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A Short Tutorial: Some Things You Might Not Know About k-Means Clustering

IEEE SYSTEMS MAN AND CYBERNETICS MAGAZINE 2025年第1期11卷 23-33页

作者： Bezdek, James C. Cornell Univ Ithaca NY 14850 USA

The k-means model and algorithms to optimize it are ubiquitous in cluster analysis. It is impossible to overstate the popularity of this method, which is by far the most heavily cited and studied approach to hard (i.e., non-soft) clustering on earth. This limited tutorial dispels some popularly held misconceptions about this basic method. It begins with a short history of the two algorithms commonly called k-means. Then the geometric structure of hard and soft partition sets underlying all hard, probabilistic, and fuzzy clustering algorithms is presented. The structural theory illuminates some little-known facts about the foundations of k-means and some of its soft relatives. Finally, two soft (probabilistic and fuzzy) generalizations of k-means that should be of interest to practitioners in this area are briefly discussed.

关键词： Earth Analytical models Clustering algorithms Tutorials Probabilistic logic partitioning algorithms History Cybernetics

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Review of Serial and Parallel Min-Cut/Max-Flow algorithms for Computer Vision

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2023年第2期45卷 2310-2329页

作者： Jensen, Patrick M. M. Jeppesen, Niels Dahl, Anders B. B. Dahl, Vedrana A. A. Tech Univ Denmark Dept Appl Math & Comp Sci DK-2800 Lyngby Denmark

Minimum cut/maximum flow (min-cut/max-flow) algorithms solve a variety of problems in computer vision and thus significant effort has been put into developing fast min-cut/max-flow algorithms. As a result, it is difficult to choose an ideal algorithm for a given problem. Furthermore, parallel algorithms have not been thoroughly compared. In this paper, we evaluate the state-of-the-art serial and parallel min-cut/max-flow algorithms on the largest set of computer vision problems yet. We focus on generic algorithms, i.e., for unstructured graphs, but also compare with the specialized GridCut implementation. When applicable, GridCut performs best. Otherwise, the two pseudoflow algorithms, Hochbaum pseudoflow and excesses incremental breadth first search, achieves the overall best performance. The most memory efficient implementation tested is the Boykov-Kolmogorov algorithm. Amongst generic parallel algorithms, we find the bottom-up merging approach by Liu and Sun to be best, but no method is dominant. Of the generic parallel methods, only the parallel preflow push-relabel algorithm is able to efficiently scale with many processors across problem sizes, and no generic parallel method consistently outperforms serial algorithms. Finally, we provide and evaluate strategies for algorithm selection to obtain good expected performance. We make our dataset and implementations publicly available for further research.

关键词： Computer vision Parallel algorithms Benchmark testing Image segmentation Sun partitioning algorithms Heuristic algorithms algorithms computer vision graph algorithms graph-theoretic methods parallel algorithms performance evaluation of algorithms and systems

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An Efficient Method to Accurately Cluster Large Number of High Dimensional Facial Images

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IEEE ACCESS 2023年 11卷 39934-39949页

作者： Kumar, K. B. Shibu Samuel, Philip Coll Engn Trivandrum Dept Comp Sci & Engn Thiruvananthapuram 695016 India Cochin Univ Sci & Technol Dept Comp Sci Kochi 682022 India

Accurately clustering large, high dimensional datasets is a challenging problem in unsupervised learning. K-means is considered to be a fast, widely used and accurate centroid based data partitioning algorithm for spherical datasets. However, its non-determinism and heavy dependence on the selection of initial cluster centers along with vulnerability to noise make it a poor candidate for clustering large datasets with high dimensionality. To overcome these, we develop a novel, nature inspired, centroid based clustering algorithm, inspired from the principles of particle physics. Our method ensures that the convergence to local optima and non-deterministic outputs are avoided. We experiment the method on large datasets of human face images. Besides, our method addresses the problem of outliers and presence of not well-separated data in these datasets. We use a deep learning model for extracting facial features into a vector of 128 dimensions. We validate the quality and accuracy of our methods using different statistical parameters like f-measure, accuracy, error rate, average in group proportion and normalized cluster size rand index. These evaluations show that our method exhibits better accuracy and quality in clustering large face image datasets, in comparison with other existing mechanisms. The strength of our algorithms is more visible as the size of the dataset grows.

关键词： Face recognition Clustering algorithms Feature extraction partitioning algorithms Videos Social networking (online) Centroid based celestial clustering face clustering on large datasets optimization on clustering refined celestial PSO clustering

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SPACE4AI-D: A Design-Time Tool for AI Applications Resource Selection in Computing Continua

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IEEE TRANSACTIONS ON SERVICES COMPUTING 2024年第6期17卷 4324-4339页

作者： Sedghani, Hamta Filippini, Federica Ardagna, Danilo Politecn Milan I-20133 Milan Italy

Nowadays, Artificial Intelligence (AI) applications are becoming increasingly popular in a wide range of industries, mainly thanks to Deep Neural Networks (DNNs) that needs powerful resources. Cloud computing is a promising approach to serve AI applications thanks to its high processing power, but this sometimes results in an unacceptable latency because of long-distance communication. Vice versa, edge computing is close to where data are generated and therefore it is becoming crucial for their timely, flexible, and secure management. Given the more distributed nature of the edge and the heterogeneity of its resources, efficient component placement and resource allocation approaches become critical in orchestrating the application execution. In this paper, we formulate the resource selection and AI applications component placement problem in a computing continuum as a Mixed Integer Non-Linear Problem (MINLP), and we propose a design-time tool for its efficient solution. We first propose a Random Greedy algorithm to minimize the cost of the placement while guaranteeing some response time performance constraints. Then, we develop some heuristic methods such as Local Search, Tabu Search, Simulated Annealing and Genetic algorithms, to improve the initial solutions provided by the Random Greedy. To evaluate our proposed approach, we designed an extensive experimental campaign, comparing the heuristics methods with one another and then the best heuristic against Best Cost Performance Constraint (BCPC) algorithm, a state-of-the-art approach. The results demonstrate that our proposed approach finds lower-cost solution than BCPC (27.6% on average) under the same time limit in large-scale systems. Finally, during the validation in a real edge system including FaaS resources our approach finds the globally optimal solution, suffering a deviation of around 12% between actual and predicted costs.

关键词： Artificial intelligence Cloud computing Time factors Quality of service Costs Containers partitioning algorithms Runtime Heuristic algorithms Delays AI services component placement cloud edge computing resource selection

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SimpleMKKM: Simple Multiple Kernel K-Means

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2023年第4期45卷 5174-5186页

作者： Liu, Xinwang Natl Univ Def Technol Coll Comp Changsha 410073 Peoples R China

We propose a simple yet effective multiple kernel clustering algorithm, termed simple multiple kernel k-means (SimpleMKKM). It extends the widely used supervised kernel alignment criterion to multi-kernel clustering. Our criterion is given by an intractable minimization-maximization problem in the kernel coefficient and clustering partition matrix. To optimize it, we equivalently rewrite the minimization-maximization formulation as a minimization of an optimal value function, prove its differenentiablity, and design a reduced gradient descent algorithm to decrease it. Furthermore, we prove that the resultant solution of SimpleMKKM is the global optimum. We theoretically analyze the performance of SimpleMKKM in terms of its clustering generalization error. After that, we develop extensive experiments to investigate the proposed SimpleMKKM from the perspectives of clustering accuracy, advantage on the formulation and optimization, variation of the learned consensus clustering matrix with iterations, clustering performance with varied number of samples and base kernels, analysis of the learned kernel weight, the running time and the global convergence. The experimental study demonstrates the effectiveness of the proposed SimpleMKKM by considerably and consistently outperforming state of the art multiple kernel clustering alternatives. In addition, the ablation study shows that the improved clustering performance is contributed by both the novel formulation and new optimization. Our work provides a more effective approach to integrate multi-view data for clustering, and this could trigger novel research on multiple kernel clustering. The source code and data for SimpleMKKM are available at https://***/xinwangliu/SimpleMKKMcodes/.

关键词： Kernel Optimization Clustering algorithms Minimization partitioning algorithms Linear programming Task analysis Multi-view clustering multiple kernel clustering kernel alignment maximization

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Transfer Learning-Based Collaborative Multiview Clustering

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IEEE TRANSACTIONS ON FUZZY SYSTEMS 2023年第4期31卷 1163-1177页

作者： Liu, Xiangdao Wang, Rongrong Zhou, Jin Chen, C. L. Philip Zhang, Tong Chen, Yuehui Han, Shiyuan Du, Tao Ji, Ke Zhang, Kun Univ Jinan Shandong Prov Key Lab Network Based Intelligent Co Jinan 250022 Peoples R China South China Univ Technol Sch Comp Sci & Engn Guangzhou 510641 Peoples R China

Collaborative multiview clustering methods can efficiently realize the view fusion by exploring complementary and consistent information among multiple views. However, these studies ignore all the differences between multiple views in fusion. In fact, in the multiview clustering, the data are diverse from view to view. The larger the difference between any two views is, the more the fusion of these views is required. Moreover, a global tradeoff parameter is generally adopted to restrain the penalty related to the disagreement of all views, which is often defined empirically. Inspired by the idea of transfer learning, a series of novel collaborative multiview clustering algorithms are proposed to tackle these challenges. In the most basic one, each view performs clustering independently and learns from others to improve its own clustering performance, in which a global learning factor is defined to control the interaction between multiple views. The fuzzy memberships are regarded as the important knowledge to provide guidance between views, and the consensus constraint is defined to ensure the consistent partitions of all views. In addition, the local adaptive learning factors between any two views instead of a global fixed one are adopted in an improved version to emphasize the difference between views, and the adjustment strategy for the learning factor is further designed to guarantee the stability of multiview clustering without the influence of initial values. Finally, to identify the significance of different views to the clustering, the extended versions are excavated with the assignment of view weights and the maximum entropy regularization technique is employed to optimize the weights. Experiments on various real-world multiview datasets verify the superiority of the presented approaches.

关键词： Collaboration Clustering algorithms Transfer learning partitioning algorithms Clustering methods Entropy Adaptive learning Adaptive learning factor adjustment collabo- rative multiview clustering entropy regularization transfer clustering

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Spatiotemporal Sequence Prediction With Point Processes and Self-Organizing Decision Trees

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023年第6期34卷 3097-3110页

作者： Karaahmetoglu, Oguzhan Kozat, Suleyman Serdar Bilkent Univ Dept Elect & Elect Engn TR-06800 Ankara Turkey Data Boss AS TR-06800 Ankara Turkey

We study the spatiotemporal prediction problem and introduce a novel point-process-based prediction algorithm. Spatiotemporal prediction is extensively studied in machine learning literature due to its critical real-life applications, such as crime, earthquake, and social event prediction. Despite these thorough studies, specific problems inherent to the application domain are not yet fully explored. Here, we address the nonstationary spatiotemporal prediction problem on both densely and sparsely distributed sequences. We introduce a probabilistic approach that partitions the spatial domain into subregions and models the event arrivals in each region with interacting point processes. Our algorithm can jointly learn the spatial partitioning and the interaction between these regions through a gradient-based optimization procedure. Finally, we demonstrate the performance of our algorithm on both simulated data and two real-life datasets. We compare our approach with baseline and state-of-the-art deep learning-based approaches, where we achieve significant performance improvements. Moreover, we also show the effect of using different parameters on the overall performance through empirical results and explain the procedure for choosing the parameters.

关键词： Spatiotemporal phenomena Data models Adaptation models Standards Predictive models partitioning algorithms Optimization Adaptive decision trees crime prediction earthquake prediction Hawkes process nonstationary time-series data online learning spatiotemporal point process

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Advanced Clustering Approach for Peer-to-Peer Local Energy Markets Considering Prosumers' Preference Vectors

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IEEE ACCESS 2023年 11卷 33607-33627页

作者： Okwuibe, Godwin C. Gazafroudi, Amin Shokri Mengelkamp, Esther Hambridge, Sarah Tzscheutschler, Peter Hamacher, Thomas Tech Univ Munich Sch Engn & Design D-80333 Munich Germany OLI Syst GmbH D-67376 Harthausen Germany StromDAO GmbH D-69256 Mauer Germany MK Consulting D-21365 Adendorf Germany Grid Singular D-10965 Berlin Germany

Local energy markets (LEMs) are utilized in a bottom-up power systems approach for reducing the complexity of the traditional, centralized power system and to enable better integration of decentralized renewable energy resources (RES). Peer-to-peer (P2P) energy trading creates opportunities for prosumers to trade their RES with other prosumers in the LEM. Although several scenarios were proposed in the literature for modelling P2P energy trading, there is still a gap in the literature considering the heterogeneous characteristics of prosumers' bidding preferences during P2P matching in the LEM. In this paper, we present heterogeneous characteristics of bidding preferences for prosumers considering energy quantity, bid/offer price, geographic location, location of agents on the local community and cluster welfare. Moreover, this paper proposes an advanced clustering model for P2P matching in the energy community considering the heterogeneous characteristics of bidding preferences for prosumers. For evaluating our proposed model performance, two German real case scenarios of a small and large communities were studied. The simulations results show that using price preference, as the criterion for clustering, offers more technical and economic benefits to energy communities compared to other clustering scenarios. On the other hand, clustering scenarios based on location of prosumers ensure that energy is traded among prosumers who are closer to each other.

关键词： Clustering algorithms Peer-to-peer computing partitioning algorithms Data models Classification algorithms Power system stability Load modeling Energy community advanced clustering local energy market matching mechanism peer-to-peer trading

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Fusion of Centroid-Based Clustering With Graph Clustering: An Expectation-Maximization-Based Hybrid Clustering

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023年第8期34卷 4068-4082页

作者： Uykan, Zekeriya Amer Univ Middle East Coll Engn & Technol Egaila Kuwait

This article extends the expectation-maximization (EM) formulation for the Gaussian mixture model (GMM) with a novel weighted dissimilarity loss. This extension results in the fusion of two different clustering methods, namely, centroid-based clustering and graph clustering in the same framework in order to leverage their advantages. The fusion of centroid-based clustering and graph clustering results in a simple ``soft'' asynchronous hybrid clustering method. The proposed algorithm may start as a pure centroid-based clustering algorithm (e.g., k-means), and as the time evolves, it may eventually and gradually turn into a pure graph clustering algorithm [e.g., basic greedy asynchronous distributed interference avoidance (GADIA) (Babadi and Tarokh, 2010)] as the algorithm converges and vice versa. The ``hard'' version of the proposed hybrid algorithm includes the standard Hopfield neural networks (and, thus, Bruck's Ln algorithm by (Bruck, 1990) and the Ising model in statistical mechanics), Babadi and Tarokh's basic GADIA in 2010, and the standard k-means (Steinhaus, 1956), (MacQueen, 1967) [i.e., the Lloyd algorithm (Lloyd, 1957, 1982)] as its special cases. We call the ``hard version'' of the proposed clustering as ``hybrid-nongreedy asynchronous clustering (H-NAC).'' We apply the H-NAC to various clustering problems using well-known benchmark datasets. The computer simulations confirm the superior performance of the H-NAC compared to the k-means clustering, k-GADIA, spectral clustering, and a very recent clustering algorithm structured graph learning (SGL) by Kang et al. (2021), which represents one of the state-of-the-art clustering algorithms.

关键词： Clustering algorithms Clustering methods partitioning algorithms Wireless communication Standards Principal component analysis Image segmentation Bruck's Ln algorithm centroid-based clustering expectation-maximization (EM) greedy asynchronous distributed interference avoidance (GADIA) graph clustering hybrid-nongreedy asynchronous clustering (H-NAC) k-means clustering

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Variational Bayesian Inference for Robust Identification of PWARX Systems With Time-Varying Time-Delays

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IEEE TRANSACTIONS ON CYBERNETICS 2023年第6期53卷 3613-3623页

作者： Bai, Wentao Guo, Fan Chen, Lei Hao, Kuangrong Huang, Biao Donghua Univ Coll Informat Sci & Technol Engn Res Ctr Digitized Text & Apparel Technol Minist Educ Shanghai 201620 Peoples R China Univ Alberta Dept Chem & Mat Engn Edmonton AB T6G 2G6 Canada

This article presents a robust variational Bayesian (VB) algorithm for identifying piecewise autoregressive exogenous (PWARX) systems with time-varying time-delays. To alleviate the adverse effects caused by outliers, the probability distribution of noise is taken to follow a $t$ -distribution. Meanwhile, a solution strategy for more accurately classifying undecidable data points is proposed, and the hyperplanes used to split data are determined by a support vector machine (SVM). In addition, maximum-likelihood estimation (MLE) is adopted to re-estimate the unknown parameters through the classification results. The time-delay is regarded as a hidden variable and identified through the VB algorithm. The effectiveness of the proposed algorithm is illustrated by two simulation examples.

关键词： Time-varying systems Support vector machines partitioning algorithms Bayes methods Maximum likelihood estimation Delays Probability distribution Piecewise autoregressive exogenous (PWARX) robust identification support vector machine (SVM) t-distribution time-delay variational Bayesian (VB)

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