The Global Kernel k-Means Algorithm for Clustering in Feature Space

• Published in: IEEE transactions on neural networks Vol. 20; no. 7; pp. 1181 - 1194
• Main Authors: Tzortzis, G.F., Likas, A.C.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2009; Institute of Electrical and Electronics Engineers
• Subjects: Algorithms; Applied sciences; Artificial Intelligence; Clustering; Clustering algorithms; Clusters; Computational complexity; Computational efficiency; Computer science; control theory; systems; Computer Simulation; Connectionism. Neural networks; Costs; Data Interpretation, Statistical; Data processing. List processing. Character string processing; Exact sciences and technology; graph partitioning; Iterative algorithms; k -means; Kernel; kernel k -means; Kernels; Mathematical models; Memory organisation. Data processing; Neural networks; Neural Networks (Computer); Optimization methods; Partitioning algorithms; Pattern Recognition, Automated; Searching; Signal Processing, Computer-Assisted; Software; Software Validation; Cluster analysis; Initialization; Probabilistic approach; Refinement method; Iterative method; K means algorithm; Graph theory; Neural network; Data mining; Clustering; Kernel method; Graph decomposition; Optimal solution; Classification; k-means; graph partitioning; Deterministic approach; kernel k-means
• ISSN: 1045-9227; 1941-0093
• DOI: 10.1109/TNN.2009.2019722

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. Our method adds one cluster at each stage, through a global search procedure consisting of several executions of kernel k-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. Furthermore, two modifications are developed to reduce the computational cost that do not significantly affect the solution quality. The proposed methods are extended to handle weighted data points, which enables their application to graph partitioning. We experiment with several data sets and the proposed approach compares favorably to kernel k-means with random restarts.