The autoencoder (AE) is an efficient feature extraction tool that learns latent representations from raw data by minimizing the reconstruction loss. Building upon the AE architecture, deep clustering models are designed to jointly optimize the deep neural network and perform unsupervised clustering. However, existing methods directly impose the clustering objective on the latent features produced by the AE network, thereby neglecting the potential conflict between data clustering and data representation. Specifically, data clustering aims to enhance data aggregation, whereas data representation focuses on ensuring that latent features faithfully reflect the manifold structure of the raw data. To address this issue, this article proposes an innovative expanded deep embedding clustering (E-DEC) model, in which the AE network is employed to seek better latent representations, and a novel residual expansion module (REM) is integrated to construct an expanded feature space that better serves clustering tasks. Furthermore, adversarial learning between the soft cluster assignments and a prior one-hot distribution is adopted in lieu of the conventional Kullback–Leibler (KL) divergence, so as to enhance the discrimination of different clusters and avoid the degeneracy problem. Finally, an entropy regularization technique is incorporated to adaptively refine the affinity graph throughout the clustering process, thereby reducing the sensitivity of clustering performance to the initial affinity graph. Extensive experiments on real-world benchmark datasets demonstrate the superiority of the proposed model over state-of-the-art deep clustering methods.

Real-world data tends to exhibit an inherent hierarchical structure, providing a natural multiview perspective where features at different scales can be treated as distinct views. However, most existing multiview clustering algorithms primarily focus on the inter-sample relationships at a single level. These methods overlook the hierarchical structures present in the data and are specifically designed for native multiview data. This article introduces a comprehensive multiview clustering framework that transforms both typical data and images into a unified multiview feature representation. The framework allows for extracting multiscale features from the raw data and clustering different types of data with the same algorithm. A novel scale-driven pre-processing approach unifies the feature structure across various data types and explores local relationships among samples at multiple scales. Features at larger scales delineate the global cluster contours, while features at smaller scales reveal fine-grained local details. Subsequently, the proposed method learns the view-specific partitions from different scales of views and derives consensus features through tensor low-rank representation. By optimizing these consensus features, the approach effectively captures the precise cluster shapes from coarse to fine-grained levels. The final label indicator matrix is directly obtained from these consensus features. To demonstrate the effectiveness and versatility of the proposed method, we conducted experimental comparisons with state-of-the-art (SOTA) algorithms in both multiview clustering and image segmentation across diverse datasets. The source code and datasets are released at https://github.com/ChuanbinZhang/SDTR.

Deep multiview clustering provides an efficient way to analyze the data consisting of multiple modalities and features. Recently, the autoencoder (AE)-based deep multiview clustering algorithms have attracted intensive attention by virtue of their rewarding capabilities of extracting inherent features. Nevertheless, most existing methods are still confronted by several problems. First, the multiview data usually contains abundant cross-view information, thus parallel performing an individual AE for each view and directly combining the extracted latent together can hardly construct an informative view-consensus feature space for clustering. Second, the intrinsic local structures of multiview data are complicated, hence simply embedding a preset graph constraint into multiview clustering models cannot guarantee expected performance. Third, current methods commonly utilize the Kullback-Leibler (KL) divergence as clustering loss and accordingly may yield appalling clusters that lack discriminate characters. To solve these issues, in this article we propose two new AE-based deep multiview clustering algorithms named AE-based deep multiview clustering model incorporating graph embedding (AG-DMC) and deep discriminative multiview clustering algorithm with adaptive graph constraint (ADG-DMC). In AG-DMC, a novel cross-view representation learning model is established delicately by performing decoding processes based on the cascaded view-specific latent to learn sound view-consensus features for inspiring clustering results. In addition, an entropy-regularized adaptive graph constraint is imposed on the obtained soft assignments of data to precisely preserve potential local structures. Furthermore, in the improved model ADG-DMC, the adversarial learning mechanism is adopted as clustering loss to strengthen the discrimination of different clusters for better performance. In the comprehensive experiments carried out on eight real-world datasets, the proposed algorithms have achieved superior performance in the comparison with other advanced multiview clustering algorithms.

The graph-information-based fuzzy clustering has shown promising results in various datasets. However, its performance is hindered when dealing with high-dimensional data due to challenges related to redundant information and sensitivity to the similarity matrix design. To address these limitations, this article proposes an implicit fuzzy k-means (FKMs) model that enhances graph-based fuzzy clustering for high-dimensional data. Instead of explicitly designing a similarity matrix, our approach leverages the fuzzy partition result obtained from the implicit FKMs model to generate an effective similarity matrix. We employ a projection-based technique to handle redundant information, eliminating the need for specific feature extraction methods. By formulating the fuzzy clustering model solely based on the similarity matrix derived from the membership matrix, we mitigate issues, such as dependence on initial values and random fluctuations in clustering results. This innovative approach significantly improves the competitiveness of graph-enhanced fuzzy clustering for high-dimensional data. We present an efficient iterative optimization algorithm for our model and demonstrate its effectiveness through theoretical analysis and experimental comparisons with other state-of-the-art methods, showcasing its superior performance.

Unmanned aerial vehicle (UAV) visual tracking has been a hot research topic in the field of remote sensing. Many filter-based UAV trackers have achieved excellent performance. However, existing methods do not distinguish the importance of different feature channels with semantic information and background information, which may hinder the tracker’s ability to adapt to changing environments. To deal with this problem, we propose a channel attentional correlation filters learning model (CACF). Specifically, we introduce the fuzzy C-means algorithm to pre-classify the extracted features and then perform weight penalty to feature channels with different membership degrees. In addition, the filter can adapt more effectively to the background’s rapid changes during the UAV tracking process by learning the second-order difference between adjacent three frame features. Finally, the comparative experiments are conducted on three mainstream UAV datasets, including DTB70, UAV123@10fps, and UAVDT. The experimental results demonstrate the effectiveness of the proposed method. The tracking performance of CACF surpasses that of other state-of-the-art trackers.

The ensemble of fuzzy clustering can address the problems presented in the base clustering, such as fluctuations in results due to random initialization and performance degradation due to outliers. However, the performance of fuzzy clustering ensembles is still hampered by some challenges that include misaligned membership matrices, loss of information in the cosimilarity matrix, large storage space, unstable ensemble results due to an additional reclustering, the need for original data information for assistance, etc. To address these issues, we propose a parameter-free robust ensemble framework for fuzzy clustering. After obtaining the set of membership matrices, we cascade these membership matrices and mine the latent spectral matrix of the raw data. Benefiting from this step, we obtain global features of the dataset without knowing the specific data. Then, our framework uses transition matrices to solve the alignment problem, avoiding the storage of large-scale matrices. Most importantly, we introduce a robust weighted mechanism in the optimization model, where each base clustering is adaptively adjusted and the effect of outliers is suppressed by a robust function. In addition, the model yields the results as a membership matrix, which produces the exact partition results directly without any subsequent clustering operations. Finally, since our model is a parameter-free model, the setting of hyperparameters is avoided and the applicability of the model is improved as well. The effective algorithm of the optimization model is derived and its time complexity and convergence are analyzed. The results of competitive experiments on benchmark data show that the proposed ensemble framework is effective compared to state-of-the-art methods.

Kernel clustering has the ability to get the inherent nonlinear structure of the data. But the high computational complexity and the unknown representation of the kernel space make it unavailable for the data clustering in distributed peer-to-peer (P2P) networks. To solve this issue, we propose a new series of random feature-based collaborative kernel clustering algorithms in this article. In the most basic algorithm, each node in a distributed P2P network first maps its data into a low-dimensional random feature space with the approximation of the given kernel by using the random Fourier feature mapping method. Then, each node independently searches the clusters with its local data and the collaborative knowledge from its neighbor nodes, and the distributed clustering is performed among all network nodes until reaching the global consensus result, i.e., all nodes have the same cluster centers. In addition, an improved version is designed with assignment of feature weights, which is optimized by the maximum-entropy technique to extract important features for the cluster identification. What’s more, to relief the impact of different kernel functions and related parameters on clustering results, the combination of multiple kernels rather than a single kernel is adopted for the low-dimensional approximation, and the optimized weights are assigned to provide the guidance on the choice of the kernels and their parameters and discover significant features at the same time. Experiments on synthetic and real-world datasets show that the proposed methods achieve similar and even better results than the traditional kernel clustering methods on various performance metrics, including the average classification rate, the average normalized mutual information, and the average adjusted rand index. More importantly, the low-dimensional random features approximated to kernels and the distributed clustering mechanism adopted in these methods bring the greatly lower temporal complexity.

Categorical data are widely available in many real-world applications, and to discover valuable patterns in such data by clustering is of great importance. However, the lack of a decent quantitative relationship among categorical values makes traditional clustering approaches, which are usually developed for numerical data, perform poorly on categorical datasets. To solve this problem and boost the performance of clustering for categorical data, we propose a novel fuzzy clustering model in this article. At first, by approximating the maximum a posteriori (MAP) estimation of a discrete distribution of data partition, a new fuzzy clustering objective function is designed for categorical data. The Bayesian dissimilarity measure is formulated in this objective to tackle the subtle relationships between categorical values efficiently. Then, to further enhance the performance of clustering, a novel Kullback–Leibler divergence-based graph regularization is integrated into the clustering objective to exploit the prior knowledge on datasets, for example, the information about correlations of data points. The proposed model is solved by the alternative optimization and the experimental results on the synthetic and real-world datasets show that it outperforms the classical and relevant state-of-the-art algorithms. We also present the parameter analysis of our approach, and conduct a comprehensive study on the effectiveness of the Bayesian dissimilarity measure and the KL divergence-based graph regularization.

The traditional collaborative fuzzy clustering can effectively perform data clustering in distributed peer-to-peer networks, which is an impossible task to complete for the centralized clustering methods due to privacy and security requirements or network transmission technology constraints. But it will increase the number of clustering iterations and lead to lower efficiency of the clustering. Moreover, the collaborative mechanism hidden in the iterative process of clustering cannot be well revealed and explained. In this article, a novel series of transfer collaborative fuzzy clustering algorithms are proposed to solve these issues. In the first basic algorithm, the transfer learning among neighbor nodes vividly expresses the collaborative mechanism and enhances the information collaboration to accelerate the convergence of fuzzy clustering. Meanwhile, neighbor nodes can learn the knowledge from each other to further promote their respective clustering performance. Then, an improved version, with the learning-rate-adjustable strategy instead of fixed values, is designed to highlight the different influence between neighbor nodes, and the appropriate learning rates between neighbor nodes are achieved to ensure the stable clustering accuracy. Finally, two extended versions with the attribute-weight-entropy regularization technique are presented for the clustering of high dimensional sparse data and the extraction of important subspace features. Experiments show the efficiency of the proposed algorithms compared with the related prototype-based clustering methods.

Tensor-based robust principal component analysis (PCA) methods are efficient to discover the low-rank part of a hyperspectral image for reducing redundant information and guarantee good classification results. However, current methods cannot remove noise adequately, and the residual noise remaining in the low-rank image limits the further improvement of classification performance. Thus, enhancing the robustness to noise is important and helpful for tensor-based robust PCA (RPCA) methods to process hyperspectral images. To this end, we propose a tensor-based RPCA method with a locality preserving graph and frontal slice sparsity (LPGTRPCA) for hyperspectral image classification. Specifically, a tensor$l_{2,2,1}$norm that requires the frontal slice sparsity of a tensor is defined to extract the noise in the hyperspectral image from the frontal direction. What is more, a position-based Laplacian graph that preserves the local structures of a tensor according to the spatial position is designed for relieving the impact of the residual noise remaining in the low-rank image. Based on the tensor nuclear norm, the tensor$l_{2,2,1}$norm, and the position-based Laplacian graph, LPGTRPCA efficiently separates the low-rank part with little noise from a raw hyperspectral image and achieves more robust classification results than current methods. LPGTRPCA is optimized by the alternative direction multiplier method (ADMM), and the convergence of solutions is experimentally demonstrated. In the experiments conducted on Indian Pines, Pavia University, and Salinas datasets, LPGTRPCA outperformed various state-of-the-art and classical tensor-based RPCA methods in terms of average class classification accuracy (AA), overall classification accuracy (OA), and kappa coefficient (KC).

Uncertain data clustering has been recognized as an essential task in the research of data mining. Many centralized clustering algorithms are extended by defining new distance or similarity measurements to tackle this issue. With the fast development of network applications, these centralized methods show their limitations in conducting data clustering in a large dynamic distributed peer-to-peer network due to the privacy and security concerns or the technical constraints brought by distributive environments. In this paper, we propose a novel distributed uncertain data clustering algorithm, in which the centralized global clustering solution is approximated by performing distributed clustering. To shorten the execution time, the reduction technique is then applied to transform the proposed method into its deterministic form by replacing each uncertain data object with its expected centroid. Finally, the attribute-weight-entropy regularization technique enhances the proposed distributed clustering method to achieve better results in data clustering and extract the essential features for cluster identification. The experiments on both synthetic and real-world data have shown the efficiency and superiority of the presented algorithm.

Spectral clustering is one of the most effective methods of data mining, in which the adjacency matrix is constructed by using the similarity matrix. In this paper, to extend spectral clustering method for uncertain data clustering, we propose a new spectral clustering method based on JS-divergence. In the proposed method, the JS-divergence is used to construct the adjacency matrix in the spectral clustering, which is more suitable to calculate the similarity between uncertain data objects as a symmetrical measurement compared to the KL-divergence.