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The large number of distributed resources in the distribution network provides new resources for grid interactive regulation. First, the regulation characteristics of distributed resources are analyzed, and a method for calculating adjustable capacity is established. Then, the k-means++ algorithm with indicator weights is used to cluster the distributed resources. Finally, a simulation is conducted on a photovoltaic cluster with 60 units, and the results are compared with traditional methods.

Clustering has primarily been used as an analytical technique to group unlabeled data for extracting meaningful information. The fact that no clustering algorithm can solve all clustering problems has resulted in the development of several clustering algorithms with diverse applications. We review data clustering, intending to underscore recent applications in selected industrial sectors and other notable concepts. In this paper, we begin by highlighting clustering components and discussing classification terminologies. Furthermore, specific, and general applications of clustering are discussed. Notable concepts on clustering algorithms, emerging variants, measures of similarities/dissimilarities, issues surrounding clustering optimization, validation and data types are outlined. Suggestions are made to emphasize the continued interest in clustering techniques both by scholars and Industry practitioners. Key findings in this review show the size of data as a classification criterion and as data sizes for clustering become larger and varied, the determination of the optimal number of clusters will require new feature extracting methods, validation indices and clustering techniques. In addition, clustering techniques have found growing use in key industry sectors linked to the sustainable development goals such as manufacturing, transportation and logistics, energy, and healthcare, where the use of clustering is more integrated with other analytical techniques than a stand-alone clustering technique.

This survey rigorously explores contemporary clustering algorithms within the machine learning paradigm, focusing on five primary methodologies: centroid-based, hierarchical, density-based, distribution-based, and graph-based clustering. Through the lens of recent innovations such as deep embedded clustering and spectral clustering, we analyze the strengths, limitations, and the breadth of application domains—ranging from bioinformatics to social network analysis. Notably, the survey introduces novel contributions by integrating clustering techniques with dimensionality reduction and proposing advanced ensemble methods to enhance stability and accuracy across varied data structures. This work uniquely synthesizes the latest advancements and offers new perspectives on overcoming traditional challenges like scalability and noise sensitivity, thus providing a comprehensive roadmap for future research and practical applications in data-intensive environments.

The Shipboard Automatic Identification System (AIS) is crucial for navigation safety and maritime surveillance, data mining and pattern analysis of AIS information have attracted considerable attention in terms of both basic research and practical applications. Clustering of spatio-temporal AIS trajectories can be used to identify abnormal patterns and mine customary route data for transportation safety. Thus, the capacities of navigation safety and maritime traffic monitoring could be enhanced correspondingly. However, trajectory clustering is often sensitive to undesirable outliers and is essentially more complex compared with traditional point clustering. To overcome this limitation, a multi-step trajectory clustering method is proposed in this paper for robust AIS trajectory clustering. In particular, the Dynamic Time Warping (DTW), a similarity measurement method, is introduced in the first step to measure the distances between different trajectories. The calculated distances, inversely proportional to the similarities, constitute a distance matrix in the second step. Furthermore, as a widely-used dimensional reduction method, Principal Component Analysis (PCA) is exploited to decompose the obtained distance matrix. In particular, the top k principal components with above 95% accumulative contribution rate are extracted by PCA, and the number of the centers k is chosen. The k centers are found by the improved center automatically selection algorithm. In the last step, the improved center clustering algorithm with k clusters is implemented on the distance matrix to achieve the final AIS trajectory clustering results. In order to improve the accuracy of the proposed multi-step clustering algorithm, an automatic algorithm for choosing the k clusters is developed according to the similarity distance. Numerous experiments on realistic AIS trajectory datasets in the bridge area waterway and Mississippi River have been implemented to compare our proposed method with traditional spectral clustering and fast affinity propagation clustering. Experimental results have illustrated its superior performance in terms of quantitative and qualitative evaluations.

In this book, top researchers from around the world cover the entire area of clustering, from basic methods to more refined and complex data clustering approaches. They pay special attention to recent issues in graphs, social networks, and other domains. The book explores the characteristics of clustering problems in a variety of application areas. It also explains how to glean detailed insight from the clustering process--including how to verify the quality of the underlying clusters--through supervision, human intervention, or the automated generation of alternative clusters.

The evaluation of clustering effects has been an important issue for a long time. How to effectively evaluate the clustering results of clustering algorithms is the key to the problem. The clustering effect evaluation is generally divided into internal clustering effect evaluation and external clustering effect evaluation. This paper focuses on the internal clustering effect evaluation, and proposes an improved index based on the Silhouette index and the Calinski-Harabasz index: Peak Weight Index (PWI). PWI combines the characteristics of Silhouette index and Calinski-Harabasz index, and takes the peak value of the two indexes as the impact point and gives appropriate weight within a certain range. Silhouette index and Calinski-Harabasz index will help improve the fluctuation of clustering results in the data set. Through the simulation experiments on four self-built influence data sets and two real data sets, it will prove that the PWI has excellent evaluation of clustering results.

In multi-core in-order processing systems, only one core can be utilised when the instruction at the head of the instruction queue produces data input for the next instruction in the queue. Although, in-order processing has been studied in the past, the influence of data clustering, i.e., the extent to which subsequent instructions rely on each other's data, has been largely overlooked. Therefore, a queueing model is developed and closed-form formulae are provided for the stability condition and the average time before instructions are executed. These expressions clearly reflect that data clustering can have a devastating impact.