The clustering method has been widely used in data mining, pattern recognition, and image identification. Fuzzy c-means (FCM) is a soft clustering method that introduces the concept of membership. In this method, the fuzzy membership matrix is obtained by calculating the distance between data points in the original space. However, these methods may yield suboptimal results owing to the influence of redundant features. Moreover, FCM is always sensitive to noise points and heavily subject to outliers. In this paper, we propose a method called sparsity FCM clustering with principal component analysis embedding (P_SFCM). We simultaneously conduct principal component analysis (PCA) and membership learning, and then add an additional weighting factor for each data point. The goal of this operation is to identify the noise or outliers. Overall, the benefit of our framework is that it retains most of the information in the subspace while improving the robustness of the noise. In this paper, we employ an iterative optimization algorithm to efficiently solve our model. To verify the reliability of the proposed method, we conduct a convergence analysis, noise robustness analysis, and multi-cluster experiments. Furthermore, comparative experiments are conducted on both synthetic and real benchmark datasets. The experimental results show that the P_SFCM is competitive with comparable methods.

As one of the classical clustering techniques, spectral embedding boasts extensive applicability across numerous domains. Traditional spectral embedding techniques entail the mapping of graph models to low-dimensional vector spaces (indicator vectors) to facilitate hard partitioning. However, data boundaries occasionally exhibit ambiguity, thereby constraining the utility of hard partitioning. In this paper, we introduce an innovative spectral embedding method, namely, joint learning of anchor graph-based fuzzy spectral embedding model and fuzzy K-means (AFSEFK). Drawing inspiration from fuzzy logic, our method employs a membership vector in lieu of the conventional indicator vector for spectral embedding, amalgamating it with fuzzy K-means to concurrently optimize membership, thereby simultaneously learning the local and global structures inherent in the data. Moreover, to enhance the quality of similarity graphs and augment clustering performance, we implement the balanced K-means based hierarchical K-means (BKHK) technique to generate representative anchors. Subsequently, an anchor-based similarity graph is devised through a parameter-free neighbor assignment strategy. Comprehensive extensive experimentation with synthetic and real-world datasets substantiates the efficacy of the AFSEFK algorithm.

This article presents a learning-based adaptive optimal control approach for flotation processes subject to input constraints and disturbances using adaptive dynamic programming (ADP) along with double-loop iteration. First, the principle of the operational pattern is adopted to preset reagents’ addition based on the feeding condition. Then, this article leverages a deep learning model, which is composed of multiple neural layers to detect flotation indexes directly from the raw froth images. After that, the tracking error between the detected flotation indexes and the reference values can be minimized by using ADP-based double-loop iteration. Particularly, a policy-iteration (PI) method is utilized for the proposed learning-based ADP algorithm. In the inner loop, the optimal control problem is formulated as a linear quadratic regulator (LQR) problem using the low-gain feedback design method. In the outer loop, the design parameters, i.e., weighting matrices, are tuned automatically to satisfy the input constraints. Finally, the analytical results demonstrate that the proposed scheme can guarantee asymptotic tracking in the presence of actuator saturation and disturbances.

Differential Evolution (DE) stands as a potent global optimization algorithm, renowned for its application in addressing a myriad of practical engineering issues. The efficacy of DE is profoundly influenced by its control parameters and mutation strategies. In light of this, we introduce a refined DE algorithm characterized by adaptive parameters and dual mutation strategies (APDSDE). APDSDE inaugurates an adaptive switching mechanism that alternates between two innovative mutation strategies: DE/current-to-pBest-w/1 and DE/current-to-Amean-w/1. Furthermore, a novel parameter adaptation technique rooted in cosine similarity is established, with the derivation of explicit calculation formulas for both the scaling factor weight and crossover rate weight. In pursuit of optimizing convergence speed whilst preserving population diversity, a sophisticated nonlinear population size reduction method is proposed. The robustness of each algorithm is rigorously evaluated against the CEC2017 benchmark functions, with empirical evidence underscoring the superior performance of APDSDE in comparison to a host of advanced DE variants.

In traditional graph embedding methods, graph construction is sensitive to high-dimensional data with noise and outliers, making an effective exploration of the neighborhood structure of the data difficult. Besides, with these methods, constructing graphs and reducing dimensions are disconnected and cannot be mutually optimized. To address these problems, we propose an unsupervised dimensionality reduction method based on bipartite graph, named unsupervised adaptive bipartite graph embedding (UABGE). First, the anchors are generated from the raw data by K-means or random sampling. Second, the bipartite graph, which is constructed between the samples and the anchors in the low-dimensional subspace, utilizes the adaptive allocation method to assign neighbors for each sample, so that the local structure of high-dimensional data can be captured effectively. Third, we present an objective function that combines bipartite graph construction and projection matrix learning to achieve mutual optimization between them, which can be solved with an alternating optimization algorithm. Finally, the computational complexity and the convergence of the algorithm are analyzed. Experimental results on synthetic data and publicly available datasets illustrate the effectiveness of the proposed method.

Clustering ensemble technique has been shown to be effective in improving the accuracy and stability of single clustering algorithms. With the development of information technology, the amount of data, such as image, text and video, has increased rapidly. Efficiently clustering these large-scale datasets is a challenge. Clustering ensembles usually transform clustering results to a co-association matrix, and then to a graph-partition problem. These methods may suffer from information loss when computing the similarity among samples or base clusterings. Rich information between samples and base clusterings is ignored. Moreover, the results are not discrete. They need post-processing steps to obtain the final clustering result, which will deviate greatly from the real clustering result. To address this problem, we propose a co-clustering ensemble based on bilateral k-means (CEBKM) algorithm. Our algorithm can simultaneously cluster samples and base clusterings of a dataset, to fully exploit the potential information between the samples and the base clusterings. In addition, it can directly obtain the final clustering results without using other clustering algorithms. The proposed method, outperformed several state-of-the-art clustering ensemble methods in experiments conducted on real-world and toy datasets.