attribute surprisingness, as a factor influencing the interestingness of discovered rules.
  @cite_11: 
summary: @cite_7 proposed the following 5 properties in addition to the 3 proposed by @cite_1 : symmetry under variable permutation (O1), row column scaling invariance (O2), anti-symmetry under row column permutation (O3), inversion invariance (O4) and null invariance (O5). They conducted a comparative study, testing 21 different IMs against the resulting 8 properties. The authors further proposed that the optimal way of finding a suitable IM would be to let the user define a property vector indicating the properties that would be ideally required for the given application. This property vector would then be compared to the property vectors of the different objective measure to pick out the ideal interestingness measure for that particular case. For instance, the null-invariance property is considered to be important for interestingness measures used in the context of small probability events in a large dataset @cite_11 . While there has been further work in introducing new properties (e.g., @cite_14 , @cite_10 , @cite_3 , @cite_13 , @cite_5 ), these have not been as commonly used or cited as the work of @cite_1 and @cite_9 .