Joint Learning of Latent Similarity and Local Embedding for Multi-View Clustering

Spectral clustering has been an attractive topic in the field of computer vision due to the extensive growth of applications, such as image segmentation, clustering and representation. In this problem, the construction of the similarity matrix is a vital element affecting clustering performance. In this paper, we propose a multi-view joint learning (MVJL) framework to achieve both a reliable similarity matrix and a latent low-dimensional embedding. Specifically, the similarity matrix to be learned is represented as a convex hull of similarity matrices from different views, where the nuclear norm is imposed to capture the principal information of multiple views and improve robustness against noise/outliers. Moreover, an effective low-dimensional representation is obtained by applying local embedding on the similarity matrix, which preserves the local intrinsic structure of data through dimensionality reduction. With these techniques, we formulate the MVJL as a joint optimization problem and derive its mathematical solution with the alternating direction method of multipliers strategy and the proximal gradient descent method. The solution, which consists of a similarity matrix and a low-dimensional representation, is ultimately integrated with spectral clustering or K-means for multi-view clustering. Extensive experimental results on real-world datasets demonstrate that MVJL achieves superior clustering performance over other state-of-the-art methods.