A new method to build the adaptive k-nearest neighbors similarity graph matrix for spectral clustering

In spectral clustering (SC), the clustering result highly depends on the similarity graph matrix. The k-nearest neighbors graph is a popular method to build the similarity graph matrix with a sparse structure for better graph cutting. However, many current methods require that the parameter k is specified by the user, and specifying an appropriate k for an unknown data set is often a difficult task. In this paper, we propose a new method for building the adaptive k-nearest neighbors similarity graph (AKNNG). The AKNNG specifies different k values for different data points to obtain a better graph structure. Specifically, it sets a maximum number of the nearest neighbors kmax and assigns a different k value (k⩽kmax) for each data point. The k value is adjusted automatically by cutting some weak connections from each data point according to the m powers transform of the similarity graph. The experimental results on Spiral, Multi-clusters, Yale and Coil20 datasets have shown that when setting kmax=20, the new method has improved the clustering accuracies of these four datasets over 4%, 6%, 4%, 5%, respectively, in comparison with those by the existing methods. The new method can also reduce the sensitiveness of the number of nearest neighbors, and build the similarity graph with less time.