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

Abstract

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.

Learning and Classification of Car Trajectories in Road Video by String Kernels

“…The above mentioned index has been used to compare the proposed method with other state of the art approaches. In particular, we considered the traditional Kernel k-mean with its two improved versions, the Global Kernel k-means (Tzortzis and Likas, 2009) and the Fast Global Kernel k-means (Tzortzis and Likas, 2009). A comparison in terms of C-Index and computational cost is shown in Tables 1a and 1b.…”

“…In (Tzortzis and Likas, 2009) an improved version of the basic Kernel k-means, the Global Kernel k-means, has been proposed. The main idea is that a near-optimal solution with k clusters can be obtained by starting with a near-optimal solution with k − 1 clusters and initializing the kth cluster appropriately based on a local search.…”

“…It is an important and not negligible feature, since a lot of recently proposed clustering algorithms (Tzortzis and Likas, 2009) are very expensive from a computational point of view, as we will show in Section 5.…”

A Classification Technique using Associative Classification

“…Kernel k-means algorithm [4] avoids the limitation of linearly separable clusters and it mapped the data points from input space to a higher dimensional feature through a nonlinear transformation Ø and the k-means is applied in the feature space. Global kernel k-means [5] is an algorithm which mapped data points from input space to a higher dimensional feature space through the use of a kernel function and optimizes the clustering error in the feature space by locating nearoptimal solution. Because of its deterministic nature, this makes it independent of the initialization problem, and the ability to identify nonlinearly separable cluster in input space.…”

Generalized hard cluster analysis

“…The contribution of this paper is to generalize hard cluster analysis by allowing that a given data element can belong to more than one cluster, while in hard cluster analysis a given data element belongs to one and only one cluster [6]. The most well-known hard clustering algorithm is k-means [12]. An interesting discussion about the evolution of this still widely used algorithm is given in [7].…”