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_43: We trained a large, deep convolutional neural network to classify the 1.2 million high-resolution images in the ImageNet LSVRC-2010 contest into the 1000 different classes. On the test data, we achieved top-1 and top-5 error rates of 37.5 and 17.0 which is considerably better than the previous state-of-the-art. The neural network, which has 60 million parameters and 650,000 neurons, consists of five convolutional layers, some of which are followed by max-pooling layers, and three fully-connected layers with a final 1000-way softmax. To make training faster, we used non-saturating neurons and a very efficient GPU implementation of the convolution operation. To reduce overriding in the fully-connected layers we employed a recently-developed regularization method called "dropout" that proved to be very effective. We also entered a variant of this model in the ILSVRC-2012 competition and achieved a winning top-5 test error rate of 15.3 , compared to 26.2 achieved by the second-best entry.
  @cite_8: Subspace clustering refers to the problem of segmenting high dimensional data drawn from a union of subspaces into the respective subspaces. In some applications, partial side-information to indicate “must-link” or “cannot-link” in clustering is available. This leads to the task of subspace clustering with side-information. However, in prior work the supervision value of the side-information for subspace clustering has not been fully exploited. To this end, in this paper, we present an enhanced approach for constrained subspace clustering with side-information, termed Constrained Sparse Subspace Clustering plus (CSSC+), in which the side-information is used not only in the stage of learning an affinity matrix but also in the stage of spectral clustering. Moreover, we propose to estimate clustering accuracy based on the partial side-information and theoretically justify the connection to the ground-truth clustering accuracy in terms of the Rand index. We conduct experiments on three cancer gene expression datasets to validate the effectiveness of our proposals.
summary: In this paper, we attempt to develop a joint optimization framework for combining feature learning and subspace clustering, such that the useful self-supervision information from subspace clustering result could be used to guide the feature learning and to refine the self-expression model. Inspired by the success of Convolutional Neural Networks in recent years for classification tasks on images and videos datasets @cite_43 and the recent work @cite_8 , we integrate the convolutional feature extraction module into subspace clustering to form an end-to-end trainable joint optimization framework, called Self-Supervised Convolutional Subspace Clustering Network (S @math ConvSCN). In S @math ConvSCN, both the stacked convolutional layers based feature extraction and the self-expression based affinity learning are effectively self-supervised by exploiting the feedback from spectral clustering.