Consensus learning has been widely adopted in clustering tasks due to its robustness to noise and outliers, as well as its ability to aggregate diverse base results from multiple models. However, existing methods are often limited by feature alignment issues arising from heterogeneous feature dimensionalities and label permutation inconsistencies across models. To address these limitations, this paper introduces a novel Consensus Fuzzy Representation Learning (CFRL) framework. The CFRL framework initially employs various fuzzy clustering methods to generate diverse membership matrices, which are then transformed into affinity matrices to serve as base fuzzy representations. This transformation strategy not only effectively resolves feature alignment issues but also provides a unified processing mechanism for both single-view and multi-view data scenarios. To derive robust consensus features, the tensor Schatten$p$-norm encourages low-rank structure in the tensorized fuzzy representations, whereas an$l_{1}$-norm regularized error term captures and suppresses sparse noise. Moreover, a block diagonal regularizer is incorporated into the objective function, which guides the consensus feature matrix toward an optimal block diagonal structure. This structural constraint enhances cluster discriminability and enables reliable final cluster assignments. Comprehensive experimental evaluations validate that the proposed CFRL method achieves superior performance compared to state-of-the-art approaches.

Affine Frequency Division Multiplexing (AFDM) is a chirp-transform modulation technique that has shown reliable performance in high-mobility scenarios, making it an attractive option for next generation communication systems. Recent literature suggests that under chirp parameter adjustment, AFDM can achieve optimal diversity performance in delay-doppler channels with maximum likelihood (ML) detection. However, the performance of AFDM with minimum mean square error equalization (MMSE-Eq) has not been extensively investigated in the existing literature. In this paper, we analyze the performance of AFDM with MMSE-Eq, derive a lower bound for the theoretical bit error rate (BER) of the AFDM system, and discuss the relationship between chirp parameters and performance degradation. To optimize BER performance, we propose two distinct chirp parameter selection strategies for frequency selective and doubly selective channels, respectively. These strategies offer the advantage of avoiding extensive computations. Additionally, we propose a low-complexity and high-performance iterative MMSE-Eq algorithm based on time-domain channel matrix operations. The algorithm resolves the issue encountered in existing low-complexity methods, where different chirp parameter selections significantly impact the complexity. Simulation results demonstrate the efficacy of our proposed parameter selection strategies and the outstanding BER performance achieved by the iterative MMSE-Eq algorithm.

Discriminative correlation filter (DCF)-based tracking algorithms continue to advance in the field of UAV tracking due to their computational efficiency. The idea of integrating the advantages of historical information and response adjustments into the CF tracking framework is continuously being developed. However, maintaining the stability of mobile video tracking in highly dynamic environments is extremely challenging. This difficulty arises from frequent changes in targets and backgrounds, as well as the stochastic noise generated by the photon-counting process in sensors. In addition, the inconsistent rates of these changes are often overlooked and require further scrutiny. In this paper, we propose a dynamic sensitivity enhanced correlation filter with adaptive second-order difference spatial regularization to address the issue of inconsistent motion rates in dynamic videos. We use the non-local means algorithm to denoise template images before feature extraction, improving the discriminative power of target contours. Then, we incorporate the proposed dynamic-sensitivity error method into CF learning and employ a novel adaptive second-order difference spatial regularization to simultaneously optimize the filter coefficients and spatial regularization weights. This regularization effectively works in synergy with the dynamic-sensitivity error strategy. Furthermore, an additional ADMM optimizer is introduced to derive the solution, thereby improving the convergence and computational efficiency of the algorithm. This algorithm supports the adjustment of filter updates in dynamic environments by balancing consistency with previous filter templates and flexibility to accommodate rapid target changes. By conducting extensive experiments on three challenging UAV tracking databases, we compare the proposed model with existing models. The experimental results demonstrate our superior performance. Code is released at:https://github.com/Johnsonirene/LDECF.

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.

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.

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.

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.

This paper proposes a path planner for autonomous underwater vehicles (AUVs) in 3-D underwater space. We simulate an underwater space with rugged seabed and suspending obstacles, which is close to real world. In the proposed representation scheme, the problem space is decomposed into parallel subspaces and each subspace is described by a grid method. The paths of AUVs are simplified as a set of successive points in the problem space. By jointing these waypoints, the entire path of the AUV is obtained. A cost function with penalty method takes into account the length, energy consumption, safety and curvature constraints of AUVs. It is applied to evaluate the quality of paths. Differential evolution (DE) algorithm is used as a black-box optimization tool to provide optimal solutions for the path planning. In addition, we adaptively adjust the parameters of DE according to population distribution and the blockage of parallel subspaces so as to improve its performance. Experiments are conducted on 6 different scenarios. The results validate that the proposed algorithm is effective for improving solution quality and avoiding premature convergence.