CHAPTER - 7 FUZZY LOGIC IN DATA MINING

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1 CHAPTER - 7 FUZZY LOGIC IN DATA MINING 7.1. INTRODUCTION Fuzzy logic is an approach of data mining that involves computing the data based on the probable predictions and clustering as opposed to the traditional true or false. Algorithms that use fuzzy logic are increasingly being applied in several disciplines to help in mining of databases. One of the potential applications of Fuzzy logic algorithms is the clustering of breast cancer data to enable oncologists detect and evaluate breast cancer risks such as malignant tumors. Breast cancer is currently one of the major health problems as well as the leading cause of death amongst women worldwide (Jemal A, et.al, 2011). Consequently, early detection of cancer risks is one of the key ways of improving the prognosis of the disease. Although there are a number radiological techniques such as mammography that can be used in the early detection of breast cancer risks, the enormous data generated by these techniques often make it difficult for radiologists to accurately evaluate breast cancer data (Dorf RC, et.al, 2001). The major variables in breast cancer databases include the information regarding the risk factors and as well as mammographic findings. Although the primary causes of cancer are not yet known, there are a number of risk factors that have been identified and can therefore be fixed to particular classes. Generally, tumors can be malignant (cancerous) or benign (non-cancerous). In most cases, malignant tumors have rapid growth that often results in the destruction of normal tissues and their eventual spread to all parts of the body. On the other hand, benign tumors tend to be localized and grow sly without any significant spread to the other parts of the body (Mukherjee S 2010). Consequently, the risk of breast cancer development is generally higher when malignant tumors are detected in an individual. 79

2 Artificial intelligence techniques such as fuzzy clustering algorithms can therefore significantly improve the diagnosis and evaluation of breast cancer risks through clustering of the particular data elements (Jalil Addeh, et.al, 2012). The incorporation of fuzzy logic algorithms in data mining is a powerful tool that can be employed in the extraction, clustering, quantification and analysis of the data base information regarding the assessment and diagnosis of cancer risks. Association rule mining is an active data mining research area. The key strength of fuzzy association rule mining is its completeness (Gautam Pratima, et.al, 2010). The strength also produces a huge number of candidate itemsets. This makes it ineffective for a data mining system to analyze them. It produces a huge number of fuzzy associations. The huge number makes it difficult for a human user to analyze them. One of the greatest potential advantages of incorporating fuzzy logic in data mining is the fact that such algorithms can significantly be used in the modeling of inaccurate, nonlinear and complex data systems by implementing human knowledge and experience as a set of fuzzy rules that uses fuzzy variables for inference purposes (Nguyen HT, et.al, 2003) (Luo J, et.al, 2000). For example, when using fuzzy algorithm for the prediction and clustering of breast cancer data, the human experience and knowledge related to breast cancer risks can be expressed as a set of inference rules of deduction that are then attached to the fuzzy logic system (Mangalampalli Ashish, et.al, 2009). Another important advantage of fuzzy algorithms systems for prediction and clustering of breast cancer data is that they usually have a significantly high inference speed. This chapter proposes a fuzzy association and clustering algorithm that can be used in the data mining of breast cancer data and consequently in the evaluation and prediction of cancer risks in patients with suspected cancer cases INPUT The breast cancer domain was obtained from the University Medical Centre, Institute of Oncology, Ljubljana, Yugoslavia. M. Zwitter and M. Soklic have provided the data (Michalski RS, et.al, 1986). The Arff conversion of the data set was provided by Håkan Kjellerstrand. This data set has 286 instances described by 9 attributes + one class attribute. The set includes 201 instances of one class and 85 instances of another class. 80

3 7.3. ASSOCIATION RULE MINING Mining association rule is one of the important research problems in data mining. There are many known algorithms for mining Boolean association rule such as Apriori, AprioriTID and AprioriHybrid algorithms for mining association rule (Ada Wai- Chee Fu, et.al, 1998). Although the current quantitative association rule mining algorithms can solve some of the problems introduced by quantitative attributes, they introduce some problems (Subramanyam RBV, et.al, 2006). The first problem is caused by the sharp boundary between intervals. The algorithms either ignore or over-emphasize the elements near the boundary of the intervals in the mining process. The use of shape boundary interval is also not intuitive with respect to human perception (Zuoliang Chen, et.al, 2007) (Zuoliang Chen, et.al, 2008). The fuzzy association rule is of the form, If X is A then Y is B. As in the binary association rule, X is A is called the antecedent of the rule while Y is B is called the consequent of the rule. X and Y are sets of attributes of database and A, B are sets containing fuzzy sets which characterize X and Y respectively (Subramanyam RBV, et.al, 2006). The fuzzy association rule is easily understandable because of linguistic terms associated with the fuzzy set. Many ARM algorithms are more concerned with efficient implementations than producing effective rules. In almost all ARM algorithms, thresholds (both confidence and support) are crisp values. This support specification may not suffice for queries and rule representations that require generating rules that have linguistic terms such as protein etc. Fuzzy approaches deal with quantitative attributes by mapping numeric values to real values FUZZY ASSOCIATION RULE MINING i. Candidate itemsets are generated with predefined minimum support and minimum confidence. ii. Implement the k-means clustering algorithm to find centroids or mid-points. iii. Using these centroids fuzzy sets and membership degree is calculated. iv. Fuzzy rules are generated using the fuzzy support and confidence found. 81

4 7.4. CLUSTERING When dealing with uncertainties in databases, fuzzy logic clustering algorithms can be used to cluster different elements of data into various membership levels depending on their closeness (Castillo O, et.al, 2008). For example, during the evaluation of breast cancer risks, mammogram data may possess some degree of fuzziness such as ill-defined shapes, indistinct borders and different densities. In this regard, a fuzzy clustering algorithm can be one of the most effective ways of handling the fuzziness of data related to breast cancer. As an intelligent technique, Fuzzy logic data mining algorithms not only provide excellent analysis of the data but can also be used to develop accurate results that are easy to implement. The foling Fuzzy data clustering algorithm for clustering of data related to breast cancer risks works by dividing cancer risk data elements into clusters which share many similarities. Each of the data clusters is then associated with a specific set of fuzzy member ship functions which will indicate the extent of closeness between the data element and the cluster (Bezdek JC 1984). The central notion of the fuzzy clustering algorithm is based on the fact that the membership values of the fuzzy sets or the truth values of fuzzy logic ranging from 0.0 to 1.0 (Chih-Tang Chang, et.al, 2011) (Deng Jiabin, et.al, 2010). The major variables in breast cancer databases includes the information regarding the risk factors and as well as mammographic findings. Two important clustering algorithms namely centroid based K-Means and representative object based FCM (Fuzzy C-Means) clustering algorithms are compared (Ghosh Soumi, et.al, 2013). These algorithms are applied and performance is evaluated on the basis of the efficiency of clustering output. 82

5 FUZZY K-MEANS ALGORITHM i. By using k-means algorithm and the number of clusters, centroid point will be calculated. ii. The data points will be grouped by calculating the distance between centroid points and the data points. iii. The result of the k-means taken as input for the fuzzy k-means algorithm. iv. The centroid point of the resultant cluster will be taken and average of the centroid of the cluster is compared with the data points which are present in border of the respective clusters and finally the border points are included in the clusters FUZZY C-MEANS ALGORITHM i. Initial centroid point will be assigned using the number of c clusters. ii. The data points will be grouped by calculating the distance between centroid points and the data points. iii. The centroid point of the resultant cluster and each data point will be taken and the membership value will be calculated. iv. Using the membership value, the new centroid point is calculated. v. Calculate the distance between new centroid point and the data point present in the file. vi. The membership value of the data point which is closer to centroid point of the clusters will be found and added to the respective clusters EXPERIMENT EXPERIMENT USING ASSOCIATION RULE MINING ALGORITHM The data was processed by the Association Rule Mining algorithm with minimum support 0.25 and minimum confidence 0.9 to find the fuzzy rules. The rules generated with a minimum confidence measure of 0.90 and above are given be in Table

6 Table 7.1: Association Data Analysis for ARM Algorithm Sl. Confidence If Then No. Measure 1 node-cap no inv-nodes between inv-nodes between 0-2 node-cap no node-cap no, breast-side inv-nodes between left 4 breast side is left and invnode node-cap no 0.95 is node-cap is no and class is inv-node no-recurrence-event 6 class is no-recurrenceevents node-cap no 0.95 and inv-node is menopause is premeno node-cap no 0.93 and inv-node is irradiate is No and class is node-cap no 0.91 no-recurrence-events 9 node-cap is no and inv-node irradiate is No 10 irradiate is No and invnode node-cap no 0.96 is irradiate is No, class is inv-node no-recurrence-events and node-cap is no 12 ays irradiate is No, class is no-recurrence-events and inv-node is 0-2 node-cap no 0.98 According to the above output, the percentage of the attribute node-cap with value no along with the attribute inv-node with value 0-2 is The attribute node-cap with the value no alone occurs in 11 rules and the attribute inv-node with value 0-2 occurs in 11 rules along with the other attributes. In the above output the attributes node-cap with value no and inv-node with value 0-2 plays a major role in forming association rules. The output changes with the change in the values of minimum support and minimum confidence. 84

7 EXPERIMENT USING FUZZY ASSOCIATION RULE MINING ALGORITHM The case study was processed by the Fuzzy ARM algorithm with minimum support 0.25 and minimum confidence 0.9 to find the fuzzy rules. Table 7.2. The rules generated with only a confidence measure of 1.0 are given be in Table 7.2: Association Data Analysis for Fuzzy ARM Algorithm Sl. Confidence If Then No. Measure 1 age between tumor size between age between tumor size between age between inv-node between age between inv-node between age between deg-malignant age between deg-malignant tumor size between inv-node between tumor size between inv-node between tumor size between deg-malignant tumor size between deg-malignant inv-node between deg-malignant inv-node between deg-malignant From the above table the analysis highlights the foling information. The attribute age [40-99] plays a major role in generating the rules. The attributes tumorsize [15-59] and inv-node [20-59] take part in both sides of the rule generation. The attribute deg-malignant 2 plays a major role in forming the remaining fuzzy rules EXPERIMENT USING FUZZY K-MEANS ALGORITHM The input was processed by the Fuzzy k-means algorithm with k as 5 to find the tuples in clusters. It was found that Cluster 1 contains 30 data points, Cluster 2 contains 49 data points, Cluster 3 contains 41 data points, Cluster 4 contains 79 data points and Cluster 5 contains 87 data points. 85

8 Table 7.3: Cluster Data Analysis for Fuzzy K means Algorithm Attribute Name Percentage of data present in each attribute Cluster 1 Cluster 2 Cluster 3 Cluster 4 Cluster : 10% 30-39: 10 % 40-49: 31% 50-59: 32% : 3% : 1% Age 40-49: 43 % 50-59: 37 % : 58% 50-59: 67% : 30% 50-59: 40 % : 18% :10% : 30% : 69% 70-79: 4 % Menopause premeno : 67% ge40: 51 % premeno : 49% ge40: 67% lt40: 5% ge40: 67% premeno: 28% premeno: 90% Tumor_size 0-4: 23% 5-9: 10% : 57% : 10% : 33% : 45% : 6% : 16% 0-4, 5-9: 2% : 27% :47% : 22% : 18% : 38% : 44% : 9% : 31% : 28% : 29% : 3% Inv-nodes 3-5 : 23% 9-11 : 10% : 57% : 10% : 100% 3-5: 2% 9-11: 2% 12-14: 27% 18-20: 47% :22% :18% 27-29: 38% 33-35: 44% 18-20: 9% :31% 27-29: 28% 30-32:29% 36-39: 3% Node_caps No : 97% No : 70% No : 93% No : 68% No : 80% Degree_mali gnant 1:37% 2:53% 3:10% 1:18% 2:45% 3:37% 1:41% 2:44% 3:15% 1:24% 2:38% 3:38% 1:22% 2:46% 3:32% Breast Left : 53% Right :55% Left : 45 % Left : 64% Left : 57% Left: 54% Breast Quadrant Left_up:30% Left_:47% Right_up:7% Right_:16% Left_up:41% Left_:41% Right_up:18% Left_up:46% Left_:37% Right_up:10% Right_:7% Left_up:37% Left_:43% Right_up:11% Right_:9% Left_up:36% Left_:39% Right_up:14% Right_:11% Irradiate No : 87% No : 67% No : 88% No : 75% No : 74% 86

9 From the above table the analysis shows the foling information. In cluster 1 the attributes that are important in forming the cluster are age [40-49], menopause premeno, tumor size [10-14], Inv node [12-14], Node caps No, Degree of malignant 2, Breast Quadrant Left Low, Irradiate No. In the formation of cluster 2 the attributes that are taking part are age [50-59], menopause ge40, tumor size [40-49], Inv node [36-39], Node caps No, Degree of malignant 2, Right Breast, Breast Quadrant Left Low and Left Up, Irradiate No. In cluster 3 the attributes that play an important role are age [60-69], menopause ge40, tumor size [15-19], Inv node [18-20], Node caps No, Degree of malignant 2, Left Breast, Breast Quadrant Left up, Irradiate No. In cluster 4 the attributes that are essential are age [50-59], menopause ge40, tumor size [30-34], Inv node [33-35], Node caps No, Degree of malignant 2 and 3, Left Breast, Breast Quadrant Left Low, Irradiate No. In cluster 5 the attributes that take part in the formation of cluster are age [40-49], menopause premeno, tumor size [20-24], Inv node [24-26], Node caps No, Degree of malignant 2, Left Breast, Breast Quadrant Left Low, Irradiate No. The analysis shows that the occurrence of cancer depends on the attributes of age with the range from 40-69, menopause with the value being either ge40, premeno, breast quadrant being left, degree of malignant being 2 and irradiate being No EXPERIMENT USING FUZZY C-MEANS ALGORITHM The input of breast cancer data was processed by the Fuzzy C-means algorithm with c 5 to find the tuples in clusters. It was found that Cluster 1 contains 130 data points, Cluster 2 contains 218 data points, Cluster 3 contains 130 data points, Cluster 4 contains 130 data points and Cluster 5 contains 218 data points. 87

10 Table 7.4: Cluster Data Analysis for Fuzzy C means Algorithm Attribute Name Age Percentage of data present in each attribute Cluster 1 Cluster 2 Cluster 3 Cluster 4 Cluster : 3% : 10% : 32% : 36% : 15% : 4% Menopause premeno : 53% Tumor_size Inv-nodes 0-4 : 4% 5-9 : 2% :11% : 8% : 21% : 16% : 22% : 6% : 8% : 0.25% : 2% 3-5 : 4% 9-11 : 2% : 11% : 2% : 20% : 17% : 22% : 16% : 1% : 10% : 31% : 37% : 18% : 4% ge40 : 51 % premeno : 49% : 33% : 45% : 6% : 16% : 100% : 1% : 10.8% : 32% : 37% : 15% : 5% ge40 : 67% 0-4 : 2% 5-9 : 2% : 27% : 47% : 22% 3-5 : 2% 9-11 : 2% : 27% : 47% : 22% : 1% : 10% : 32% : 37% : 15% : 4% lt40 : 5% ge40 : 67% premeno : 28% : 18% : 38% : 44% : 18% : 38% : 44% : 1% : 30% : 69% : 29% : 37% : 19% premeno : 90% : 9% : 31% : 28% : 29% : 3% : 9% : 31% : 28% : 29% : 3% Node_caps No : 87% No : 70% No : 93% No : 68% No : 80% 1 : 30% 1 : 18% 1 : 41% 1 : 24% 1 : 22% Degree_mali 2 : 43% 2 : 45% 2 : 44% 2 : 38% 2 : 46% gnant 3 : 27% 3 : 37% 3 : 15% 3 : 38% 3 : 32% Breast Right : 57% Breast Quadrant Left_up:67% Right_up:23% Right_:13% Right :55% Left : 45 % Left_up:41% Left_:41% Right_up:18% Left : 64% Left : 57 % Left : 54 % Left_up:46% Left_:37% Right_up:10% Right_:7% Left_up:37% Left_:43% Right_up:11% Right_:9% Left_up:36% Left_:39% Right_up:14% Right_:11% Irradiate No : 100% No : 67% No : 88% No : 75% No : 74% The analysis of the above table leads to the interpretation of the foling information. In cluster 1 the attributes that are measurable are age [50-59], menopause premeno, tumor size [20-24], Inv node [33-35], Node caps No, Degree of malignant 2, Breast Quadrant Left up, Irradiate No. 88

11 In cluster 2 the attributes that are distinguishable are age [50-59], menopause ge40, tumor size [40-49], Inv node [36-39], Node caps No, Degree of malignant 2, Right Breast, Breast Quadrant Left Low and Left Up, Irradiate No. In cluster 3 the attributes that are key in the formation are age [50-59], menopause ge40, tumor size [15-19], Inv node [18-20], Node caps No, Degree of malignant 2, Left Breast, Breast Quadrant Left up, Irradiate No. In cluster 4 the attributes that are central are age [50-59], menopause ge40, tumor size [30-34], Inv node [33-35], Node caps No, Degree of malignant 2 and 3, Left Breast, Breast Quadrant Left Low, Irradiate No. In cluster 5 the attributes that are essential are age [40-49], menopause premeno, tumor size [20-24], Inv node [24-26], Node caps No, Degree of malignant 2, Left Breast, Breast Quadrant Left Low, Irradiate No. The analysis testifies that the occurrence of cancer depends on the attributes of age [40-59], menopause with the value being either ge40 or premeno, breast quadrant being left, degree of malignant being 2 and irradiate being No. 89

12 Table 7.5 Common Data Analysis for Fuzzy K means and Fuzzy C means Algorithms Attribute Name Age Menopause Tumor_size Inv-nodes Node_caps Degree_malig nant Breast Breast Quadrant Irradiate Percentage of common data present in each attribute Cluster 1 Cluster 2 Cluster 3 Cluster 4 Cluster % % 32% 3% % 43 % % 37% 32% % % 58% 67% 40% % % % % % 10% % 36% % 15% % 67% ge40 51 % lt40 5% premeno 53% ge40 67% ge40 67% premeno 90% premeno 49% premeno 28% % % % 0-4 2% % 4% % % 2% % 5-9 2% % % 57% % % % 11% % 10% % % % 8% % 23% 3-5 2% % 3-5 4% % % % 10% % % 2% % 57% % % % 11% % 2% % % % No 97% 87% No 70% No 93% no 68% No 80% 1 37% 30% 1 18% 1 41% 1 24% 1 22% 2 53% 43% 2 45% 2 44% 2 38% 2 46% 3 10% 27% 3 37% 3 15% 3 38% 3 32% Right 55 % Left 45% Left 64% left 57% left 54% left_up up No 67% 7% 7% 23% left_ 16% 13% up 87% 100% left_up 41% 41% 18% left_up left_ up 46% 37% 10% 7% left_up 37% left_up 36% left_ up 43% 11% 9% left_ up No 67% No 88% no 75% No 74% 39% 14% 11% 90

13 The analysis shows that for a few attributes the percentage of occurrence varies in different clusters. The attributes that take part in the determination of cancer are age [40-49] [50-59], menopause with value being premeno, node-caps being no, degree of malignancy being 2, breast quadrant being left_up and irradiate being no CONCLUSION Fuzzy Association Rule Mining only works on quantifiable data that are given in different ranges. To implement fuzzy logic in association rule mining clustering has to be applied first and later association rule mining. The analysis shows that the occurrences of cancer depend on the attributes of age and degree of malignant. Applying Fuzzy logic on both Association Rule Mining and Clustering techniques on this data set shows that attribute age [40-99] plays a major role in generating the rules and forming clusters. The analysis shows that for a few attributes the percentage of occurrence varies in different clusters. The attributes that take part in the determination of cancer are age [40-49][50-59], menopause with value being premeno, node-caps being no, degree of malignancy being 2, breast quadrant being left_up and irradiate being no. FARM algorithm works for quantifiable data and not textual data. Although the primary causes of cancer are not yet known, there are a number of risk factors that have been identified and can therefore be fixed to particular classes. Generally, tumors can be malignant (cancerous) or benign (non-cancerous). In most cases, malignant tumors have rapid growth that often results in the destruction of normal tissues and their eventual spread to all parts of the body. The experiment results in the findings that age, menopause and degree of malignancy are some of the reasons for breast cancer. 91