Two-class clustering of nonlinearly separable data by using shape-specific points

摘要

Shape-specific points are special data points invariant to translation, scaling, and rotation. The radius weighted mean (RWM) and the system center are two examples of shape-specific points. These points feature in contour registration, color quantization, and the detection of rotationally symmetric shape orientations. This study uses shape-specific points to cluster nonlinearly separable data into two classes. To bisect nonlinearly separable data, input data are transformed into a higher dimensional space, called the feature space, within which transformed data are linearly separable. The proposed methods then use hyperplanes normal to the line connecting the RWM and the center in the feature space to bisect the transformed data. This produces two nonlinearly separable classes in the original space. With the help of kernel functions, all the computations are accomplished in the original data space. The proposed methods are applicable to data of any dimension. Compared to traditional methods, such as the global kernel k-means, the proposed methods do not require cluster initialization or iterative procedures to obtain clustering results. Experiments show that the proposed methods have better clustering results than the global kernel k-means.