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Table III. Upper and lower limit of threshold (a; = 1.0) Jo. ivecasurement Of the association rules USINE xX~ test The proposed method measures the significance of associations via the x? test for correlation used in classical statistics. For example, we are able to calculate the support of A3 and A3 A Ag [7] if we change the connection of P; node from A; > a; node to A3 > a3 node in Fig. 4. We can repeat this like a chain operation in each generation [7]. Now, we define important association rules one by one, which satisfy

Figure 4 III. Upper and lower limit of threshold (a; = 1.0) Jo. ivecasurement Of the association rules USINE xX~ test The proposed method measures the significance of associations via the x? test for correlation used in classical statistics. For example, we are able to calculate the support of A3 and A3 A Ag [7] if we change the connection of P; node from A; > a; node to A3 > a3 node in Fig. 4. We can repeat this like a chain operation in each generation [7]. Now, we define important association rules one by one, which satisfy

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Fig. 1 The basic structure of the GNP individual
Fig. 1 The basic structure of the GNP individual
(N: the number of tuples (= |TID|)) Table I. The contingency of X and Y
(N: the number of tuples (= |TID|)) Table I. The contingency of X and Y
5.2. GNP structure for association rule mining GNP examines the attribute values of database tuples using judgment nodes and calculates the measurements of association rules using processing nodes [6]. Attributes and their values correspond to judgment nodes and their judgments in GNP, respectively. Therefore, the connections of judgment nodes are represented as association rules. The measurements include support and x? value. Judgment node determines the next node by a judgment result (Yes/No). Figure 4 shows a sample of the connection of nodes in GNP for association rule mining. P| is a processing node and is a starting point of association rules. Each processing node has an inherent numeric order
5.2. GNP structure for association rule mining GNP examines the attribute values of database tuples using judgment nodes and calculates the measurements of association rules using processing nodes [6]. Attributes and their values correspond to judgment nodes and their judgments in GNP, respectively. Therefore, the connections of judgment nodes are represented as association rules. The measurements include support and x? value. Judgment node determines the next node by a judgment result (Yes/No). Figure 4 shows a sample of the connection of nodes in GNP for association rule mining. P| is a processing node and is a starting point of association rules. Each processing node has an inherent numeric order
(a) Calculate the mean and standard deviation of every attribute in the database.
(a) Calculate the mean and standard deviation of every attribute in the database.
Fig. 3 Determination of the initial threshold values
Fig. 3 Determination of the initial threshold values
Fig. 5 Basic structure of GNP association rule mining for databases with continuous items (Pi, P2,..., Ps) and is connected to a judgment node. The Yes- side of the judgment node is connected to another judgment node. Judgment nodes can be reused and shared with some other association rules because of the GNP’s features. The No- side of the judgment node is connected to the next numbered processing node. Figure 5 shows the basic structure of the GNP for association rule mining. In Fig. 5, the No-side of judgment nodes are abbreviated. The number of types of
Fig. 5 Basic structure of GNP association rule mining for databases with continuous items (Pi, P2,..., Ps) and is connected to a judgment node. The Yes- side of the judgment node is connected to another judgment node. Judgment nodes can be reused and shared with some other association rules because of the GNP’s features. The No- side of the judgment node is connected to the next numbered processing node. Figure 5 shows the basic structure of the GNP for association rule mining. In Fig. 5, the No-side of judgment nodes are abbreviated. The number of types of
judgment node functions equals the number of attributes in a database. The above is explained using an example. From Tables II and III, the threshold of the attribute A, is 4.70; and A, of tuple 1 € TJD satisfies the condition of the threshold because A; = 8 in tuple 1. On the other hand, the threshold of the attribute A» is 117.30; but the attribute value of Az does not satisfy the condition of the threshold because Az = 115 in tuple 1, and therefore the node transition from P, to P occurs in Fig. 3. If the examination of the connection from the starting point P; ends, then GNP examines tuple 2 «¢ TJD likewise. Thus, all tuples in the database will be examined. The total number of tuples moving to the Yes-side at each judgment node is calculated for every processing node, which is the starting point for calculating association rules. All GNP individuals are searched in parallel at the same time. If the Yes- side connection of judgment nodes continues and the number of the judgment nodes becomes a cutoff value (maximum number of attributes in extracted association rules), then the Yes-side connection is transferred to the next processing node obligatorily.
judgment node functions equals the number of attributes in a database. The above is explained using an example. From Tables II and III, the threshold of the attribute A, is 4.70; and A, of tuple 1 € TJD satisfies the condition of the threshold because A; = 8 in tuple 1. On the other hand, the threshold of the attribute A» is 117.30; but the attribute value of Az does not satisfy the condition of the threshold because Az = 115 in tuple 1, and therefore the node transition from P, to P occurs in Fig. 3. If the examination of the connection from the starting point P; ends, then GNP examines tuple 2 «¢ TJD likewise. Thus, all tuples in the database will be examined. The total number of tuples moving to the Yes-side at each judgment node is calculated for every processing node, which is the starting point for calculating association rules. All GNP individuals are searched in parallel at the same time. If the Yes- side connection of judgment nodes continues and the number of the judgment nodes becomes a cutoff value (maximum number of attributes in extracted association rules), then the Yes-side connection is transferred to the next processing node obligatorily.
Table IV. Support and confidence of association rules
Table IV. Support and confidence of association rules
See OS EE ee ee ee a Lee wwe Vo VY the frequency of the attributes of all extracted rules, or rules extracted in some of the latest generations when doing Mutation-2. We define the probability of selecting the attribute 5.6. Use of Acquired Information 5.5. Genetic Operators of GNP The following genetic operators are executed to GNP individuals: All programs in a population have the same number of nodes, but the node with the same node number need not have the same function. All the connections of the process- ing nodes are changed randomly in order to extract rules efficiently.
See OS EE ee ee ee a Lee wwe Vo VY the frequency of the attributes of all extracted rules, or rules extracted in some of the latest generations when doing Mutation-2. We define the probability of selecting the attribute 5.6. Use of Acquired Information 5.5. Genetic Operators of GNP The following genetic operators are executed to GNP individuals: All programs in a population have the same number of nodes, but the node with the same node number need not have the same function. All the connections of the process- ing nodes are changed randomly in order to extract rules efficiently.
Fig. 6 Flowchart of the GNP-based data mining method
Fig. 6 Flowchart of the GNP-based data mining method
6. Simulation Results Aj; for judgment nodes by the following: ASSOCIATION RULE MINING FOR CONTINUOUS ATTRIBUTES USING GNP
6. Simulation Results Aj; for judgment nodes by the following: ASSOCIATION RULE MINING FOR CONTINUOUS ATTRIBUTES USING GNP
Fig. 9 Number of rules extracted in the pool for Simulation 2 (Changes thresholds every generation) Fig. 8 Average fitness values of GNP for Simulation 1 (Fixed thresholds)
Fig. 9 Number of rules extracted in the pool for Simulation 2 (Changes thresholds every generation) Fig. 8 Average fitness values of GNP for Simulation 1 (Fixed thresholds)
the results of adjusting the mutation rate r gradually by selecting it randomly from the interval [r, — 0.02, r- + 0.02], where r-, is the current mutation rate. The four simulations were carried out using different intervals of thresholds, that is [u; — aj;0;, Lj; +aj;o;], wo; = 1/6, 1/5, 1/4, 1/3, 1/2, 1, 2 and 3. All experiments were run on a real database [26] that contains continuous attributes about heart disease. It consists of 50 attributes (A;,i = 1,2,...,50) and 115 tuples. In simulations, the population size is 120. The number of processing nodes and judgment nodes are 10 and 78, respectively. We use (3) (x* = 6.63), (4) (supmin = 0.1), and (6) (@pew = 150). In addition, the detailed conditions of extracting association rules in the simulations are as follows: Ngnte(i) + Neon (i) = 6, Nante(i) < 5, Ncon(t) <5. The probability of crossover and mutation are P. = 15/78, Piny = 1/3 and Py2 = 1/5 (78 corresponds to the number of judgment nodes). The number of changes of the connections of the processing nodes at each generation is 5. The simulations were executed for 500 generations, and 20 trials are studied here for all the experiments by changing the random sequences. All algorithms were coded in Java.
the results of adjusting the mutation rate r gradually by selecting it randomly from the interval [r, — 0.02, r- + 0.02], where r-, is the current mutation rate. The four simulations were carried out using different intervals of thresholds, that is [u; — aj;0;, Lj; +aj;o;], wo; = 1/6, 1/5, 1/4, 1/3, 1/2, 1, 2 and 3. All experiments were run on a real database [26] that contains continuous attributes about heart disease. It consists of 50 attributes (A;,i = 1,2,...,50) and 115 tuples. In simulations, the population size is 120. The number of processing nodes and judgment nodes are 10 and 78, respectively. We use (3) (x* = 6.63), (4) (supmin = 0.1), and (6) (@pew = 150). In addition, the detailed conditions of extracting association rules in the simulations are as follows: Ngnte(i) + Neon (i) = 6, Nante(i) < 5, Ncon(t) <5. The probability of crossover and mutation are P. = 15/78, Piny = 1/3 and Py2 = 1/5 (78 corresponds to the number of judgment nodes). The number of changes of the connections of the processing nodes at each generation is 5. The simulations were executed for 500 generations, and 20 trials are studied here for all the experiments by changing the random sequences. All algorithms were coded in Java.
Fig. 11 Number of rules extracted in the pool for Simulation 3 (Change thresholds by mutation rate based on the number of rules) Fig. 10 Average fitness values of GNP for Simulation 2 (Changes thresholds every generation)
Fig. 11 Number of rules extracted in the pool for Simulation 3 (Change thresholds by mutation rate based on the number of rules) Fig. 10 Average fitness values of GNP for Simulation 2 (Changes thresholds every generation)
ASSOCIATION RULE MINING FOR CONTINUOUS ATTRIBUTES USING GNP
ASSOCIATION RULE MINING FOR CONTINUOUS ATTRIBUTES USING GNP
Fig. 12 Average fitness values of GNP for Simulation 3 (Change thresholds by mutation rate based on the number of rules) Fig. 13. Evolution of the mutation rate for Simulation 3 (Change thresholds by mutation rate based on the number of rules)
Fig. 12 Average fitness values of GNP for Simulation 3 (Change thresholds by mutation rate based on the number of rules) Fig. 13. Evolution of the mutation rate for Simulation 3 (Change thresholds by mutation rate based on the number of rules)
Fig. 14 Number of rules extracted in the pool for Simulation 4 (Change thresholds by a gradual change of the mutation rate)
Fig. 14 Number of rules extracted in the pool for Simulation 4 (Change thresholds by a gradual change of the mutation rate)
which means that simulation 4 outperforms simulation 1, simu- lation 2 and also simulation 3. Figure 15 shows that the average fitness value has also increased compared to other simulations, because the threshold change is not so drastic. Figure 16 shows that the evolution of the mutation rate r changes fairly, which shows the fact that a reasonable, frequent change of the thresh- old values is helpful for extracting many rules. The most suit- able a; value for the interval is also a; = 1/6 because higher and lower values than a; = 1/6 generates fewer association rules, as explained in simulations 2 and 3. at later generations, generally, the rules do not come to be gen- erated, so the mutation rate is increased to a certain value so that more rules are obtained.
which means that simulation 4 outperforms simulation 1, simu- lation 2 and also simulation 3. Figure 15 shows that the average fitness value has also increased compared to other simulations, because the threshold change is not so drastic. Figure 16 shows that the evolution of the mutation rate r changes fairly, which shows the fact that a reasonable, frequent change of the thresh- old values is helpful for extracting many rules. The most suit- able a; value for the interval is also a; = 1/6 because higher and lower values than a; = 1/6 generates fewer association rules, as explained in simulations 2 and 3. at later generations, generally, the rules do not come to be gen- erated, so the mutation rate is increased to a certain value so that more rules are obtained.
ASSOCIATION RULE MINING FOR CONTINUOUS ATTRIBUTES USING GNP Fig. 16 Evolution of the mutation rate for Simulation 4 (Change thresholds by < gradual change of the mutation rate)
ASSOCIATION RULE MINING FOR CONTINUOUS ATTRIBUTES USING GNP Fig. 16 Evolution of the mutation rate for Simulation 4 (Change thresholds by < gradual change of the mutation rate)
Related topics:
Association Rule MiningEvolutionary AlgorithmElectrical and Electronic EngineeringGenetic Network Programming
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