Classical clustering algorithms such as k-means face limitations in handling clusters with heterogeneous shapes, densities, and sizes, while exhibiting sensitivity to initial centroid selection. To overcome these challenges, this article proposes a novel clustering framework based on regenerated granular ball (RGGB) with the principle of justifiable granularity. Unlike existing granular-ball (GB) techniques that overemphasize purity criteria at the expense of uncontrolled ball sizes, RGGB dynamically adjusts granularity levels through iterative regeneration, achieving an optimal balance between detailed data representation and computational efficiency. This adaptability enhances stability in capturing data similarities while mitigating sensitivity to initialization. To validate the method, we integrate RGGB with a novel k-nearest neighbor (KNN) classifier using regenerated GBs to evaluate classification performance and demonstrate practical applications. Experiments on diverse public and realistic datasets demonstrate that the RGGB-based KNN algorithm consistently outperforms existing techniques, including traditional KNN and other methods, making a promising advancement in clustering and classification tasks.

This article investigates the adaptive sliding mode control (ASMC) for a class of nonlinear impulsive hybrid systems with time-varying delay, adopting a creative approach that emphasizes the switching perspective. When both impulse and sliding mode control are involved in the time-delay system, ensuring the continuity of the sliding mode function (SMF) and achieving the reachability of system states become crucial challenges that need to be addressed. In view of this, a novel impulse-based SMF is developed such that the impulsive effect can be avoided on sliding surface, and the difficulty of its continuity is also settled at impulsive instants. By using the state augmented approach, the delay-dependent Lyapunov function with switched systems is formulated to guarantee robust stability of the given sliding mode dynamics. Meanwhile, the designed ASMC law is derived to achieve the finite reachability of switching surface for system states. It is shown that the proposed ASMC law offers a high degree of freedom for adjusting the constants in nonlinear assumptions. Finally, comparative studies are conducted to validate the theoretical results and demonstrate their practical applicability.

Fuzzy C-means (FCM) is a clustering algorithm based on partition of the universe. However, the partition generated by an equivalence relation is strict in practical application and exhibits relatively poor fault-tolerant mechanism. In this article, a novel binary relation based on improved FCM with the principle of refined justifiable granularity is presented. Different expressions of the proposed binary relation under different values of weight parameter are discussed, and the changes of the properties of the binary relation under different parameter values are provided. By measuring the significance of attributes in the feature space, a feature selection method, called forward heuristic feature selection (FHFS), is designed to construct the low-dimension feature space based on maximizing the original data and information retention through the defined degrees of aggregation and dispersion. It is shown how the results of feature selection and classification performance vary when the values of the weight factor locate in different ranges. To illustrate the superiority and effectiveness of the proposed FHFS algorithm, nine high-dimensional datasets and eight image datasets from University of California-Irvine (UCI) repository are used and compared with other feature selection methods, respectively. The results of experimental evaluation and the significance test show that the proposed learning mechanism is a superior algorithm.

Most exiting results for impulsive switched systems (ISSs) are mainly built on the synchronous switching and impulses case; however, the impulses can not only occur in switched interval including switched instants but also the switched signals may exist between two impulsive points in practical instants. Under asynchronous impulses and switching signals, the main objective of this article is to study the exponential stability of fractional-order hybrid systems. In order to better characterize stability, some novel criteria are presented by adopting the mode-dependent average impulsive interval and induction method. The obtained impulsive switched criteria lead to a tradeoff between fractional-order α and impulsive strength. Especially, the impulsive effects (positive or negative) with the order α are also discussed in detail, which extends the previous integer order results. Moreover, numerical examples are given to interpret and verify the effectiveness of the obtained criteria.