Sparsity-constrained optimization problems are common in machine learning, such as sparse coding, low-rank minimization and compressive sensing. However, most of previous studies focused on constructing various hand-crafted sparse regularizers, while little work was devoted to learning adaptive sparse regularizers from given input data for specific tasks. In this paper, we propose a deep sparse regularizer learning model that learns data-driven sparse regularizers adaptively. Via the proximal gradient algorithm, we find that the sparse regularizer learning is equivalent to learning a parameterized activation function. This encourages us to learn sparse regularizers in the deep learning framework. Therefore, we build a neural network composed of multiple blocks, each being differentiable and reusable. All blocks contain learnable piecewise linear activation functions which correspond to the sparse regularizer to be learned. Furthermore, the proposed model is trained with back propagation, and all parameters in this model are learned end-to-end. We apply our framework to multi-view clustering and semi-supervised classification tasks to learn a latent compact representation. Experimental results demonstrate the superiority of the proposed framework over state-of-the-art multi-view learning models.

Deep multi-view representation learning focuses on training a unified low-dimensional representation for data with multiple sources or modalities. With the rapidly growing attention of graph neural networks, more and more researchers have introduced various graph models into multi-view learning. Although considerable achievements have been made, most existing methods usually propagate information in a single view and fuse multiple information only from the perspective of attributes or relationships. To solve the aforementioned problems, we propose an efficient model termed Dual Fusion-Propagation Graph Neural Network (DFP-GNN) and apply it to deep multi-view clustering tasks. The proposed method is designed with three submodules and has the following merits: a) The proposed view-specific and cross-view propagation modules can capture the consistency and complementarity information among multiple views; b) The designed fusion module performs multi-view information fusion with the attributes of nodes and the relationships among them simultaneously. Experiments on popular databases show that DFP-GNN achieves significant results compared with several state-of-the-art algorithms.

Existing multi-view graph learning methods often rely on consistent information for similar nodes within and across views, however they may lack adaptability when facing diversity challenges from noise, varied views, and complex data distributions. These challenges can be mainly categorized into: 1) View-specific diversity within intra-view from noise and incomplete information; 2) Cross-view diversity within inter-view caused by various latent semantics; 3) Cross-group diversity within inter-group due to data distribution differences. To this end, we propose a universal multi-view consensus graph learning framework that considers both original and generative graphs to balance consistency and diversity. Specifically, the proposed framework can be divided into the following four modules. i) Multi-channel graph module to extract principal node information, ensuring view-specific and cross-view consistency while mitigating view-specific and cross-view diversity within original graphs; ii) Generative module to produce cleaner and more realistic graphs, enriching graph structure while maintaining view-specific consistency and suppressing view-specific diversity; iii) Contrastive module to collaborate on generative semantics to facilitate cross-view consistency and reducing cross-view diversity within generative graphs; iv) Consensus graph module to consolidate learning a consensual graph, pursuing cross-group consistency and cross-group diversity. Extensive experimental results on real-world datasets demonstrate its effectiveness and superiority.

Deep multi-view clustering utilizes neural networks to extract the potential peculiarities of complementarity and consistency information among multi-view features. This can obtain a consistent representation that improves clustering performance. Although a multitude of deep multi-view clustering approaches have been proposed, most lack theoretic interpretability while maintaining the advantages of good performance. In this paper, we propose an effective differentiable network with alternating iterative optimization for multi-view co-clustering termed differentiable bi-sparse multi-view co-clustering (DBMC) and an extension named elevated DBMC (EDBMC). The proposed methods are transformed into equivalent deep networks based on the constructed objective loss functions. They have the advantages of strong interpretability of the classical machine learning methods and the superior performance of deep networks. Moreover, DBMC and EDBMC can learn a joint and consistent collaborative representation from multi-source features and guarantee sparsity between multi-view feature space and single-view sample space. Meanwhile, they can be converted into deep differentiable network frameworks with block-wise iterative training. Correspondingly, we design two three-step iterative differentiable networks to resolve resultant optimization problems with theoretically guaranteed convergence. Extensive experiments on six multi-view benchmark datasets demonstrate that the proposed frameworks outperform other state-of-the-art multi-view clustering methods.

In the last two decades, object tracking has been one of the prevalent fields in social media. Object tracking uses a dynamic model to track the same target, aiming to analyze the same social object and its behavior in a set of consecutive video frames. In this article, we provide a comprehensive survey on some representative and latest correlation-filter-based object tracking methods and compare their respective strengths and weaknesses under the theoretical and experimental analyses. First of all, we divide these correlation-filter-based object tracking methods into four categories according to their characteristics, including categorized features, space weight factors, scale factors, and expert strategies. Second, extensive experiments on benchmark datasets with 11 tracking challenges are performed and discussed. Finally, this article also attempts to provide some insights for the readers to comprehend and improve the involved tracking algorithms. It is expected that the overview would present a detailed framework and some enlightenments of object tracking to readers who are new in this area.

Existing representation learning approaches lie predominantly in designing models empirically without rigorous mathematical guidelines, neglecting interpretation in terms of modeling. In this work, we propose an optimization-derived representation learning network that embraces both interpretation and extensibility. To ensure interpretability at the design level, we adopt a transparent approach in customizing the representation learning network from an optimization perspective. This involves modularly stitching together components to meet specific requirements, enhancing flexibility and generality. Then, we convert the iterative solution of the convex optimization objective into the corresponding feed-forward network layers by embedding learnable modules. These above optimization-derived layers are seamlessly integrated into a deep neural network architecture, allowing for training in an end-to-end fashion. Furthermore, extra view-wise weights are introduced for multi-view learning to discriminate the contributions of representations from different views. The proposed method outperforms several advanced approaches on semi-supervised classification tasks, demonstrating its feasibility and effectiveness.