Multi-view clustering indicator learning with scaled similarity

The similarity of data plays an important role in clustering task, and good clustering performance often requires a reliable similarity matrix. A variety of metrics are used to define a similarity matrix in the past, and great achievements are obtained. However, due to the noise and outliers of data in the real world, the quality of the similarity matrix is often poor. Besides, the similarity matrix is often inflexible, which will degrade the clustering performance. To solve this problem, in this paper, we proposed a novel Multi-view Clustering Indicator Learning with Scaled Similarity (MCILSS). Our model uses the self-representation method to reconstruct the data matrix, and then obtain the similarity matrix by minimizing the reconstruction error. More importantly, in our model, we can adjust s \(\left( {0 < s \le 1} \right)\) to constrain the similarity matrix to gain the best clustering indicator matrix. In addition, the rank constraint is further used to improve the clustering performance. Finally, the indicator matrix is applied to obtain clustering results by k-means. Considering the nonlinear relationship in the data, we also proposed the kernel MCILSS which maps the original data to the kernel space. To solve the proposed models, two efficient optimization algorithms based on Augmented Lagrange Method (ALM) are also designed. The experimental results on some data sets show that our algorithm has better clustering performance than some representative algorithms.