Nowadays, data in the real world often comes from multiple sources, but most existing multi-view ${K}$ -Means perform poorly on linearly non-separable data and require initializing the cluster centers and calculating the mean, which causes the results to be unstable and sensitive to outliers. This paper proposes an efficient multi-view ${K}$ -Means to solve the above-mentioned issues. Specifically, our model avoids the initialization and computation of clusters centroid of data. Additionally, our model use the Butterworth filters function to transform the adjacency matrix into a distance matrix, which makes the model is capable of handling linearly inseparable data and insensitive to outliers. To exploit the consistency and complementarity across multiple views, our model constructs a third tensor composed of discrete index matrices of different views and minimizes the tensor's rank by tensor Schatten ${p}$ -norm. Experiments on two artificial datasets verify the superiority of our model on linearly inseparable data, and experiments on several benchmark datasets illustrate the performance.

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.