Stratified multi-density spectral clustering using Gaussian mixture model

Spectral clustering aims to minimise inter-cluster similarity by constructing graph model, which possesses a significant effect in data of arbitrary shape. Nonetheless, there are still two limitations in the existing algorithms. First, spectral methods perform poorly if the densities of instances vary greatly. Second, they are challenging to handle the complex distribution that different objects of densities are mixed. To address the two limitations, in this paper, a novel spectral clustering algorithm is constructed to accommodate more complex multi-density data. The idea of density stratification is proposed through the probability density of Gaussian mixture model, and the number of layers can be automatically determined by the defined scatter index. Then, a new density ratio is established to effectively reduce the density imbalance of diverse instances based on mutual nearest-neighbour and density stratification, which is more advantageous in the clusters with less clear boundaries. Finally, the optimised adjacency matrix and multi-density spectral clustering algorithm are induced to improve the effect of multi-density data. As per experimental results, the proposed algorithm generally outperforms the popular representative algorithms for both synthetic and benchmark datasets, and works more effectively on multi-density as well as single-density data, which illustrates the superiority of the proposed algorithm.