Performance analysis of the ellipsoidal support vector clustering algorithm on various synthetic and biomedical data sets

Along with the development of communication and technology, the amount of digital data in the world is increasing. Therefore, it has become very important to obtain meaningful information by using these data especially in recent years. In particular, clustering methods are one of the most important algorithms used to extract hidden patterns within the data. In most clustering methods, the Euclidean distance is used as a similarity metric between data samples. At the Euclidean distance, the variance of the data is considered equal. However, most real world data may contain data in different variances. For this, kernel-based Ellipsoidal Support Vector Clustering (ESVC) algorithm was developed using Mahalanobis distance. The ESVC method can automatically generate the appropriate cluster boundaries according to the data samples without having to specify the number of clusters by means of the variance parameter of the kernel function. This study is divided into two parts. In the first part, the ESVC method was first time applied to the real biomedical data sets such as Hepatitis and Parkinsons, and then was compared with clustering algorithms that use Euclidean distance such as k-means, fuzzy c-means and hierarchical. From the simulation results, it was observed that the ESVC algorithm performed quite well. In the second part, Cauchy, Laplacian, hyper tangent kernels were proposed as an alternative to Gaussian kernel for ESVC and then performance analyzes were performed. According to the results of the analysis, it was shown that Cauchy and hyper tangent kernel functions could be used as an alternative to Gaussian kernel.