Clustering, the goal of which is to partition data points into homogeneous groups, arises in a number of fields such as pattern recognition, machine learning, data mining, and image processing. One of the most popular clustering algorithms is k-means, where groups are identified
by minimizing the clustering error defined as the sum of the squared Euclidean distances between each data set point and the corresponding cluster center. This algorithm suffers from two serious limitations. First, the solution depends heavily on the initial positions of the cluster centers, resulting in poor minima, and second, it can only find linearly separable clusters.
    In this design the global kernel k-means algorithm, a deterministic algorithm for optimizing the clustering error in feature space that employs kernel k-means as a local search procedure in order to solve the M-clustering problem.  The algorithm works in an incremental fashion by solving all intermediate problems with 1,....M clusters, using kernel k-means. The idea behind the proposed method is that a near-optimal solution with k-1 clusters can be obtained by starting with a near-optimal solution with clusters and initializing he the cluster appropriately based on a local search.
    Kernel k-means is an extension of the standard k-means clustering algorithm that identifies nonlinearly separable clusters. In order to overcome the cluster initialization problem associated with this method, we propose the global kernel k-means algorithm, a deterministic and incremental approach to kernel-based clustering. The proposed method adds one cluster at each stage, through a global search procedure consisting of several executions of the kernel -means from suitable initializations. This algorithm does not depend on cluster initialization, identifies nonlinearly separable clusters, and, due to its incremental nature and search procedure, locates near-optimal solutions avoiding poor local minima. 

Reference Paper: The Global Kernel k-Means Algorithm for Clustering in Feature Space
Author’s Name:  Grigorios F. Tzortzis and Aristides C. Likas
Source: IEEE

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