Comparative studyon Partition Based Clustering Algorithms

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International Journal of Research in Advent Technology, Vol.6, No.9, September 18 Comparative studyon Partition Based Clustering Algorithms E. Mahima Jane 1 and Dr. E. George Dharma Prakash Raj 2 1 Asst. Prof., Department of Computer Applications, Madras Christian College, Tambaram 600 059 2 Asst. Prof., Department of Computer Science and Engineering, Bharathidasan University, Trichy - 6 023. 1 mahima.jane@gmail.com, 2 geor9geprakashraj@yahoo.com Abstract- are formed by assemblage input data sets in which the objects in the same group are most similar than objects of other groups and the process is called clustering. This paper compares the various enhance k-means partition clustering algorithms for Big Data by proposing new methods to initialize new center values. In order to improve the dependence on the initial values, it proposes various sorting methods. The execution time and the number of iterations are taken into consideration. Keywords: Clustering, Big Data, Partition, Big Data 1. INTRODUCTION Clustering is the task of dividing the data points into a number of groups such that data points in the same groups are more alike to other data points in the same group than those in other groups. A Cluster is a set of entities which are similar inside the same cluster which is a powerful mechanism to analyze when the size of the data is huge. In Partitioning-based algorithms, initial groups are specified and reallocated towards a union. These clusters should fulfill the following requirements: (1) each group must contain at least one object, and (2) each object must belong to exactly one group. This paper is structured as follows Section II Related work onpartition based algorithms, Section III discusses the performance of the various enhanced clustering algorithms and Section IV concludes the paper. 2. RELATED WORK Traditional K Algorithm Yamini[1] k- algorithm using Hadoop MapReduce randomly choose centroids and k for the cluster formations.they have performed in distributed environment. Chitra et al [7] and Kavya et al[8] have compared the various clustering algorithms. The Traditional K means algorithm is given is given below. 1. Step 1: Randomly select k data objects from data set D as initial centers. 2. Step 2: Repeat; 3. Step 3: Calculate the distance between each data object di (1 <= i<=n) and all k clusters C j(1 <= j<=k) and assign data object di to the nearest cluster. 4. Step 4: For each cluster j (1 <= j<=k), recalculate the cluster center. 5. Step 5: Until no change in the center of clusters. The - algorithm is given below in two phases. AzharRauf[2] In the enhanced K- algorithm performs the distance calculation. Using arithmetic mean initial cluster centers are calculated. Phase-I: To find the initial clusters Step 1: Find the size of cluster Si (1= i = k) by Floor (n/k). Where n= number of data points Dp (a1, a2, a3 an) K= number of clusters. Step 2: Create K number of Arrays Ak Step 3: Move data points (Dp) from Input Array to Ak until Si =Floor (n/k). Step 4: Continue Step 3 until all Dp removed from input array Step 5: Exit with having k initial clusters. Phase-II: To find the final clusters Step 1: Compute the Arithmetic Mean M of allinitial clustersci Step 2:Set 1 j k Step 3:Compute the distance D of all Dp to M of Initial Cj Step 4:If D of Dp and M is less than or equal tootherdistances of Mi (1 i k) then Dp stay in same cluster Dp having less D is assigned to CorrespondingCi Step 5:For each cluster Cj (1 j k), Recompute the M 2398

International Journal of Research in Advent Technology, Vol.6, No.9, September 18 and move Dp until no change in clusters. : Sorting based K- Clustering Algorithm using Multi Machine Technique for Big Data[3]is a efficient partition based clustering algorithm which minimizes the execution time and reduces the number of iterations. algorithm loads the data into the available nodes. Each nodes are the partition where the data are sorted by the attributes given. All the partitions are merged to form sorted dataset. K clusters are randomly generated. Depending on the size of K the sorted data are partitioned into equal size. Mean of each partition is calculated and taken as initial centroids. Distance is calculated using Euclidean distance. Objects are compared with the initial centroids. Objects are grouped with the nearest cluster. The process of distance calculation and mean are repeated till there is no change in the cluster formation. Algorithm Step 1:Start Step 2:Load the dataset into the multiple nodes Step 3: Generate random value for clusters K Step4: Divide the dataset D into number of nodes n Each node is sorted with the pivot element Step 5: Sorted data Si are divided into K Random generated Step 6: Mean Mi of every partition is calculated Step 7: Mean of the datapoints dp is taken as centroids of each cluster Step 8: Compute the distance between each data point di (1<= i<= n) to all the initial centroids cj (1 <= j <= k). Step 9: For each data point di, find the nearest centroid cj and assign di to cluster j. Step : Set ClusterNo[i]=j. Step 11: Set Clustergroup[i]=d(di, cj). Step 12: For each data point di, Compute the distance from the centroid to the nearest cluster If this distance is less than or equal to the presentcentroid the data point stays in the same cluster Compute the distance d(di, cj) and recalculate the centroid End for; Step 13: Repeat step 9 to 12 till there is no change in the cluster formation. Step 14: End SBKMEDA: Sorting based K- Median Clustering Algorithm using Multi Machine Technique for Big Data[4] is an efficient partitionbased clustering algorithm which reduces the execution time even when the data are skewed.sbkmeda algorithm loads the data in available nodes given. Each partition are sorted by the attributes given. The merged data from all the partitions form the sorted list. The number of cluster K is randomly generated. Depending on the size of the K the sorted data are partitioned into equal size. Median is taken as initial centroids. Distance is calculated using distance formula. Objects are compared with the initial centroids. Objects are grouped with the nearest cluster. Distance calculation and mean calculation for centroids are repeated till there is no change in the cluster formation. SBKMEDA Algorithm Step 1:Start Step 2:Load the dataset into the multiple nodes Step 3: Generate random value for clusters K Step4: Divide the dataset D into number of nodes n Each node is sorted with the pivot element Step 5: Sorted data Si are divided into K Random generated Step 6: Median Mi of every partition is calculated Step 7: Median of the datapoints dp is taken as centroids of each cluster Step 8: Compute the distance between each data point di (1<= i<= n) to all the initial centroids cj (1 <= j <= k). Step 9: For each data point di, find the nearest cent*roid cj and assign di to cluster j. Step : Set ClusterNo[i]=j. Step 11: Set Clustergroup[i]= d(di, cj). Step 12: For each data point di, Compute the distance from the centroid to the nearest cluster If this distance is less than or equal to the present centroid the data point stays in the same cluster Compute the distance d(di, cj) and recalculate the centroid End for; Step 13: Repeat step 9 to 12 till there is no 2399

Time ( In Seconds) International Journal of Research in Advent Technology, Vol.6, No.9, September 18 change in the cluster formation. Step 14: End SBKMMA[5] : Sorting based K and Median based Clustering Algorithm using Multi MachineTechnique for Big Datais a clustering based algorithm where the execution time decreases for any type of integer data and reduces the iterations by initializing calculating the centroid values. This algorithm loads the data into the number of nodes given. Total cluster K is randomly generated. Depending on the size of the K the sorted data are partitioned into equal size. Mean and Median of each partition is calculated. When the difference between the mean and median are more median will be taken as centroids else the value of mean will be taken as centroids. Centroids are initialized to the objects which they belong. Distance is calculated using Euclidean distance. Objects are compared with the initial centroids. Objects are grouped with the nearest cluster. Object comparison and distance calculation are repeated till there is no change in the cluster formation. SBKMMA: Sorting based K and Median based Clustering Algorithm using Multi Machine Technique for Big Data Step 1:Start Step 2:Load the dataset into the multiple nodes Step 3: Generate random value for clusters K Step4: Divide the dataset D into number of nodes n Each node is sorted with the pivot element Step 5: Sorted data Si are divided into K Random generated Step 6: Mean and Median of every partition is calculated. Step 7: If the value of mean and median differs more Median will be taken as initial centroids Mean will be taken as initial centroids Step 8: Initial data points are assigned to the centroids cj of the clusters they belong. Step : Set ClusterNo[i]=j. Step 11: Set Clustergroup[i]= d(di, cj). Step 13: For each data point di, Compute the distance from the centroid to the nearest cluster If this distance is less than or equal to the present centroid the data point stays in the same cluster. Compute the distance d(di, cj) and recalculate the centroid End for Step 14: Calculate the distance between the objects to all the centroids and assign it to the nearest Step : Repeat step to 14 till there is no change in the cluster formation. Step : End 3. PERFORMANCE ANALYSIS OF PARTITION BASED CLUSTERING ALGORITHMS The performance of the clustering algorithms is analyzed using Hadoop MapReduce. The execution time and the numberof iterations are considered. Table 1: Execution time VS number of nodes K- 5 28.2 24.4.56 23.5 19.33 16.46.5 11 9.83 8 5.9 4.56 Comparative View on Reduction of Execution Time 30 0 28.2 24.4 23.5.56 19.33 16.46.5 119.83 8 5.94.56 5 Number of K- Figure 1 Execution time vs number of nodes 2400

International Journal of Research in Advent Technology, Vol.6, No.9, September 18 Fig. 1 shows the execution time of three algorithms. From the Table 1 we find the execution time of is less when compared to enhanced k- means and traditional k-means. Table shows the execution time using 5nodes nodes and nodes. Table 2: Execution time VS number of nodes SBKMEDA 5 24.4.56 18.5 19.33 16.46 14.3 11 9.83 8.1 5.9 4.56 4 16.46 14.3 13.2 9.83 8.1 7.7 4.56 4 3.8 Figure 3: Execution time vs number of nodes Figure2. Execution time vs number of nodes Fig. 2 shows the execution time of three algorithms. From the table 2 we find the execution time of SBKMEDA is less when compared to enhanced k- means and. Table shows the execution time using 5nodes nodes and nodes. Here median is taken is taken as centroid after sorting which improves the execution time and reduces iterations even when the data items are skewed. Table 3: Execution time VS number of nodes SBKMEDA SBKMMA Fig. 3 shows the execution time of three algorithms. From the Table 3 we find the execution time of SBKMMA is less when compared to and SBKMEDA. Table shows the execution time using 5nodes nodes and nodes. Here initially centroids are directly assigned to form initial cluster which makes the algorithm to perform faster. Table 4 : Iterations VS no. of K- 26 21 16 19 12 13 11 8 5 8 6 4 5.56 18.5 2401

Count of Iterations International Journal of Research in Advent Technology, Vol.6, No.9, September 18 Comparative View on Reduction of Iterations 30 25 5 0 26 21 19 16 12 13 11 8 8 6 4 5 Number of Figure 4 Iterations VS no. of clusters Figure 4 shows the number of iterations reduces when the number of clusters are decreased. uses lessiterations when compared to other two algorithms. Table 4 gives the details about the number of iterations iterationof the various algorithms. Sorting the data in the beginning reduces the repetition in the distance calculation by reducing the number of iterations. No of K- Table5: Iterations VS no. of SBKMEDA 21 16 12 12 9 11 8 6 5 6 4 3 Figure 5 Iterations VS no. of clusters Figure 5 shows the number of iterations reduces when the number of clusters are decreased. uses less iterations when compared to other two algorithms. Table 4 gives the details about the number of iterations iterationof the various algorithms. Sorting the data in the beginning reduces the repetition in the distance calculation by reducing the number of iterations. Table 6: Iterations VS no. of clusters SBKMEDA SBKMMA 16 12 6 12 9 4 8 6 3 5 4 3 2 Figure 6 Iterations VS no. of clusters 2402

International Journal of Research in Advent Technology, Vol.6, No.9, September 18 Fig6 shows the number of iterations reduces when the number of clusters are decreased. uses less iterations when compared to other two algorithms. Sorting the data in the beginning reduces the repetition in the distance calculation by reducing the number of iterations in a distributed environment. 4. CONCLUSION In this paper Partition based ClusteringAlgorithms are compared for Big Data. The ultimate aim of those algorithms is to reduce the execution time by doing it distributed and sorting solves the drawback of iterating data points repeatedly.the performances of traditional K-, enhanced K-means,, SBKMEDA and SBKMMA are discussed in this paper. The process of initial centroid assignment in multiple nodes reduces the executiontimeincreases the speed of the processing when compared with the previous algorithms. SBKMMAselects initial centroids and assigns centroids to the datapoints to form the initial clusters which makes it fasterin execution time and iterationsthan other existing algorithms. [5] Mahima Jane and Dr. E. George Dharma Prakash RajSBKMMA: Sorting Based K and Median Based Clustering Algorithm Using Multi Machine Technique for Big Data. International Journal of Computer (IJC),p. 1-7, Jan. 18. ISSN 2307-4523. [6] E. Mahima Jane and E. George Dharma Prakash Raj, "Survey on Partition based Clustering Algorithms in Big Data", International Journal of Computer Sciences and Engineering, Vol.5, Issue.12, pp.323-325, 17. [7] K.Chitra and D Maheshwari, A Comparative study of various clustering algorithms in Data Mining International Journal of Computer Science and Mobile Computing, Vol.6 Issue.8, August- 17, pg. 9-1 [8] Kavya D S, Chaitra D Desai Comparative Analysis of K means Clustering Sequentially Andparallely International Research Journal Of Engineering And Technology (IRJET) E- ISSN: 2395-0056VOLUME: 03 ISSUE: 04 APR-16. REFERENCES [1]Yaminee S. Patil, M. B. Vaidya K-means Clustering with MapReduce Technique, International Journal of Advanced Research in Computer and Communication Engineering,Nov, () [2] AzharRauf, Sheeba, SaeedMahfooz, Shah Khusro and HumaJaved -Mean Clustering Algorithm to Reduce Number of Iterations and Time Complexity Middle-East Journal of Scientific Research 12 (7): 959-963, 12 [3] Mahima Jane and Dr. E. George Dharma Prakash Raj : Sorting based K- Clustering Algorithm using Multi Machine Technique for Big Data in the International Journal of Control Theory and Applications Volume 8 pp 25-21 [4] Mahima Jane and Dr. E. George Dharma Prakash Raj SBKMEDA : Sorting based K- Median Clustering Algorithm using Multi Machine Technique for Big Data Advances in Intelligent Systems and Computing(Springer) April 18. 2403

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