G. Piatetski-Shapiro. Discovery, analysis, and presentation of strong rules. In Knowledge Discovery in Databases, pages 229-248, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....dicult to identify the n best ones. 10 4. 2 Functions that are Linear in g and (p p 0 ) The rst class of nontrivial utility functions that we study weight the generality g of a subgroup and the deviation of the probability of a certain feature p from the default probability p 0 equally [22]. Hence, these functions multiply generality and distributional unusualness of subgroups. Alternatively, we can use the absolute distance jp p 0 j between probability p and default probability p 0 . The multi class version of this function is g 1 c P c jp i p 0 i j where p 0 i is the default ....

.... (76) 3 4 s 2 16 81 = 2 (77) This completes the proof. 4. 5 Negative Results Several independent impurity criteria have led to utility functions which are factorequivalent to f(h) g 1 g (p p 0 ) 2 ; e.g. Gini diversity index and twoing criterion [2] and the chi square test [22]. Note that it is also order equivalent to the utility measure used in Inferrule [26] Unfortunately, this utility function is not bounded and a few examples that have not been included in the sample can impose dramatic changes on the values of this function. This motivates our negative result. ....

G. Piatetski-Shapiro. Discovery, analysis, and presentation of strong rules. In Knowledge Discovery in Databases, pages 229-248, 1991.

.... [Cat91] FWD93] HCC92] Qui93] discovery of causal rules [CH92] Pea92] learning of logical definitions [MF92] Qui90] fitting of functions to data [LSBZ87] Sch90] and clustering [ANB92] C 88] Fis87] The closest work in the machine learning literature is the KID3 algorithm presented in [PS91a] If used for finding all association rules, this algorithm will make as many passes over the data as the number of combinations of items in the antecedent, which is exponentially large. Related work in the database literature is the work on inferring functional dependencies from data [Bit92] ....

....X Y A also holds because the latter may not have minimum support. Similarly, the presence of rules X Y and Y Z does not necessarily mean that X Z holds because the latter may not have minimum confidence. There has been work on quantifying the usefulness or interestingness of a rule [PS91a] What is useful or interesting is often application dependent. The need for a human in the loop and providing tools to allowhuman guidance of the rule discovery process has been articulated, for example, in [B 93] KI91] Tsu90] We do not discuss these issues in this paper, except to point ....

G. Piatestsky-Shapiro. Discovery, analysis, and presentation of strong rules. In G. Piatestsky-Shapiro, editor, Knowledge Discovery in Databases. AAAI/MIT Press, 1991.

....these two properties of hypotheses. We refer the reader to [11] for a discussion on the background of these utility functions. One class of utility functions weights the generality g of a subgroup and the deviation of the probability p of a certain feature from the default probability p0 equally [16]. Hence, these functions multiply generality and distributional unusualness of subgroups. Alternatively, we can use the absolute distance jp p0 j between probability p and default probability p0 . The multi class version of this function is g 1 c P c jp i p0 i j where p0 i is the default ....

....function have been used. See Table 2 for the results. 4. 3 Negative Result Several independent impurity criteria have led to utility functions which are equivalent (up to a constant factor) to f(h) g 1 g (p p0) 2 ; e.g. Gini diversity index, twoing criterion [3] and the chi square test [16]. The order which this criterion imposes on hypotheses is also equal to the order imposed by the criterion of Inferrule [2] Unfortunately, this utility function is not bounded and a few examples that have not been included in the sample can impose dramatic changes on the values of this function. ....

G. Piatetski-Shapiro. Discovery, analysis, and presentation of strong rules. In Knowledge Discovery in Databases, pages 229-248, 1991.

.... [FWD93] HCC92] Qui93] discovery of causal rules [CH92] Pea92] learning of logical definitions [MF92] Qui90] fitting of functions to data [LSBZ87] Sch90] and clustering [ANB92] C 88] Fis87] The closest work in the machine learning literature is the KID3 algorithm presented in [PS91a] If used for finding all association rules, this algorithm will make as many passes over the data as the number of combinations of items in the antecedent, which is exponentially large. Related work in the database literature is the work on inferring functional dependencies from data [Bit92] ....

....X Y A also holds because the latter may not have minimum support. Similarly, the presence of rules X Y and Y Z does not necessarily mean that X Z holds because the latter may not have minimum confidence. There has been work on quantifying the usefulness or interestingness of a rule [PS91a] What is useful or interesting is often application dependent. The need for a human in the loop and providing tools to allow human guidance of the rule discovery process has been articulated, for example, in [B 93] KI91] Tsu90] We do not discuss these issues in this paper, except to point ....

G. Piatestsky-Shapiro. Discovery, analysis, and presentation of strong rules. In G. Piatestsky-Shapiro, editor, Knowledge Discovery in Databases. AAAI/MIT Press, 1991.

.... applicable, work includes the induction of classification rules [8] 11] 22] discovery of causal rules [19] learning of logical definitions [18] fitting of functions to data [15] and clustering [9] 10] The closest work in the machine learning literature is the KID3 algorithm presented in [20]. If used for finding all association rules, this algorithm will make as many passes over the data as the number of combinations of items in the antecedent, which is exponentially large. Related work in the database literature is the work on inferring functional dependencies from data [16] ....

....X Y A also holds because the latter may not have minimumsupport. Similarly, the presence of rules X Y and Y Z does not necessarily mean that X Z holds because the latter may not have minimum confidence. There has been work on quantifying the usefulness or interestingness of a rule [20]. What is useful or interesting is often application dependent. The need for a human in the loop and providing tools to allow human guidance of the rule discovery process has been articulated, for example, in [7] 14] We do not discuss these issues in this paper, except to point out that these ....

G. Piatestsky-Shapiro. Discovery, analysis, and presentation of strong rules. In G. Piatestsky-Shapiro, editor, Knowledge Discovery in Databases. AAAI/MIT Press, 1991.

....algorithms for computing them can be found in [AS94, MTV94, PCY95, SON95, HF95, SA95, SA96] In [SA95, HF95] the generalization of association rules to multiple levels of taxonomies over items is studied. Association rules containing quantitative and categorical attributes are studied in [PS91] and [SA96] The work in [PS91] restricts association rules to be of the form A 1 = v 1 A 2 = v 2 only. They suggest ways to extend their framework to have a range (that is, A 1 2 [l 1 ; u 1 ] rather than a single value in the left hand side of a rule. To achieve this, they partition numeric ....

....them can be found in [AS94, MTV94, PCY95, SON95, HF95, SA95, SA96] In [SA95, HF95] the generalization of association rules to multiple levels of taxonomies over items is studied. Association rules containing quantitative and categorical attributes are studied in [PS91] and [SA96] The work in [PS91] restricts association rules to be of the form A 1 = v 1 A 2 = v 2 only. They suggest ways to extend their framework to have a range (that is, A 1 2 [l 1 ; u 1 ] rather than a single value in the left hand side of a rule. To achieve this, they partition numeric attributes into intervals. ....

G. Piatetsky-Shapiro. Discovery, analysis, and presentation of strong rules. In G. PiatetskyShapiro and W.J. Frawley, editors, Knowledge Discovery in Databases, pages 229--248. AAAI/MIT Press, Menlo Park, CA, 1991.

....the bias toward the formulas that are appropriate for the domain. Examples of some well known systems in this category include ABACUS[5] Bacon[7] and COPER[6] Business databases reflect the uncontrolled real world, where many different causes overlap and many patterns are likely to co exist [10]. Rules in such data are likely to have some uncertainty. The qualitative rule discovery programs are targeted at such business data and they generally use little or no domain knowledge. There has been considerable work in discovering classification rules: Given examples that belong to one of the ....

....in this paper is targeted at discovering qualitative rules. However, the rules we discover are not classification rules. We have no pre specified classes. Rather, we find all the rules that describe association between sets of items. An algorithm, called the KID3 algorithm, has been presented in [10] that can be used to discover the kind of association rules we have considered. The KID3 algorithm is fairly straightforward. Attributes are not restricted to be binary in this algorithm. To find the rules comprising (A = a) as the antecedent, where a is a specific value of the attribute A, one ....

G. Piatetsky-Shapiro, Discovery, Analysis, and Presentation of Strong Rules, In [11], 229--248.

....g 4 f Outerwear, Hiking Boots g 2 f Clothes, Hiking Boots g 2 f Outerwear, Footwear g 2 f Clothes, Footwear g 2 Rules Rule Support Conf. Outerwear ) Hiking Boots 33 66.6 Outerwear ) Footwear 33 66.6 Hiking Boots ) Outerwear 33 100 Hiking Boots ) Clothes 33 100 Figure 2: Example [8], Piatetsky Shapiro argues that a rule X ) Y is not interesting if support(X ) Y ) support(X) Theta support(Y ) We implemented this idea, and used the chi square value to check if the rule was statistically significant. However, this measure did not prune many rules; on two real life datasets ....

G. Piatetsky-Shapiro. Discovery, analysis, and presentation of strong rules. In G. PiatetskyShapiro and W. Frawley, editors, Knowledge Discovery in Databases, pages 229--248. AAAI/MIT Press, Menlo Park, CA, 1991.

....are disjoint sets of items. Efficient algorithms for computing them can be found in [2, 7, 6, 10, 11, 3] In [10, 6] the generalization of association rules to multiple levels of taxonomies over items is studied. Association rules containing quantitative and categorical attributes are studied in [8] and [11] The work in [8] restricts association rules to be of the form A 1 = v 1 A 2 = v 2 only. They suggest ways to extend their framework to have a range (that is, A 1 2 [l 1 ; u 1 ] rather than a single value in the left hand side of a rule. To achieve this, they partition numeric ....

....Efficient algorithms for computing them can be found in [2, 7, 6, 10, 11, 3] In [10, 6] the generalization of association rules to multiple levels of taxonomies over items is studied. Association rules containing quantitative and categorical attributes are studied in [8] and [11] The work in [8] restricts association rules to be of the form A 1 = v 1 A 2 = v 2 only. They suggest ways to extend their framework to have a range (that is, A 1 2 [l 1 ; u 1 ] rather than a single value in the left hand side of a rule. To achieve this, they partition numeric attributes into intervals. ....

G. Piatetsky-Shapiro. Discovery, analysis, and presentation of strong rules. In G. Piatetsky-Shapiro and W. Frawley, editors, Knowledge Discovery in Databases, pages 229--248. AAAI/MIT Press, Menlo Park, CA, 1991.

....denotes the strength of implication and support indicates the frequencies of the occurring patterns in the rule. It is often desirable to pay attention to only those rules which may have reasonably large support. Such rules with high confidence and strong support are referred to as strong rules in [4, 68]. The task of mining association rules is essentially to discover strong association rules in large databases. In [4, 7, 66] the problem of mining association rules is decomposed into the following two steps: 1. Discover the large itemsets, i.e. the sets of itemsets that have transaction support ....

....Clearly, the factor of statistical dependence among various user behaviors analyzed has to be taken into consideration for the determination of the usefulness of association rules. There have been some interesting studies on the interestingness or usefulness of discovered rules, such as [68, 78, 77]. The notion of interestingness on discovered generalized association rules is introduced in [78] The subjective measure of interestingness in knowledge discovery is studied in [77] 3.4 Improving the efficiency of mining association rules Since the amount of the processed data in mining ....

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G. Piatetsky-Shapiro. Discovery, analysis, and presentation of strong rules. In G. PiatetskyShapiro and W. J. Frawley, editors, Knowledge Discovery in Databases, pages 229--238. AAAI/MIT Press, 1991.

....in Section 3.2.3. The types of rules considered include: functional and multivalued dependencies (see e.g. Flach, 1993; Savnik and Flach, 1993; Kantola et al. 1992] determinations (see e.g. Schlimmer, 1991; Shen, 1992] association rules (cf. Agrawal et al. 1993] and strong rules (cf. [Piatetsky Shapiro, 1991]) Various special purpose algorithms have been developed to handle the different types of rules. However, it turns out that because of the expressiveness of first order logic and the Dlab formalism of Claudien, that many of the tasks performed by these special purpose algorithms can be ....

G. Piatetsky-Shapiro. Discovery, analysis, and presentation of strong rules. In G. Piatetsky-Shapiro and W. Frawley, editors, Knowledge Discovery in Databases, pages 229--248. The MIT Press, 1991.

....as an important issue in data mining [4] most of the data mining techniques and tools do not deal with this problem. Instead, their primary concern is to discover all the patterns in the given databases [4, 11, 15] To date, some studies have been performed on the interestingness problem [1, 4, 8, 11, 12, 13, 15]. A number of interestingness measures have also been proposed. These measures can be classified into two classes: objective measures and subjective measures. Objective measures typically involve analyzing the discovered patterns structures, their predictive performances, and their statistical ....

....of interestingness measures have also been proposed. These measures can be classified into two classes: objective measures and subjective measures. Objective measures typically involve analyzing the discovered patterns structures, their predictive performances, and their statistical significance [4, 8, 12]. Examples of objective measures are: coverage, certainty factor, strength, statistical significance and simplicity [3, 6, 8, 11] It has been noted in [11] however, that objective measures are insufficient for determining the interestingness of the discovered patterns. Subjective measures are ....

G. Piatesky-Shapiro. Discovery, analysis, and presentation of strong rules. In G. PiatetskyShapiro and W.J Frawley (eds), Knowledge Discovery in Databases, AAAI/MIT Press, 1991, pg 231-233.

....that is all previous values, and all relevant normative values. We call such a set of deviations a finding. We will also argue that a good measure of the interestingness of a finding is the estimated benefit that could be realized by taking a specific action in response. In an earlier work [ Piatetsky Shapiro, 1991 ] we examined various mathematical and statistical factors for interestingness of rules. Here, we will argue that such objective factors are insufficient and that domain specific, knowledge based factors also have to be included. To set the stage for our discussion on interestingness, we start ....

G. Piatetsky-Shapiro. Discovery, analysis, and presentation of strong rules. In G. Piatetsky-Shapiro and W. J. Frawley, editors, Knowledge Discovery in Databases, pages 229--248. AAAI/MIT Press, Cambridge, MA, 1991.

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