Classic k-means clustering algorithm randomly selects centroids for initialization to possibly output unstable clustering results. Moreover, random initialization makes the clustering result hard to reproduce. Spectral clustering algorithm is a two-step strategy, which first generates a similarity matrix and then conducts eigenvalue decomposition on the Laplacian matrix of the similarity matrix to obtain the spectral representation. However, the goal of the first step in the spectral clustering algorithm does not guarantee the best clustering result. To address the above issues, this paper proposes an Initialization-Similarity (IS) algorithm which learns the similarity matrix and the new representation in a unified way and fixes initialization using the sum-ofnorms regularization to make the clustering more robust. The experimental results on ten realworld benchmark datasets demonstrate that our IS clustering algorithm outperforms the comparison clustering algorithms in terms of three evaluation metrics for clustering algorithm including accuracy (ACC), normalized mutual information (NMI), and Purity.

K-means clustering is one of the most popular clustering algorithms and has been embedded in other clustering algorithms, e.g. the last step of spectral clustering. In this paper, we propose two techniques to improve previous k-means clustering algorithm by designing two different adjacent matrices. Extensive experiments on public UCI datasets showed the clustering results of our proposed algorithms significantly outperform three classical clustering algorithms in terms of different evaluation metrics.