Traditional topic model with maximum likelihood estimate inevitably suffers from the conditional independence of words given the document’s topic distribution. In this paper, we follow the generative procedure of topic model and learn the topic-word distribution and topics distribution via directly approximating the word-document co-occurrence matrix with matrix decomposition technique. These methods include: (1) Approximating the normalized document-word conditional distribution with the documents probability matrix and words probability matrix based on probabilistic non-negative matrix factorization (NMF); (2) Since the standard NMF is well known to be non-robust to noises and outliers, we extended the probabilistic NMF of the topic model to its robust versions using l21-norm and capped l21-norm based loss functions, respectively. The proposed framework inherits the explicit probabilistic meaning of factors in topic models and simultaneously makes the conditional independence assumption on words unnecessary. Straightforward and efficient algorithms are exploited to solve the corresponding non-smooth and non-convex problems. Experimental results over several benchmark datasets illustrate the effectiveness and superiority of the proposed methods.

Cosegmentation jointly segments the common objects from multiple images. In this paper, a novel clustering algorithm, called Saliency-Guided Constrained Clustering approach with Cosine similarity (SGC3), is proposed for the image cosegmentation task, where the common foregrounds are extracted via a one-step clustering process. In our method, the unsupervised saliency prior is utilized as a partition-level side information to guide the clustering process. To guarantee the robustness to noise and outlier in the given prior, the similarities of instance-level and partition-level are jointly computed for cosegmentation. Specifically, we employ cosine distance to calculate the feature similarity between data point and its cluster centroid, and introduce a cosine utility function to measure the similarity between clustering result and the side information. These two parts are both based on the cosine similarity, which is able to capture the intrinsic structure of data, especially for the non-spherical cluster structure. Finally, a K-means-like optimization is designed to solve our objective function in an efficient way. Experimental results on two widely-used datasets demonstrate our approach achieves competitive performance over the state-of-the-art cosegmentation methods.

Group detection is fundamentally important for analyzing crowd behaviors, and has attracted plenty of attention in artificial intelligence. However, existing works mostly have limitations due to the insufficient utilization of crowd properties and the arbitrary processing of individuals. In this paper,we propose the Multiview-based Parameter Free (MPF) approach to detect groups in crowd scenes. The main contributions made in this study are threefold: (1) a new structural context descriptor is designed to characterize the structural property of individuals in crowd motions; (2) an self-weighted multiview clustering method is proposed to cluster feature points by incorporating their motion and context similarities;(3) a novel framework is introduced for group detection, which is able to determine the group number automatically without any parameter or threshold to be tuned. Extensive experiments on various real world datasets demonstrate the effectiveness of the proposed approach, and show its superiority against state-of-the-art group detection techniques.

In this paper, we study the problem of user clustering in the context of their published short text streams. Clustering users by short text streams is more challenging than in the case of long documents associated with them as it is difficult to track users' dynamic interests in streaming sparse data. To obtain better user clustering performance, we propose a user collaborative interest tracking model (UCIT) that aims at tracking changes of each user's dynamic topic distributions in collaboration with their followees', based both on the content of current short texts and the previously estimated distributions. We evaluate our proposed method via a benchmark dataset consisting of Twitter users and their tweets. Experimental results validate the effectiveness of our proposed UCIT model that integrates both users' and their collaborative interests for user clustering by short text streams.

This paper proposes a one-step spectral clustering method by learning an intrinsic affinity matrix (i.e., the clustering result) from the low-dimensional space (i.e., intrinsic subspace) of original data. Specifically, the intrinsic affinitymatrix is learnt by: 1) the alignment of the initial affinity matrix learnt from original data; 2) the adjustment of the transformation matrix, which transfers the original feature space into its intrinsic subspace by simultaneously conducting feature selection and subspace learning; and 3) the clustering result constraint, i.e., the graph constructed by the intrinsic affinity matrix has exact c connected components where c is the number of clusters. In this way, two affinity matrices and a transformation matrix are iteratively updated until achieving their individual optimum, so that these two affinity matrices are consistent and the intrinsic subspace is learnt via the transformation matrix. Experimental results on both synthetic and benchmark datasets verified that our proposed method outputted more effective clustering result than the previous clustering methods.

Multi-View Clustering (MVC) has garnered more attention recently since many real-world data are comprised of different representations or views. The key is to explore complementary information to benefit the clustering problem. In this paper, we present a deep matrix factorization framework for MVC, where semi-nonnegative matrix factorization is adopted to learn the hierarchical semantics of multi-view data in a layer-wise fashion. To maximize the mutual information from each view, we enforce the non-negative representation of each view in the final layer to be the same. Furthermore, to respect the intrinsic geometric structure in each view data, graph regularizers are introduced to couple the output representation of deep structures. As a non-trivial contribution, we provide the solution based on alternating minimization strategy, followed by a theoretical proof of convergence. The superior experimental results on three face benchmarks show the effectiveness of the proposed deep matrix factorization model.

Clustering tasks often requires multiple views rather than a singleview to correctly reflect diverse characteristics of the cluster boundaries. The cluster boundaries estimated using a single view are incorrect in general, and those incorrect estimation should be compensated by helps of other views. If each viewis independent to other views, incorrect estimations will be mostly revised as the number of views grow. However, as the number of views grow, it is almost impossibleto avoid dependencies among views, and such dependencies often delude correct estimations. Thus, dependencies among views should be carefully considered in multi-view clustering. This paper proposes a new spectral clustering method to deal with multi-view data and dependencies among views. The proposed method is motivated by the brainstorming process. In the brainstorming process, an instance is regarded as an agenda to be discussed, while each view is considered as a brainstormer. Through the discussion step in the brainstorming process, a brainstormer iteratively suggests their opinions and accepts others’ different opinions. To compensate the biases caused by information sharing between brainstormers with dependent opinions, those having independent opinions are more encouraged to discuss together than those with dependent opinions. The conclusion step makes a compromise by merging or concatenating all opinions. The clustering is finally done after the conclusion. Experimental results in three tasks show the effectiveness of the proposed method comparing with ordinary single and multi-view spectral clusterings.

In this paper, we recast the subspace clustering as a verification problem. Our idea comes from an assumption that the distribution between a given sample x and cluster centers Omega is invariant to different distance metrics on the manifold, where each distribution is defined as a probability map (i.e. soft-assignment) between x and Omega. To verify this so-called invariance of distribution, we propose a deep learning based subspace clustering method which simultaneously learns a compact representation using a neural network and a clustering assignment by minimizing the discrepancy between pair-wise sample-centers distributions. To the best of our knowledge, this is the first work to reformulate clustering as a verification problem. Moreover, the proposed method is also one of the first several cascade clustering models which jointly learn representation and clustering in end-to-end manner. Extensive experimental results show the effectiveness of our algorithm comparing with 11 state-of-the-art clustering approaches on four data sets regarding to four evaluation metrics.

Due to the efficiency of learning relationships and complex structures hidden in data, graph-oriented methods have been widely investigated and achieve promising performance in multi-view learning. Generally, these learning algorithms construct informative graph for each view or fuse different views to one graph, on which the following procedure are based. However, in many real world dataset, original data always contain noise and outlying entries that result in unreliable and inaccurate graphs, which cannot be ameliorated in the previous methods. In this paper, we propose a novel multi-view learning model which performs clustering/semi-supervised classification and local structure learning simultaneously. The obtained optimal graph can be partitioned into specific clusters directly. Moreover, our model can allocate ideal weight for each view automatically without additional weight and penalty parameters. An efficient algorithm is proposed to optimize this model. Extensive experimental results on different real-world datasets show that the proposed model outperforms other state-of-the-art multi-view algorithms.

Multiple kernel $k$-means (MKKM) aims to improve clustering performance by learning an optimal kernel, which is usually assumed to be a linear combination of a group of pre-specified base kernels. However, we observe that this assumption could: i) cause limited kernel representation capability; and ii) not sufficiently consider the negotiation between the process of learning the optimal kernel and that of clustering, leading to unsatisfying clustering performance. To address these issues, we propose an optimal neighborhood kernel clustering (ONKC) algorithm to enhance the representability of the optimal kernel and strengthen the negotiation between kernel learning and clustering. We theoretically justify this ONKC by revealing its connection with existing MKKM algorithms. Furthermore, this justification shows that existing MKKM algorithms can be viewed as a special case of our approach and indicates the extendability of the proposed ONKC for designing better clustering algorithms. An efficient algorithm with proved convergence is designed to solve the resultant optimization problem. Extensive experiments have been conducted to evaluate the clustering performance of the proposed algorithm. As demonstrated, our algorithm significantly outperforms the state-of-the-art ones in the literature, verifying the effectiveness and advantages of ONKC.