Most existing multi-view subspace clustering approaches only capture the inter-view similarities between different views and ignore the optimal local geometric structure of the original data. To this end, in this letter, we put forward a novel method named shared latent embedding learning for multi-view subspace clustering (SLE-MSC), which can efficiently capture a better latent space. To be specific, we introduce a pseudo-label constraint to capture the intra-view similarities within each view. Meanwhile, we utilize a novel optimal graph Laplacian to learn the consistent latent representation, in which the common manifold is considered as the optimal manifold to obtain a more reasonable local geometric structure. Comprehensive experimental results indicate the superiority and effectiveness of the proposed method.

In this paper, we consider the clustering problem of independent general subspaces. That is, with given data points lay near or on the union of independent low-dimensional linear subspaces, we aim to recover the subspaces and assign the corresponding label to each data point. To settle this problem, we take advantages of both greedy strategy and energy minimization strategy to propose a simple yet effective algorithm based on the assumption that an m-branched (i.e., perfect m-ary) tree which is constructed by collecting m-nearest neighbor points in each node has a high probability of containing the near-exact subspace. Specifically, at first, subspace candidates are enumerated by multiple m-branched trees. Each tree starts with a data point and grows by collecting nearest neighbors in the breadth-first search order. Then, subspace proposals are further selected from the enumeration to initialize the energy minimization algorithm. Eventually, both the proposals and the labeling result are finalized by iterative re-estimation and labeling. Experiments with both synthetic and real-world data show that the proposed method can outperform state-of-the-art methods and is practical in real application.

The problem of multi-body motion segmentation is important in many computer vision applications. In this paper, we propose a novel algorithm called fuzzy k-subspace clustering for robust segmentation. The proposed method exploits the property that under orthographic camera model the tracked feature points of moving objects reside in multiple subspaces. We compute a partition of feature points into corresponding subspace clusters. First, we find a "soft partition" of feature points based on fuzzy k-subspace algorithm. The proposed fuzzy k-subspace algorithm iteratively minimizes the objective function using Weighted Singular Value Decomposition. Then the points with high partition confidence are gathered to form the subspace bases and the remaining points are classified using their distance to the bases. The proposed method can handle the case of missing data naturally, meaning that the feature points do not have to be visible throughout the sequence. The method is robust to noise and insensitive to initialization. Extensive experiments on synthetic and real data show the effectiveness of the proposed fuzzy k-subspace clustering algorithm.