Asymptotic Properties of Kernel K-means and Its Comparison with Conventional K-means in High-Dimensional Settings

The asymptotic properties of k-means clustering in high-dimensional settings have been studied extensively. Similarly, research on kernel k-means has shown that when using Gaussian kernel, its asymptotic behavior remains unchanged from conventional k-means. However, studies on high-dimensional kernel methods suggest that the choice of kernel function can significantly impact clustering performance. For instance, previous research has demonstrated that polynomial kernel functions exhibit distinct properties compared to Gaussian kernels in high-dimensional classification tasks. Given this, it is crucial to investigate behavior of kernel k-means when employing a polynomial kernel. This study explores theoretical properties of kernel k-means with polynomial kernel in high-dimensional settings and provides a comparative analysis with existing methods. Our findings contribute to a deeper understanding of kernel-based clustering techniques and their applicability to high-dimensional data.