High-dimension data clustering is a fundamental topic in machine learning and data mining areas. In recent year, researchers have proposed a series of effective methods based on Low Rank Representation (LRR) which could explore low-dimension subspace structure embedded in original data effectively. The traditional LRR methods usually treat original data as samples in Euclidean space. They generally adopt linear metric to measure the distance between two data. However, high-dimension data (such as video clip or imageset) are always considered as non-linear manifold data such as Grassmann manifold. Therefore, the traditional linear Euclidean metric would be no longer suitable for these special data. In addition, traditional LRR clustering method always adopt nuclear norm as low rank constraint which would lead to suboptimal solution and decrease the clustering accuracy. In this paper, we proposed a new low rank method on Grassmann manifold for high-dimension data clustering task. In the proposed method, a double low rank representation approach is proposed by combining the nuclear norm and bilinear representation for better construct the representation matrix. The experimental results on several public datasets show that the proposed method outperforms the state-of-the-art clustering methods.

Non-negative matrix factorization (NMF) is an important method in learning latent data representation. The local geometrical structure can make the learned representation more effectively and significantly improve the performance of NMF. However, most of existing graph-based learning methods are determined by a predefined similarity graph which may be not optimal for specific tasks. To solve the above the problem, we propose the Double Manifolds Regularized NMF (DMR-NMF) model which jointly learns an adaptive affinity matrix with the non-negative matrix factorization. The learned affinity matrix can guide the NMF to fit the clustering task. Moreover, we develop the iterative updating optimization schemes for DMR-NMF, and provide the strict convergence proof of our optimization strategy. Empirical experiments on four different real-world data sets demonstrate the state-of-the-art performance of DMR-NMF in comparison with the other related algorithms.

Clustering high dimension multi-view data with complex intrinsic properties and nonlinear manifold structure is a challenging task since these data are always embedded in low dimension manifolds. Inspired by Low Rank Representation (LRR), some researchers extended classic LRR on Grassmann manifold or Product Grassmann manifold to represent data with non-linear metrics. However, most of these methods utilized convex nuclear norm to leverage a low-rank structure, which was over-relaxation of true rank and would lead to the results deviated from the true underlying ones. And, the computational complexity of singular value decomposition of matrix is high for nuclear norm minimization. In this paper, we propose a new low rank model for high-dimension multi-view data clustering on Product Grassmann Manifold with the matrix tri-factorization which is used to control the upper bound of true rank of representation matrix. And, the original problem can be transformed into the nuclear norm minimization with smaller scale matrices. An effective solution and theoretical analysis are also provided. The experimental results show that the proposed method obviously outperforms other state-of-the-art methods on several multi-source human/crowd action video datasets.

Clustering is a crucial but challenging task in pattern analysis and machine learning. Recent many deep clustering methods combining representation learning with cluster techniques emerged. These deep clustering methods mainly focus on the correlation among samples and ignore the relationship between samples and their representations. In this paper, we propose a novel end-to-end clustering framework, namely variational deep embedding clustering by augmented mutual information maximization (VCAMI). From the perspective of VAE, we prove that minimizing reconstruction loss is equivalent to maximizing the mutual information of the input and its latent representation. This provides a theoretical guarantee for us to directly maximize the mutual information instead of minimizing reconstruction loss. Therefore we proposed the augmented mutual information which highlights the uniqueness of the representations while discovering invariant information among similar samples. Extensive experiments on several challenging image datasets show that the VCAMI achieves good performance. we achieve state-of-the-art results for clustering on MNIST (99.5%) and CIFAR-10 (65.4%) to the best of our knowledge.

As a challenging task of Natural Language Processing(NLP), zero-shot text classification has attracted more and more attention recently. It aims to detect classes that the model has never seen in the training set. For this purpose, a feasible way is to construct connection between the seen and unseen classes by semantic extension and classify the unseen classes by information propagation over the connection. Although many related zero-shot text classification methods have been exploited, how to realize semantic extension properly and propagate information effectively is far from solved. In this paper, we propose a novel zero-shot text classification method called Semantically Extended Graph Convolutional Network (SEGCN). In the proposed method, the semantic category knowledge from ConceptNet is utilized to semantic extension for linking seen classes to unseen classes and constructing a graph of all classes. Then, we build upon Graph Convolutional Network (GCN) for predicting the textual classifier for each category, which transfers the category knowledge by the convolution operators on the constructed graph and is trained in a semi-supervised manner using the samples of the seen classes. The experimental results on Dbpedia and 20newsgroup datasets show that our method outperforms the state of the art zero-shot text classification methods.