Centerless Multi-View K-means Based on the Adjacency Matrix

Abstract

Although K-Means clustering has been widely studied due to its simplicity, these methods still have the following fatal drawbacks. Firstly, they need to initialize the cluster centers, which causes unstable clustering performance. Secondly, they have poor performance on non-Gaussian datasets. Inspired by the affinity matrix, we propose a novel multi-view K-Means based on the adjacency matrix. It maps the affinity matrix to the distance matrix according to the principle that every sample has a small distance from the points in its neighborhood and a large distance from the points outside of the neighborhood. Moreover, this method well exploits the complementary information embedded in different views by minimizing the tensor Schatten p-norm regularize on the third-order tensor which consists of cluster assignment matrices of different views. Additionally, this method avoids initializing cluster centroids to obtain stable performance. And there is no need to compute the means of clusters so that our model is not sensitive to outliers. Experiment on a toy dataset shows the excellent performance on non-Gaussian datasets. And other experiments on several benchmark datasets demonstrate the superiority of our proposed method.