Abstract:

In order to improve the algorithmic theory and make the hierarchical cluster analysis be able to find nonlinear clusters in a data set, the authors develop a kernel-based hierarchical cluster analysis method by integrating kernel functions with the hierarchical cluster analysis algorithm. The procedure of the new cluster algorithm can be described as follows. The input samples in the low-dimensional input space are nonlinearly mapped to a high-dimensional image space where the samples are linearly separable, and then a kernel function is applied to implicitly execute the hierarchical cluster analysis in the image space. The authors conduct an experiment on the unsupervised classification of eight geochemical anomalies according to the contents of Pb, Bi, and Mo. The eight geochemical anomalies are obviously divided into the three clusters, (1, 3, 8), (2, 4), and (5, 6, 7), according to the three pair-wised scatter plots derived from the contents of Pb, Bi, and Mo. Kernel hierarchical cluster analysis is able to properly differentiate these three clusters while the conventional hierarchical cluster analysis improperly classifies the eight geochemical anomalies into the two classes, (1, 3, 8, 6) and (2, 4, 5,7). Therefore, the clustering ability of the new method exceeds that of the conventional hierarchical cluster algorithm.

Key words: kernel functions, cluster analysis, observing space, image space