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TopThe most natural and commonly used standard function in partitional clustering technique is squared-error criteria, which inclines to work well with isolated and compact clusters (Pang-Ning, Michael & Vipin, 2007; Xu & Wunsch, 2005). The sum of the squares of error between the points and the corresponding centroids is equal to the total intra-cluster variance:
(1) where
distance is Euclidean distance between two objects in the Euclidean space, c
i centroid of the i
th cluster, and x is a data object.
A standard K-means algorithm was first proposed by Stuart Lloyd in the year 1957. The term K-means was first used by James Macqueen in 1967 (Jain, Murty & Flynn, 1999). K-means is a partitioning based clustering algorithm; it groups the objects in continuous n dimensional space, which uses centroid as a mean of the group of objects (Nazeer & Sebastian, 2009; Ramakrishna, JVR, Prasad & Suresh, 2014). Let us take P = {Pi}, i=1,…n be the set of data points, to be clustered into a set of K number of clusters without any prior knowledge of the input objects. Predefined number of groups is indicated with K, where K is provided as an input parameter. Assignment of each object to a cluster is based on the objects’ proximity to the mean of the cluster. Then the mean of the cluster is in turn recomputed and the process of assigning objects to cluster resumes (Ramakrishna, JVR, Prasad & Suresh, 2014).