A multiway p-spectral clustering algorithm

Abstract

The original p-spectral clustering algorithm can obtain more balanced clustering results by introducing p-Laplacian operator. However, we may not get an ideal clustering result when clustering the multi-model or multi-scale data sets. Moreover, the original p-spectral clustering algorithm is suitable to deal with bipartition situation. when solving the multi-class partition problem, we have to recursively implement bipartition process, which will bring about ineffectiveness of the graph partition, and clustering result is not stable. Therefore, we propose a multiway p-spectral clustering algorithm, which employs local scaling parameter to optimize the calculation of similarity of the data objects. Furthermore, we use multi-eigenvectors to solve the multi-class partition problem by introducing idea of classical spectral clustering NJW algorithm, which can avoid the instability of the clustering result due to the information losing. Accordingly, we can attain the approximate optimal solution of the multi-class partition problem. Experiments show that multiway p-spectral clustering algorithm has much stronger adaptability and robustness, and can produce more balanced clusters.