Speeding-up the kernel k-means clustering method: A prototype based hybrid approach

Kernel k-means clustering method has been proved to be effective in identifying non-isotropic and linearly inseparable clusters in the input space. However, this method is not a suitable one for large data-sets because of its quadratic time complexity with respect to the size of the data-set. This paper presents a simple prototype based hybrid approach to speed-up the kernel k-means method for large data-sets. The proposed method works in two stages. First, the data-set is partitioned into a number of small grouplets by using the leaders clustering method. Each group-let is represented by a prototype called its leader. The conventional leaders clustering method is modified such that these group-lets are formed in the kernel induced feature space. The data-set is re-indexed according to these group-lets. Later, kernel k-means clustering method is applied over the set of leaders to derive a partition of the leaders set. Finally, each leader is replaced by its group to get a partition of the entire data-set. The time complexity of the proposed method ∗Corresponding Author, Tel. No. +91-9493239032, Fax: +91-8514-275123 Preprint submitted to Pattern Recognition Letters July 26, 2011 is O(n+p), where p is the size of the leaders set. Its space complexity is also O(n + p). Experimental studies with data-sets of varying sizes shows that with a small loss of quality, the proposed algorithm can significantly reduce the computation time, particularly for large data-sets.