K-Means Clustering Based on Chebyshev Polynomial Graph Filtering

Liang Du, Yunhui Liang, Mian Ilyas Ahmad, Peng Zhou

Abstract: Clustering, a key unsupervised learning method, is widely used in various fields. While the classic K-means algorithm is popular, it often neglects valuable high-order information in data. To address this, we have proposed an improved K-means algorithm incorporating a Chebyshev polynomial approximated graph filter. This approach offers two main advantages. First, the adaptive graph filter, approximated by Chebyshev polynomial, provides a smoother representation that aids subsequent clustering. Second, the clustering results guide the search for optimal adaptive coefficients. This work underscores the potential of combining filter design with machine learning tasks, thereby improving data representation capabilities and demonstrating superior performance in experiments across multiple datasets. Code is available at https://github.com/lxh8684/CGFKM.