text: Subspace clustering methods based on data self-expression have become very popular for learning from data that lie in a union of low-dimensional linear subspaces. However, the applicability of subspace clustering has been limited because practical visual data in raw form do not necessarily lie in such linear subspaces. On the other hand, while Convolutional Neural Network (ConvNet) has been demonstrated to be a powerful tool for extracting discriminative features from visual data, training such a ConvNet usually requires a large amount of labeled data, which are unavailable in subspace clustering applications. To achieve simultaneous feature learning and subspace clustering, we propose an end-to-end trainable framework, called Self-Supervised Convolutional Subspace Clustering Network (S @math ConvSCN), that combines a ConvNet module (for feature learning), a self-expression module (for subspace clustering) and a spectral clustering module (for self-supervision) into a joint optimization framework. Particularly, we introduce a dual self-supervision that exploits the output of spectral clustering to supervise the training of the feature learning module (via a classification loss) and the self-expression module (via a spectral clustering loss). Our experiments on four benchmark datasets show the effectiveness of the dual self-supervision and demonstrate superior performance of our proposed approach.
  @cite_21: Low-Rank Representation (LRR) [16, 17] is an effective method for exploring the multiple subspace structures of data. Usually, the observed data matrix itself is chosen as the dictionary, which is a key aspect of LRR. However, such a strategy may depress the performance, especially when the observations are insufficient and or grossly corrupted. In this paper we therefore propose to construct the dictionary by using both observed and unobserved, hidden data. We show that the effects of the hidden data can be approximately recovered by solving a nuclear norm minimization problem, which is convex and can be solved efficiently. The formulation of the proposed method, called Latent Low-Rank Representation (LatLRR), seamlessly integrates subspace segmentation and feature extraction into a unified framework, and thus provides us with a solution for both subspace segmentation and feature extraction. As a subspace segmentation algorithm, LatLRR is an enhanced version of LRR and outperforms the state-of-the-art algorithms. Being an unsupervised feature extraction algorithm, LatLRR is able to robustly extract salient features from corrupted data, and thus can work much better than the benchmark that utilizes the original data vectors as features for classification. Compared to dimension reduction based methods, LatLRR is more robust to noise.
  @cite_17: We propose a novel algorithm called Latent Space Sparse Subspace Clustering for simultaneous dimensionality reduction and clustering of data lying in a union of subspaces. Specifically, we describe a method that learns the projection of data and finds the sparse coefficients in the low-dimensional latent space. Cluster labels are then assigned by applying spectral clustering to a similarity matrix built from these sparse coefficients. An efficient optimization method is proposed and its non-linear extensions based on the kernel methods are presented. One of the main advantages of our method is that it is computationally efficient as the sparse coefficients are found in the low-dimensional latent space. Various experiments show that the proposed method performs better than the competitive state-of-the-art subspace clustering methods.
summary: On the other hand, the latent feature space has also been constructed via matrix decomposition, , @cite_21 , @cite_17 . In @cite_21 , a linear transform matrix and a low-rank representation are computed simultaneously; in @cite_17 , a linear transform and a sparse representation are optimized jointly. However, the representation power of the learned linear transform is still limited.