Journal articles on the topic 'Optimal clusters'
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1
GREKOUSIS, GEORGE. "GIVING FUZZINESS TO SPATIAL CLUSTERS: A NEW INDEX FOR CHOOSING THE OPTIMAL NUMBER OF CLUSTERS." International Journal on Artificial Intelligence Tools 22, no. 03 (June 2013): 1350009. http://dx.doi.org/10.1142/s0218213013500097.
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Choosing the optimal number of clusters is a key issue in cluster analysis. Especially when dealing with more spatial clustering, things tend to be more complicated. Cluster validation helps to determine the appropriate number of clusters present in a dataset. Furthermore, cluster validation evaluates and assesses the results of clustering algorithms. There are numerous methods and techniques for choosing the optimal number of clusters via crisp and fuzzy clustering. In this paper, we introduce a new index for fuzzy clustering to determine the optimal number of clusters. This index is not another metric for calculating compactness or separation among partitions. Instead, the index uses several existing indices to give a degree, or fuzziness, to the optimal number of clusters. In this way, not only do the objects in a fuzzy cluster get a membership value, but the number of clusters to be partitioned is given a value as well. The new index is used in the fuzzy c-means algorithm for the geodemographic segmentation of 285 postal codes.
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Zhong, Yanfei, and Liangpei Zhang. "A New Fuzzy Clustering Algorithm Based on Clonal Selection for Land Cover Classification." Mathematical Problems in Engineering 2011 (2011): 1–21. http://dx.doi.org/10.1155/2011/708459.
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A new fuzzy clustering algorithm based on clonal selection theory from artificial immune systems (AIS), namely, FCSA, is proposed to obtain the optimal clustering result of land cover classification withouta prioriassumptions on the number of clusters. FCSA can adaptively find the optimal number of clusters and is designed as a two-layer system: the classification layer and the optimization layer. The classification layer of FCSA, inspired by clonal selection theory, generates the optimal classification result with a fixed cluster number by utilizing the clone, mutation, and selection of immune operators. The optimization layer of FCSA evaluates the optimal solutions according to performance measures for cluster validity and then adjusts the cluster number to output the final optimal cluster number. Two experiments with different types of image evince that FCSA not only finds the optimal number of clusters, but also consistently outperforms the traditional clustering algorithms, such as K-means and Fuzzy C-means. Hence, FCSA provides an effective option for performing the task of land cover classification.
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Rosing, K. E., and C. S. ReVelle. "Optimal Clustering." Environment and Planning A: Economy and Space 18, no. 11 (November 1986): 1463–76. http://dx.doi.org/10.1068/a181463.
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Cluster analysis can be performed with several models. One method is to seek those clusters for which the total flow between all within-cluster members is a maximum. This model has, until now, been viewed as mathematically difficult because of the presence of products of integer variables in the objective function. In another optimization model of cluster analysis, the p-median, a central member is found for each cluster, so that relationships of cluster members with the various central members are maximized (or minimized). This problem, although mathematically tractable, is a less realistic formulation of the general clustering problem. The formulation of the maximum interflow problem is here transformed in stages into a linear analogue which is economically solvable. Computation experience with the several transformed stages is reported and a practical example of the analysis demonstrated.
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Ren, Min, Peiyu Liu, Zhihao Wang, and Jing Yi. "A Self-Adaptive Fuzzyc-Means Algorithm for Determining the Optimal Number of Clusters." Computational Intelligence and Neuroscience 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/2647389.
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For the shortcoming of fuzzyc-means algorithm (FCM) needing to know the number of clusters in advance, this paper proposed a new self-adaptive method to determine the optimal number of clusters. Firstly, a density-based algorithm was put forward. The algorithm, according to the characteristics of the dataset, automatically determined the possible maximum number of clusters instead of using the empirical rulenand obtained the optimal initial cluster centroids, improving the limitation of FCM that randomly selected cluster centroids lead the convergence result to the local minimum. Secondly, this paper, by introducing a penalty function, proposed a new fuzzy clustering validity index based on fuzzy compactness and separation, which ensured that when the number of clusters verged on that of objects in the dataset, the value of clustering validity index did not monotonically decrease and was close to zero, so that the optimal number of clusters lost robustness and decision function. Then, based on these studies, a self-adaptive FCM algorithm was put forward to estimate the optimal number of clusters by the iterative trial-and-error process. At last, experiments were done on the UCI, KDD Cup 1999, and synthetic datasets, which showed that the method not only effectively determined the optimal number of clusters, but also reduced the iteration of FCM with the stable clustering result.
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Feng, Xue Bo, Fang Yao, Zhi Gang Li, and Xiao Jing Yang. "Improved Fuzzy C-Means Based on the Optimal Number of Clusters." Applied Mechanics and Materials 392 (September 2013): 803–7. http://dx.doi.org/10.4028/www.scientific.net/amm.392.803.
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According to the number of cluster centers, initial cluster centers, fuzzy factor, iterations and threshold, Fuzzy C-means clustering algorithm (FCM) clusters the data set. FCM will encounter the initialization problem of clustering prototype. Firstly, the article combines the maximum and minimum distance algorithm and K-means algorithm to determine the number of clusters and the initial cluster centers. Secondly, the article determines the optimal number of clusters with Silhouette indicators. Finally, the article improves the convergence rate of FCM by revising membership constantly. The improved FCM has good clustering effect, enhances the optimized capability, and improves the efficiency and effectiveness of the clustering. It has better tightness in the class, scatter among classes and cluster stability and faster convergence rate than the traditional FCM clustering method.
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Jollyta, Deny, Syahril Efendi, Muhammad Zarlis, and Herman Mawengkang. "Optimasi Cluster Pada Data Stunting: Teknik Evaluasi Cluster Sum of Square Error dan Davies Bouldin Index." Prosiding Seminar Nasional Riset Information Science (SENARIS) 1 (September 30, 2019): 918. http://dx.doi.org/10.30645/senaris.v1i0.100.
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The clusters number optimization problem is a problem that still requires continuous research so that the information produced can be a consideration. Cluster evaluation techniques with Sum of Square Error (SSE) and Davies Bouldin Index (DBI) are techniques that can evaluate the number of clusters from a data test. Research with these two techniques utilizes Stunting data from a number of regions in Indonesia. The result is information on stunting data which is formed from the optimal number of clusters where the largest SSE is formed at k = 5 and the smallest DBI is formed at k = 5, with values of 23.403 and 1,178 respectively. Changes in the number of clusters also influence the information produced and DBI is proven to produce optimal number of clusters that contain information with a better pattern because it has a small intra-cluster value. It is expected that the results of this study can show the performance of the two evaluation techniques in producing the optimal number of clusters so that grouping information is in accordance with the expected pattern.
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Danilova, Natalia V., and Daniil I. Zhitnikov. "Dichotomous Clustering Method аnd Optimal Portfolio." UNIVERSITY NEWS. NORTH-CAUCASIAN REGION. NATURAL SCIENCES SERIES, no. 2 (214) (June 30, 2022): 15–20. http://dx.doi.org/10.18522/1026-2237-2022-2-15-20.
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The problem of optimal portfolio finding is considered in the paper. Many papers are devoted to the solving of this problem in various its formulations, that is why the problem is relevant. For the solving of the problem the methods of robust optimization and machine learning are used, namely, the splitting of the sample of the random asset returns into clusters and subsequent construction of an ellipsoid in each cluster. The method of maximal likelihood is used for dividing on two clusters, the method of dichotomous clustering is used for dividing on several clusters. The sample average and the sample covariance matrix are used for the constructing of the ellipsoid; the radius is calculated based on the assumption that the sample elements have a normal distribution. The example of calculating the optimal portfolio is given. It uses the real values of the return vectors. In this case part of the sample is used to calculate the sample means and the sample covariance matrices of the clusters, the rest part of the sample is used for verification of the portfolio. The tables show the dependence of the optimal portfolio return on the model parameter and on the number of clusters (ellipsoids). The comparing of results is considered; there are cases in which there is an increase in the income of the investor.
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Jorio, Ali, Sanaa El Fkihi, Brahim Elbhiri, and Driss Aboutajdine. "An Energy-Efficient Clustering Routing Algorithm Based on Geographic Position and Residual Energy for Wireless Sensor Network." Journal of Computer Networks and Communications 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/170138.
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Recently wireless sensor network (WSN) has become one of the most interesting networking technologies, since it can be deployed without communication infrastructures. A sensor network is composed of a large number of sensor nodes; these nodes are responsible for supervision of the physical phenomenon and transmission of the periodical results to the base station. Therefore, improving the energy efficiency and maximizing the networking lifetime are the major challenges in this kind of networks. To deal with this, a hierarchical clustering scheme, called Location-Energy Spectral Cluster Algorithm (LESCA), is proposed in this paper. LESCA determines automatically the number of clusters in a network. It is based on spectral classification and considers both the residual energy and some properties of nodes. In fact, our approach uses theK-ways algorithm and proposes new features of the network nodes such as average energy, distance to BS, and distance to clusters centers in order to determine the clusters and to elect the cluster's heads of a WSN. The simulation results show that if the clusters are not constructed in an optimal way and/or the number of the clusters is greater or less than the optimal number of clusters, the total consumed energy of the sensor network per round is increased exponentially.
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Nenashev, Vadim A., Igor G. Khanykov, and Mikhail V. Kharinov. "A Model of Pixel and Superpixel Clustering for Object Detection." Journal of Imaging 8, no. 10 (October 6, 2022): 274. http://dx.doi.org/10.3390/jimaging8100274.
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The paper presents a model of structured objects in a grayscale or color image, described by means of optimal piecewise constant image approximations, which are characterized by the minimum possible approximation errors for a given number of pixel clusters, where the approximation error means the total squared error. An ambiguous image is described as a non-hierarchical structure but is represented as an ordered superposition of object hierarchies, each containing at least one optimal approximation in g0 = 1,2,..., etc., colors. For the selected hierarchy of pixel clusters, the objects-of-interest are detected as the pixel clusters of optimal approximations, or as their parts, or unions. The paper develops the known idea in cluster analysis of the joint application of Ward’s and K-means methods. At the same time, it is proposed to modernize each of these methods and supplement them with a third method of splitting/merging pixel clusters. This is useful for cluster analysis of big data described by a convex dependence of the optimal approximation error on the cluster number and also for adjustable object detection in digital image processing, using the optimal hierarchical pixel clustering, which is treated as an alternative to the modern informally defined “semantic” segmentation.
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Shaffer, Kris, Esther Vasiete, Brandon Jacquez, Aaron Davis, Diego Escalante, Calvin Hicks, Joshua McCann, Camille Noufi, and Paul Salminen. "A cluster analysis of harmony in the McGill Billboard dataset." Empirical Musicology Review 14, no. 3-4 (July 6, 2020): 146. http://dx.doi.org/10.18061/emr.v14i3-4.5576.
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We set out to perform a cluster analysis of harmonic structures (specifically, chord-to-chord transitions) in the McGill Billboard dataset, to determine whether there is evidence of multiple harmonic grammars and practices in the corpus, and if so, what the optimal division of songs, according to those harmonic grammars, is. We define optimal as providing meaningful, specific information about the harmonic practices of songs in the cluster, but being general enough to be used as a guide to songwriting and predictive listening. We test two hypotheses in our cluster analysis — first that 5–9 clusters would be optimal, based on the work of Walter Everett (2004), and second that 15 clusters would be optimal, based on a set of user-generated genre tags reported by Hendrik Schreiber (2015). We subjected the harmonic structures for each song in the corpus to a K-means cluster analysis. We conclude that the optimal clustering solution is likely to be within the 5–8 cluster range. We also propose that a map of cluster types emerging as the number of clusters increases from one to eight constitutes a greater aid to our understanding of how various harmonic practices, styles, and sub-styles comprise the McGill Billboard dataset.
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Karanikola, Aikaterini, Charalampos M. Liapis, and Sotiris Kotsiantis. "Investigating cluster validation metrics for optimal number of clusters determination." Intelligent Decision Technologies 15, no. 4 (January 10, 2022): 809–24. http://dx.doi.org/10.3233/idt-210187.
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In short, clustering is the process of partitioning a given set of objects into groups containing highly related instances. This relation is determined by a specific distance metric with which the intra-cluster similarity is estimated. Finding an optimal number of such partitions is usually the key step in the entire process, yet a rather difficult one. Selecting an unsuitable number of clusters might lead to incorrect conclusions and, consequently, to wrong decisions: the term “optimal” is quite ambiguous. Furthermore, various inherent characteristics of the datasets, such as clusters that overlap or clusters containing subclusters, will most often increase the level of difficulty of the task. Thus, the methods used to detect similarities and the parameter selection of the partition algorithm have a major impact on the quality of the groups and the identification of their optimal number. Given that each dataset constitutes a rather distinct case, validity indices are indicators introduced to address the problem of selecting such an optimal number of clusters. In this work, an extensive set of well-known validity indices, based on the approach of the so-called relative criteria, are examined comparatively. A total of 26 cluster validation measures were investigated in two distinct case studies: one in real-world and one in artificially generated data. To ensure a certain degree of difficulty, both real-world and generated data were selected to exhibit variations and inhomogeneity. Each of the indices is being deployed under the schemes of 9 different clustering methods, which incorporate 5 different distance metrics. All results are presented in various explanatory forms.
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Chen, Min, and Simone A. Ludwig. "Particle Swarm Optimization Based Fuzzy Clustering Approach to Identify Optimal Number of Clusters." Journal of Artificial Intelligence and Soft Computing Research 4, no. 1 (January 1, 2014): 43–56. http://dx.doi.org/10.2478/jaiscr-2014-0024.
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Abstract Fuzzy clustering is a popular unsupervised learning method that is used in cluster analysis. Fuzzy clustering allows a data point to belong to two or more clusters. Fuzzy c-means is the most well-known method that is applied to cluster analysis, however, the shortcoming is that the number of clusters need to be predefined. This paper proposes a clustering approach based on Particle Swarm Optimization (PSO). This PSO approach determines the optimal number of clusters automatically with the help of a threshold vector. The algorithm first randomly partitions the data set within a preset number of clusters, and then uses a reconstruction criterion to evaluate the performance of the clustering results. The experiments conducted demonstrate that the proposed algorithm automatically finds the optimal number of clusters. Furthermore, to visualize the results principal component analysis projection, conventional Sammon mapping, and fuzzy Sammon mapping were used
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Khalifeh, Ala’, Husam Abid, and Khalid A. Darabkh. "Optimal Cluster Head Positioning Algorithm for Wireless Sensor Networks." Sensors 20, no. 13 (July 3, 2020): 3719. http://dx.doi.org/10.3390/s20133719.
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Wireless sensor networks (WSNs) are increasingly gaining popularity, especially with the advent of many artificial intelligence (AI) driven applications and expert systems. Such applications require specific relevant sensors’ data to be stored, processed, analyzed, and input to the expert systems. Obviously, sensor nodes (SNs) have limited energy and computation capabilities and are normally deployed remotely over an area of interest (AoI). Therefore, proposing efficient protocols for sensing and sending data is paramount to WSNs operation. Nodes’ clustering is a widely used technique in WSNs, where the sensor nodes are grouped into clusters. Each cluster has a cluster head (CH) that is used to gather captured data of sensor nodes and forward it to a remote sink node for further processing and decision-making. In this paper, an optimization algorithm for adjusting the CH location with respect to the nodes within the cluster is proposed. This algorithm aims at finding the optimal CH location that minimizes the total sum of the nodes’ path-loss incurred within the intra-cluster communication links between the sensor nodes and the CH. Once the optimal CH is identified, the CH moves to the optimal location. This suggestion of CH re-positioning is frequently repeated for new geometric position. Excitingly, the algorithm is extended to consider the inter-cluster communication between CH nodes belonging to different clusters and distributed over a spiral trajectory. These CH nodes form a multi-hop communication link that convey the captured data of the clusters’ nodes to the sink destination node. The performance of the proposed CH positioning algorithm for the single and multi-clusters has been evaluated and compared with other related studies. The results showed the effectiveness of the proposed CH positioning algorithm.
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Jollyta, Deny, Syahril Efendi, Muhammad Zarlis, and Herman Mawengkang. "Analysis of an optimal cluster approach: a review paper." Journal of Physics: Conference Series 2421, no. 1 (January 1, 2023): 012015. http://dx.doi.org/10.1088/1742-6596/2421/1/012015.
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Abstract Determining the optimal clusters can be regarded as a grouping problem that has produced many cluster approach methods in various studies. Each method has provisions that can solve one or more grouping problems in generating information from data set with a number of k being tested. The advantages and disadvantages of each method actually complement to each other in solving the grouping problems. This paper aims to describe the performance of cluster approach methods in determining the optimal clusters through a review by paying attention to the criteria of the problem which is an obstacle to the grouping problem. The results of this review are expected to be a reference for developing the new optimal cluster approach method through possible combinatorial optimization.
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Avrorin, A. D., A. V. Avrorin, V. M. Aynutdinov, R. Bannash, I. A. Belolaptikov, V. B. Brudanin, N. M. Budnev, et al. "Time calibration of the neutrino telescope Baikal-GVD." EPJ Web of Conferences 207 (2019): 07003. http://dx.doi.org/10.1051/epjconf/201920707003.
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Baikal-GVD is a cubic-kilometer scale neutrino telescope, which is currently under construction in Lake Baikal. Baikal-GVD is an array of optical modules arranged in clusters. The first cluster of the array has been deployed and commissioned in April 2015. To date, Baikal-GVD consists of 3 clusters with 864 optical modules. One of the vital conditions for optimal energy, position and direction reconstruction of the detected particles is the time calibration of the detector. In this article, we describe calibration equipment and methods used in Baikal-GVD and demonstrate the accuracy of the calibration procedures.
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Sambaturu, Prathyush, Aparna Gupta, Ian Davidson, S. S. Ravi, Anil Vullikanti, and Andrew Warren. "Efficient Algorithms for Generating Provably Near-Optimal Cluster Descriptors for Explainability." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 02 (April 3, 2020): 1636–43. http://dx.doi.org/10.1609/aaai.v34i02.5525.
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Improving the explainability of the results from machine learning methods has become an important research goal. Here, we study the problem of making clusters more interpretable by extending a recent approach of [Davidson et al., NeurIPS 2018] for constructing succinct representations for clusters. Given a set of objects S, a partition π of S (into clusters), and a universe T of tags such that each element in S is associated with a subset of tags, the goal is to find a representative set of tags for each cluster such that those sets are pairwise-disjoint and the total size of all the representatives is minimized. Since this problem is NP-hard in general, we develop approximation algorithms with provable performance guarantees for the problem. We also show applications to explain clusters from datasets, including clusters of genomic sequences that represent different threat levels.
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Zhang, Dawei, Fuding Xie, Dapeng Wang, Yong Zhang, and Yan Sun. "Cluster Analysis Based on Bipartite Network." Mathematical Problems in Engineering 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/676427.
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Clustering data has a wide range of applications and has attracted considerable attention in data mining and artificial intelligence. However it is difficult to find a set of clusters that best fits natural partitions without any class information. In this paper, a method for detecting the optimal cluster number is proposed. The optimal cluster number can be obtained by the proposal, while partitioning the data into clusters by FCM (Fuzzyc-means) algorithm. It overcomes the drawback of FCM algorithm which needs to define the cluster numbercin advance. The method works by converting the fuzzy cluster result into a weighted bipartite network and then the optimal cluster number can be detected by the improved bipartite modularity. The experimental results on artificial and real data sets show the validity of the proposed method.
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Asrriningtias, Salnan Ratih. "Cluster Validity Index to Determine the Optimal Number Clusters of Fuzzy Clustering for Classify Customer Buying Behavior." Journal of Development Research 5, no. 1 (May 31, 2021): 7–12. http://dx.doi.org/10.28926/jdr.v5i1.134.
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One of the strategies in order to compete in Batik MSMEs is to look at the characteristics of the customer. To make it easier to see the characteristics of customer buying behavior, it is necessary to classify customers based on similarity of characteristics using fuzzy clustering. One of the parameters that must be determined at the beginning of the fuzzy clustering method is the number of clusters. Increasing the number of clusters does not guarantee the best performance, but the right number of clusters greatly affects the performance of fuzzy clustering. So to get optimal number cluster, we can measured the result of clustering in each number cluster using the cluster validity index. From several types of cluster validity index, NPC give the best value. Optimal number cluster that obtained by the validity index is 2 and this number cluster give classify result with small variance value
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Martino, Ferdinando Di, and Salvatore Sessa. "A New Validity Index Based on Fuzzy Energy and Fuzzy Entropy Measures in Fuzzy Clustering Problems." Entropy 22, no. 11 (October 23, 2020): 1200. http://dx.doi.org/10.3390/e22111200.
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Two well-known drawbacks in fuzzy clustering are the requirement of assigning in advance the number of clusters and random initialization of cluster centers. The quality of the final fuzzy clusters depends heavily on the initial choice of the number of clusters and the initialization of the clusters, then, it is necessary to apply a validity index to measure the compactness and the separability of the final clusters and run the clustering algorithm several times. We propose a new fuzzy C-means algorithm in which a validity index based on the concepts of maximum fuzzy energy and minimum fuzzy entropy is applied to initialize the cluster centers and to find the optimal number of clusters and initial cluster centers in order to obtain a good clustering quality, without increasing time consumption. We test our algorithm on UCI (University of California at Irvine) machine learning classification datasets comparing the results with the ones obtained by using well-known validity indices and variations of fuzzy C-means by using optimization algorithms in the initialization phase. The comparison results show that our algorithm represents an optimal trade-off between the quality of clustering and the time consumption.
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Yan, Yonghang, Xuewen Xia, Lingli Zhang, Zhijia Li, and Chunbin Qin. "A Clustering Scheme Based on the Binary Whale Optimization Algorithm in FANET." Entropy 24, no. 10 (September 27, 2022): 1366. http://dx.doi.org/10.3390/e24101366.
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With the continuous development of Unmanned Aerial Vehicle (UAV) technology, UAVs are widely used in military and civilian fields. Multi-UAV networks are often referred to as flying ad hoc networks (FANET). Dividing multiple UAVs into clusters for management can reduce energy consumption, maximize network lifetime, and enhance network scalability to a certain extent, so UAV clustering is an important direction for UAV network applications. However, UAVs have the characteristics of limited energy resources and high mobility, which bring challenges to UAV cluster communication networking. Therefore, this paper proposes a clustering scheme for UAV clusters based on the binary whale optimization (BWOA) algorithm. First, the optimal number of clusters in the network is calculated based on the network bandwidth and node coverage constraints. Then, the cluster heads are selected based on the optimal number of clusters using the BWOA algorithm, and the clusters are divided based on the distance. Finally, the cluster maintenance strategy is set to achieve efficient maintenance of clusters. The experimental simulation results show that the scheme has better performance in terms of energy consumption and network lifetime compared with the BPSO and K-means-based schemes.
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Popkov, Yuri S., Yuri A. Dubnov, and Alexey Yu Popkov. "Entropy-Randomized Clustering." Mathematics 10, no. 19 (October 10, 2022): 3710. http://dx.doi.org/10.3390/math10193710.
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This paper proposes a clustering method based on a randomized representation of an ensemble of possible clusters with a probability distribution. The concept of a cluster indicator is introduced as the average distance between the objects included in the cluster. The indicators averaged over the entire ensemble are considered the latter’s characteristics. The optimal distribution of clusters is determined using the randomized machine learning approach: an entropy functional is maximized with respect to the probability distribution subject to constraints imposed on the averaged indicator of the cluster ensemble. The resulting entropy-optimal cluster corresponds to the maximum of the optimal probability distribution. This method is developed for binary clustering as a basic procedure. Its extension to t-ary clustering is considered. Some illustrative examples of entropy-randomized clustering are given.
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Joshi, Upasna, and Rajiv Sharma. "An optimal data aggregation technique for physics-based applications." Modern Physics Letters B 32, no. 25 (September 5, 2018): 1850297. http://dx.doi.org/10.1142/s0217984918502974.
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In wireless sensor network (WSN), most of the devices function on batteries. These nodes or devices have inadequate amount of initial energy which are consumed at diverse rates, based on the power level and intended receiver. In sleep scheduling algorithms, most of the sensor nodes are turned to sleep state to preserve energy and improve the network lifetime (NL). In this paper, an energy-efficient dynamic cluster-based protocol is proposed for WSN especially for physics-based applications. Initially, the network is divided into small clusters using adaptive clustering. The clusters are managed by the cluster heads. The cluster heads are elected based on the novel dynamic threshold. Afterwards, general variable neighborhood search is used to obtain the energy-efficient paths for inter-cluster data aggregation which is used to communicate with the sink. The performance of the proposed method is compared with competitive energy-efficient routing protocols in terms of various factors such as stable period, NL, packets sent to base station and packets sent to cluster head. Extensive experiments prove that the proposed protocol provides higher NL than the existing protocols.
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Carrillo-Larco, Rodrigo M., Manuel Castillo-Cara, Cecilia Anza-Ramirez, and Antonio Bernabé-Ortiz. "Clusters of people with type 2 diabetes in the general population: unsupervised machine learning approach using national surveys in Latin America and the Caribbean." BMJ Open Diabetes Research & Care 9, no. 1 (January 2021): e001889. http://dx.doi.org/10.1136/bmjdrc-2020-001889.
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IntroductionWe aimed to identify clusters of people with type 2 diabetes mellitus (T2DM) and to assess whether the frequency of these clusters was consistent across selected countries in Latin America and the Caribbean (LAC).Research design and methodsWe analyzed 13 population-based national surveys in nine countries (n=8361). We used k-means to develop a clustering model; predictors were age, sex, body mass index (BMI), waist circumference (WC), systolic/diastolic blood pressure (SBP/DBP), and T2DM family history. The training data set included all surveys, and the clusters were then predicted in each country-year data set. We used Euclidean distance, elbow and silhouette plots to select the optimal number of clusters and described each cluster according to the underlying predictors (mean and proportions).ResultsThe optimal number of clusters was 4. Cluster 0 grouped more men and those with the highest mean SBP/DBP. Cluster 1 had the highest mean BMI and WC, as well as the largest proportion of T2DM family history. We observed the smallest values of all predictors in cluster 2. Cluster 3 had the highest mean age. When we reflected the four clusters in each country-year data set, a different distribution was observed. For example, cluster 3 was the most frequent in the training data set, and so it was in 7 out of 13 other country-year data sets.ConclusionsUsing unsupervised machine learning algorithms, it was possible to cluster people with T2DM from the general population in LAC; clusters showed unique profiles that could be used to identify the underlying characteristics of the T2DM population in LAC.
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Hartke, Bernd. "Methane-water clusters under pressure: Are clathrate cages optimal clusters?" Journal of Chemical Physics 130, no. 2 (January 14, 2009): 024905. http://dx.doi.org/10.1063/1.3058479.
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Viattchenin, Dmitri A. "Heuristic possibilistic clustering for detecting optimal number of elements in fuzzy clusters." Foundations of Computing and Decision Sciences 41, no. 1 (March 1, 2016): 45–76. http://dx.doi.org/10.1515/fcds-2016-0003.
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AbstractThe paper deals with the problem of discovering fuzzy clusters with optimal number of elements in heuristic possibilistic clustering. The relational clustering procedure using a parameter that controls cluster sizes is considered and a technique for detecting the optimal number of elements in fuzzy clusters is proposed. The effectiveness of the proposed technique is illustrated through numerical examples. Experimental results are discussed and some preliminary conclusions are formulated.
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Chikumbo, Oliver, and Vincent Granville. "Optimal Clustering and Cluster Identity in Understanding High-Dimensional Data Spaces with Tightly Distributed Points." Machine Learning and Knowledge Extraction 1, no. 2 (June 5, 2019): 715–44. http://dx.doi.org/10.3390/make1020042.
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The sensitivity of the elbow rule in determining an optimal number of clusters in high-dimensional spaces that are characterized by tightly distributed data points is demonstrated. The high-dimensional data samples are not artificially generated, but they are taken from a real world evolutionary many-objective optimization. They comprise of Pareto fronts from the last 10 generations of an evolutionary optimization computation with 14 objective functions. The choice for analyzing Pareto fronts is strategic, as it is squarely intended to benefit the user who only needs one solution to implement from the Pareto set, and therefore a systematic means of reducing the cardinality of solutions is imperative. As such, clustering the data and identifying the cluster from which to pick the desired solution is covered in this manuscript, highlighting the implementation of the elbow rule and the use of hyper-radial distances for cluster identity. The Calinski-Harabasz statistic was favored for determining the criteria used in the elbow rule because of its robustness. The statistic takes into account the variance within clusters and also the variance between the clusters. This exercise also opened an opportunity to revisit the justification of using the highest Calinski-Harabasz criterion for determining the optimal number of clusters for multivariate data. The elbow rule predicted the maximum end of the optimal number of clusters, and the highest Calinski-Harabasz criterion method favored the number of clusters at the lower end. Both results are used in a unique way for understanding high-dimensional data, despite being inconclusive regarding which of the two methods determine the true optimal number of clusters.
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Mallik, Saurav, and Zhongming Zhao. "Multi-Objective Optimized Fuzzy Clustering for Detecting Cell Clusters from Single-Cell Expression Profiles." Genes 10, no. 8 (August 13, 2019): 611. http://dx.doi.org/10.3390/genes10080611.
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Rapid advance in single-cell RNA sequencing (scRNA-seq) allows measurement of the expression of genes at single-cell resolution in complex disease or tissue. While many methods have been developed to detect cell clusters from the scRNA-seq data, this task currently remains a main challenge. We proposed a multi-objective optimization-based fuzzy clustering approach for detecting cell clusters from scRNA-seq data. First, we conducted initial filtering and SCnorm normalization. We considered various case studies by selecting different cluster numbers ( c l = 2 to a user-defined number), and applied fuzzy c-means clustering algorithm individually. From each case, we evaluated the scores of four cluster validity index measures, Partition Entropy ( P E ), Partition Coefficient ( P C ), Modified Partition Coefficient ( M P C ), and Fuzzy Silhouette Index ( F S I ). Next, we set the first measure as minimization objective (↓) and the remaining three as maximization objectives (↑), and then applied a multi-objective decision-making technique, TOPSIS, to identify the best optimal solution. The best optimal solution (case study) that had the highest TOPSIS score was selected as the final optimal clustering. Finally, we obtained differentially expressed genes (DEGs) using Limma through the comparison of expression of the samples between each resultant cluster and the remaining clusters. We applied our approach to a scRNA-seq dataset for the rare intestinal cell type in mice [GEO ID: GSE62270, 23,630 features (genes) and 288 cells]. The optimal cluster result (TOPSIS optimal score= 0.858) comprised two clusters, one with 115 cells and the other 91 cells. The evaluated scores of the four cluster validity indices, F S I , P E , P C , and M P C for the optimized fuzzy clustering were 0.482, 0.578, 0.607, and 0.215, respectively. The Limma analysis identified 1240 DEGs (cluster 1 vs. cluster 2). The top ten gene markers were Rps21, Slc5a1, Crip1, Rpl15, Rpl3, Rpl27a, Khk, Rps3a1, Aldob and Rps17. In this list, Khk (encoding ketohexokinase) is a novel marker for the rare intestinal cell type. In summary, this method is useful to detect cell clusters from scRNA-seq data.
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Hung, Shih-Lin, Ching-Yun Kao, and Jyun-Wei Huang. "Constrained K-means and Genetic Algorithm-based Approaches for Optimal Placement of Wireless Structural Health Monitoring Sensors." Civil Engineering Journal 8, no. 12 (December 1, 2022): 2675–92. http://dx.doi.org/10.28991/cej-2022-08-12-01.
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Optimal placement of wireless structural health monitoring (SHM) sensors has to consider modal identification accuracy and power efficiency. In this study, two-tier wireless sensor network (WSN)-based SHM systems with clusters of sensors are investigated to overcome this difficulty. Each cluster contains a number of sensor nodes and a cluster head (CH). The lower tier is composed of sensors communicating with their associated CHs, and the upper tier is composed of the network of CHs. The first step is the optimal placement of sensors in the lower tier via the effective independence method by considering the modal identification accuracy. The second step is the optimal placement of CHs in the upper tier by considering power efficiency. The sensors in the lower tier are partitioned into clusters before determining the optimal locations of CHs in the upper tier. Two approaches, a constrained K-means clustering approach and a genetic algorithm (GA)-based clustering approach, are proposed in this study to cluster sensors in the lower tier by considering two constraints: (1) the maximum data transmission distance of each sensor; (2) the maximum number of sensors in each cluster. Given that each CH can only manage a limited number of sensors, these constraints should be considered in practice to avoid overload of CHs. The CHs in the upper tier are located at the centers of the clusters determined after clustering sensors in the lower tier. The two proposed approaches aim to construct a balanced size of clusters by minimizing the number of clusters (or CHs) and the total sum of the squared distance between each sensor and its associated CH under the two constraints. Accordingly, the energy consumption in each cluster is decreased and balanced, and the network lifetime is extended. A numerical example is studied to demonstrate the feasibility of using the two proposed clustering approaches for sensor clustering in WSN-based SHM systems. In this example, the performances of the two proposed clustering approaches and the K-means clustering method are also compared. The two proposed clustering approaches outperform the K-means clustering method in terms of constructing balanced size of clusters for a small number of clusters. Doi: 10.28991/CEJ-2022-08-12-01 Full Text: PDF
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Huang, Hsu-Yao, Lung-Chieh Lin, Ming-Tsun Ke, Tamilarasan Sathesh, and Wen-Shing Lee. "Energy performance evaluation for benchmarking school buildings using dynamic clustering analysis and particle swarm optimization." Building Services Engineering Research and Technology 41, no. 4 (October 1, 2019): 429–40. http://dx.doi.org/10.1177/0143624419879001.
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Benchmarking the energy performance of buildings has received increasing attention as striving for energy efficiency through more effective energy management has become a major concern of governments. Various methods for classifying building energy performance have been developed, and the clustering technique is considered one of the best approaches. This paper proposes a method utilizing dynamic clustering to analyze the electricity consumption patterns of buildings to decide the optimal cluster number and allocate the buildings to corresponding clusters for energy benchmarking. For the evaluation of number of clusters, this article has employed the inter–intra clustering method with particle swarm optimization algorithm. The electricity consumption data were collected through an energy survey performed in 30 junior high schools in Taipei, Taiwan. In a traditional method, the 30 schools would be grouped into one same cluster and the energy benchmarking report an average value of 541.4 kWh/year per student. The proposed method that took different electricity consumption patterns of the schools into consideration produced more detailed results as follows: the optimal cluster number was 3 with an inter–intra index value of 0.708, and the energy benchmarking index of these three clusters read, respectively, 362, 512, and 851 kWh/year per student. Practical application: The study proposed an innovative dynamic clustering technique to decide the optimal cluster number and allocate the assessed buildings. The results showed that compared to a traditional approach that tended to group assessed buildings into one cluster, the proposed method was able to classify the buildings into three clusters for further benchmarking. This method can be used by governments and large corporations. For example, in Hong Kong, primary schools are grouped into one cluster for energy benchmarking. Using the proposed method can further classify primary schools into more clusters; benchmarking index can then be developed for each cluster.
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Mohammed, Athraa Jasim, Yuhanis Yusof, and za Husni. "Discovering optimal clusters using firefly algorithm." International Journal of Data Mining, Modelling and Management 8, no. 4 (2016): 330. http://dx.doi.org/10.1504/ijdmmm.2016.081239.
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Husni, Husniza, Athraa Jasim Mohammed, and Yuhanis Yusof. "Discovering optimal clusters using firefly algorithm." International Journal of Data Mining, Modelling and Management 8, no. 4 (2016): 330. http://dx.doi.org/10.1504/ijdmmm.2016.10002309.
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Gandhi, Anshul, Naman Mittal, and Xi Zhang. "Optimal Load-Balancing for Heterogeneous Clusters." ACM SIGMETRICS Performance Evaluation Review 43, no. 3 (November 19, 2015): 43. http://dx.doi.org/10.1145/2847220.2847232.
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Jung, P., and J. W. Shuai. "Optimal sizes of ion channel clusters." Europhysics Letters (EPL) 56, no. 1 (October 2001): 29–35. http://dx.doi.org/10.1209/epl/i2001-00483-y.
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Hansen, M. N. "Optimal Number of Clusters per Milker." Journal of Agricultural Engineering Research 72, no. 4 (April 1999): 341–46. http://dx.doi.org/10.1006/jaer.1998.0377.
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Damaschke, Peter. "Sufficient conditions for edit-optimal clusters." Information Processing Letters 116, no. 4 (April 2016): 267–72. http://dx.doi.org/10.1016/j.ipl.2015.12.004.
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Virgantari, Fitria, and Yasmin Erika Faridhan. "K-Means Clustering of COVID-19 Cases in Indonesia’s Provinces." ADRI International Journal of Engineering and Natural Science 5, no. 2 (October 30, 2020): 34–39. http://dx.doi.org/10.29138/aijens.v5i2.15.
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The novel coronavirus disease (COVID-19) has been rapidly spreading, causing a severe health crisis all around the world, including Indonesia. As expected, due to Indonesia’s diverse topography and population, there are variations in the number of cases amongst its provinces. Therefore clustering is needed to develop a map of COVID-19 cases to enable optimal handling of this pandemic. The provinces are clustered using K-means method according to their respective COVID-19 case numbers. Data taken from Indonesian Ministry of Health in November 2020 is used in this study, covering COVID-19 cases in Indonesia’s 34 provinces. K-means results in seven optimal clusters with variance ratio of 0.185. Clusters 1 to 3 cover most provinces in Java, including DKI Jakarta in Cluster 1 as the province with the most cases. Each of Clusters 4 and 5 consists of 5 provinces, while each of Clusters 6 and 7 consists of 10 provinces. Cluster 7 comprises provinces with lowest cases of COVID-19.
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Banerjee, Amit. "Multi-Objective Genetic Algorithm for Robust Clustering with Unknown Number of Clusters." International Journal of Applied Evolutionary Computation 3, no. 1 (January 2012): 1–20. http://dx.doi.org/10.4018/jaec.2012010101.
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In this paper, a multi-objective genetic algorithm for data clustering based on the robust fuzzy least trimmed squares estimator is presented. The proposed clustering methodology addresses two critical issues in unsupervised data clustering – the ability to produce meaningful partition in noisy data, and the requirement that the number of clusters be known a priori. The multi-objective genetic algorithm-driven clustering technique optimizes the number of clusters as well as cluster assignment, and cluster prototypes. A two-parameter, mapped, fixed point coding scheme is used to represent assignment of data into the true retained set and the noisy trimmed set, and the optimal number of clusters in the retained set. A three-objective criterion is also used as the minimization functional for the multi-objective genetic algorithm. Results on well-known data sets from literature suggest that the proposed methodology is superior to conventional fuzzy clustering algorithms that assume a known value for optimal number of clusters.
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Arif, Besya Salsabilla Azani, Agus Rusgiyono, and Abdul Hoyyi. "PENGELOMPOKAN PROVINSI-PROVINSI DI INDONESIA MENGGUNAKAN METODE WARD (StudiKasus: Produksi Tanaman Pangan di Indonesia Tahun 2018)." Jurnal Gaussian 9, no. 1 (February 28, 2020): 112–21. http://dx.doi.org/10.14710/j.gauss.v9i1.27528.
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Cluster analysis is a technique for grouping objects or observations into homogeneous groups. Cluster analysis is divided into two methods, namely hierarchy and non-hierarchy. The hierarchy method generally involves a series of n-1 decisions (n is the number of observations) that combine observations into a tree-like structure or dendogram. Hierarchy is divided into two methods, namely agglomerative (concentration) and splitting (distribution). For non-hierarchical methods, the number of clusters can be determined by the researcher. Ward method is a hierarchical cluster analysis method that can maximize homogeneity in the cluster. The Sum-of-Square (SSE) formula is used in this method to minimize variations in the clusters that are formed. In this research, squared euclid distance is used to measure the similarity between object pairs. The data used in this study are secondary data on food crop production, namely rice, corn, soybeans, peanuts, green beans, sweet potatoes, and cassava in Indonesia 2018. To determine the cluster, the elbow method is used to form optimal clusters using WSS formula. Based on the analysis results, it was found that the optimal cluster is four clusters. The first cluster consists of 9 Province, the second cluster consists of 20 Province, the third cluster consists of 1 Province, the fourth cluster consists of 2 Province, and the fifth cluster consists of 2 Province.Keywords: Food Crop, Cluster Analysis, Ward Method, Squared Euclid, Elbow Method
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Abdellahoum, Hamza, and Abdelmajid Boukra. "A Fuzzy Cooperative Approach to Resolve the Image Segmentation Problem." International Journal of Swarm Intelligence Research 12, no. 3 (July 2021): 188–214. http://dx.doi.org/10.4018/ijsir.2021070109.
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The image segmentation problem is one of the most studied problems because it helps in several areas. In this paper, the authors propose new algorithms to resolve two problems, namely cluster detection and centers initialization. The authors opt to use statistical methods to automatically determine the number of clusters and the fuzzy sets theory to start the algorithm with a near optimal configuration. They use the image histogram information to determine the number of clusters and a cooperative approach involving three metaheuristics, genetic algorithm (GA), firefly algorithm (FA). and biogeography-based optimization algorithm (BBO), to detect the clusters centers in the initialization step. The experimental study shows that, first, the proposed solution determines a near optimal initial clusters centers set leading to good image segmentation compared to well-known methods; second, the number of clusters determined automatically by the proposed approach contributes to improve the image segmentation quality.
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Malikhatin, Hanik, Agus Rusgiyono, and Di Asih I. Maruddani. "PENERAPAN k-MODES CLUSTERING DENGAN VALIDASI DUNN INDEX PADA PENGELOMPOKAN KARAKTERISTIK CALON TKI MENGGUNAKAN R-GUI." Jurnal Gaussian 10, no. 3 (December 30, 2021): 359–66. http://dx.doi.org/10.14710/j.gauss.v10i3.32790.
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Prospective TKI workers who apply for passports at the Immigration Office Class I Non TPI Pati have countries destinations and choose different PPTKIS agencies. Therefore, the grouping of characteristics prospective TKI needed so that can be used as a reference for the government in an effort to improve the protection of TKI in destination countries and carry out stricter supervision of PPTKIS who manage TKI. The purpose of this research is to classify the characteristics of prospective TKI workers with the optimal number of clusters. The method used is k-Modes Clustering with values of k = 2, 3, 4, and 5. This method can agglomerate categorical data. The optimal number of clusters can be determined using the Dunn Index. For grouping data easily, then compiled a Graphical User Interface (GUI) based application with RStudio. Based on the analysis, the optimal number of clusters is two clusters with a Dunn Index value of 0,4. Cluster 1 consists of mostly male TKI workers (51,04%), aged ≥ 20 years old (91,93%), with the destination Malaysia country (47%), and choosing PPTKIS Surya Jaya Utama Abadi (37,51%), while cluster 2, mostly of male TKI workers (94,10%), aged ≥ 20 years old (82,31%), with the destination Korea Selatan country (77,95%), and choosing PPTKIS BNP2TKI (99,78%).
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Rasid Mamat, Abd, Fatma Susilawati Mohamed, Mohamad Afendee Mohamed, Norkhairani Mohd Rawi, and Mohd Isa Awang. "Silhouette index for determining optimal k-means clustering on images in different color models." International Journal of Engineering & Technology 7, no. 2.14 (April 6, 2018): 105. http://dx.doi.org/10.14419/ijet.v7i2.14.11464.
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Clustering process is an essential part of the image processing. Its aim to group the data according to having the same attributes or similarities of the images. Consequently, determining the number of the optimum clusters or the best (well-clustered) for the image in different color models is very crucial. This is because the cluster validation is fundamental in the process of clustering and it reflects the split between clusters. In this study, the k-means algorithm was used on three colors model: CIE Lab, RGB and HSV and the clustering process made up to k clusters. Next, the Silhouette Index (SI) is used to the cluster validation process, and this value is range between 0 to 1 and the greater value of SI illustrates the best of cluster separation. The results from several experiments show that the best cluster separation occurs when k=2 and the value of average SI is inversely proportional to the number of k cluster for all color model. The result shows in HSV color model the average SI decreased 14.11% from k = 2 to k = 8, 11.1% in HSV color model and 16.7% in CIE Lab color model. Comparisons are also made for the three color models and generally the best cluster separation is found within HSV, followed by the RGB and CIE Lab color models.
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Jensen, Grant J., and Roger D. Kornberg. "Single-particle selection and alignment with heavy atom cluster-antibody conjugates." Proceedings of the National Academy of Sciences 95, no. 16 (August 4, 1998): 9262–67. http://dx.doi.org/10.1073/pnas.95.16.9262.
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A method is proposed for selecting and aligning images of single biological particles to obtain high-resolution structural information by cryoelectron microscopy. The particles will be labeled with multiple heavy atom clusters to permit the precise determination of particle locations and relative orientations even when imaged close to focus with a low electron dose, conditions optimal for recording high-resolution detail. Heavy atom clusters should also allow selection of images free from many kinds of defects, including specimen movement and particle inhomogeneity. Heavy atom clusters may be introduced in a general way by the construction of “adaptor” molecules based on single-chain Fv antibody fragments, consisting of a constant framework region engineered for optimal cluster binding and a variable antigen binding region selected for a specific target. The success of the method depends on the mobility of the heavy atom cluster on the particle, on the precision to which clusters can be located in an image, and on the sufficiency of cluster projections alone to orient and select particles for averaging. The necessary computational algorithms were developed and implemented in simulations that address the feasibility of the method.
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Dai, Liang, Yilin Chang, and Zhong Shen. "An Optimal Task Scheduling Algorithm in Wireless Sensor Networks." International Journal of Computers Communications & Control 6, no. 1 (March 1, 2011): 101. http://dx.doi.org/10.15837/ijccc.2011.1.2205.
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Sensing tasks should be allocated and processed among sensor nodes in minimum times so that users can draw useful conclusions through analyzing sensed data. Furthermore, finishing sensing task faster will benefit energy saving, which is critical in system design of wireless sensor networks. To minimize the execution time (makespan) of a given task, an optimal task scheduling algorithm (OTSA-WSN) in a clustered wireless sensor network is proposed based on divisible load theory. The algorithm consists of two phases: intra-cluster task scheduling and inter-cluster task scheduling. Intra-cluster task scheduling deals with allocating different fractions of sensing tasks among sensor nodes in each cluster; inter-cluster task scheduling involves the assignment of sensing tasks among all clusters in multiple rounds to improve overlap of communication with computation. OTSA-WSN builds from eliminating transmission collisions and idle gaps between two successive data transmissions. By removing performance degradation caused by communication interference and idle, the reduced finish time and improved network resource utilization can be achieved. With the proposed algorithm, the optimal number of rounds and the most reasonable load allocation ratio on each node could be derived. Finally, simulation results are presented to demonstrate the impacts of different network parameters such as the number of clusters, computation/communication latency, and measurement/communication speed, on the number of rounds, makespan and energy consumption.
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Wahdan, Hayam G., Hisham M. Abdelslam, and Sally S. Kassem. "An Efficient Optimization Algorithm for Modular Product Design." Journal Européen des Systèmes Automatisés 54, no. 2 (April 27, 2021): 195–207. http://dx.doi.org/10.18280/jesa.540201.
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Modularity concepts play an important role in the process of developing new complex products. Modularization involves dividing a product into a set of modules - each of which consisting of a set of components - that are interdependent in the same cluster and independent between clusters. During this process, a product can be represented using a Design Structure Matrix (DSM). A DSM acts as a tool for system analysis to provide clear visualization of product elements. In addition, DSM, shows the interactions between these product elements. This paper aims to propose an efficient optimization algorithm that dynamically divides a DSM into an optimal number and size of clusters in a way that minimizes total coordination cost; the interactions inside clusters (modules) and interactions between clusters. Given problem complexity, five metaheuristic optimization algorithms are proposed and tested to solve it; these algorithms are used to determine: (1) the optimal clusters’ number within a DSM, and (2) the optimal components assignment clusters to minimize the total coordination cost. The five used metaheuristics are: Cuckoo Search, Modified Cuckoo Search, Particle Swarm Optimization, Simulated Annealing, and Gravitational Search Algorithm. Eighty problems with different properties are generated and used to examine the proposed algorithms for effectiveness and efficiency. Extensive comparisons are conducted and analyzed. Cuckoo Search is outperforming the other four algorithms.
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Abidi, Balkis, and Sadok Ben Yahia. "A New Algorithm for Fuzzy Clustering Handling Incomplete Dataset." International Journal on Artificial Intelligence Tools 23, no. 04 (August 2014): 1460012. http://dx.doi.org/10.1142/s0218213014600124.
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One of the most difficult problems in cluster analysis is the identification of the number of groups in a dataset especially in the presence of missing value. Since traditional clustering methods assumed the real number of clusters to be known. However, in real world applications the number of clusters is generally not known a priori. Also, most of clustering methods were developed to analyse complete datasets, they cannot be applied to many practical problems, e.g., on incomplete data. This paper focuses, first, on an algorithm of a fuzzy clustering approach, called OCS-FSOM. The proposed algorithm is based on neural network and uses Optimal Completion Strategy for missing value estimation in incomplete dataset. Then, we propose an extension of our algorithm, to tackle the problem of estimating the number of clusters, by using a multi level OCS-FSOM method. The new algorithm called Multi-OCSFSOM is able to find the optimal number of clusters by using a statistical criterion, that aims at measuring the quality of obtained partitions. Carried out experiments on real-life datasets highlights a very encouraging results in terms of exact determination of optimal number of clusters.
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Sagala, Noviyanti T. M., and Alexander Agung Santoso Gunawan. "Discovering the Optimal Number of Crime Cluster Using Elbow, Silhouette, Gap Statistics, and NbClust Methods." ComTech: Computer, Mathematics and Engineering Applications 13, no. 1 (February 3, 2022): 1–10. http://dx.doi.org/10.21512/comtech.v13i1.7270.
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In recent years, crime has been critical to be analyzed and tracked to identify the trends and associations with crime patterns and activities. Generally, the analysis is conducted to discover the area or location where the crime is high or low by using different clustering methods, including k-means clustering. Even though the k-means algorithm is commonly used in clustering techniques because of its simplicity, convergence speed, and high efficiency, finding the optimal number of clusters is difficult. Determining the correct clusters for crime analysis is critical to enhancing current crime resolution rates, avoiding future incidents, spending less time for new officers, and increasing activity quality. To address the problem of estimating the number of clusters in the crime domain without the interference of humans, the research carried out Elbow, Silhouette, Gap Statistics, and NbClust methods on datasets of Major Crime Indicators (MCI) in 2014−2019. Several stages were performed to process the crime datasets: data understanding, data preparation, cluster modelling, and cluster validation. The first two phases were performed in the R Studio environment and the last two stages in Azure Studio. From the experimental result, Elbow, Silhouette, and NbClust methods suggest a similar number of optimum clusters that is two. After validating the result using the average Silhouette method, the research considers two clusters as the best clusters for the dataset. The visualization result of Silhouette method displays the value of 0,73. Then, the observation of the data is well-grouped. It is placed in the correct group.
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Christensen, Diana Hedevang, Sia K. Nicolaisen, Emma Ahlqvist, Jacob V. Stidsen, Jens Steen Nielsen, Kurt Hojlund, Michael H. Olsen, et al. "Type 2 diabetes classification: a data-driven cluster study of the Danish Centre for Strategic Research in Type 2 Diabetes (DD2) cohort." BMJ Open Diabetes Research & Care 10, no. 2 (April 2022): e002731. http://dx.doi.org/10.1136/bmjdrc-2021-002731.
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IntroductionA Swedish data-driven cluster study identified four distinct type 2 diabetes (T2D) clusters, based on age at diagnosis, body mass index (BMI), hemoglobin A1c (HbA1c) level, and homeostatic model assessment 2 (HOMA2) estimates of insulin resistance and beta-cell function. A Danish study proposed three T2D phenotypes (insulinopenic, hyperinsulinemic, and classical) based on HOMA2 measures only. We examined these two new T2D classifications using the Danish Centre for Strategic Research in Type 2 Diabetes cohort.Research design and methodsIn 3529 individuals, we first performed a k-means cluster analysis with a forced k-value of four to replicate the Swedish clusters: severe insulin deficient (SIDD), severe insulin resistant (SIRD), mild age-related (MARD), and mild obesity-related (MOD) diabetes. Next, we did an analysis open to alternative k-values (ie, data determined the optimal number of clusters). Finally, we compared the data-driven clusters with the three Danish phenotypes.ResultsCompared with the Swedish findings, the replicated Danish SIDD cluster included patients with lower mean HbA1c (86 mmol/mol vs 101 mmol/mol), and the Danish MOD cluster patients were less obese (mean BMI 32 kg/m2 vs 36 kg/m2). Our data-driven alternative k-value analysis suggested the optimal number of T2D clusters in our data to be three, rather than four. When comparing the four replicated Swedish clusters with the three proposed Danish phenotypes, 81%, 79%, and 69% of the SIDD, MOD, and MARD patients, respectively, fitted the classical T2D phenotype, whereas 70% of SIRD patients fitted the hyperinsulinemic phenotype. Among the three alternative data-driven clusters, 60% of patients in the most insulin-resistant cluster constituted 76% of patients with a hyperinsulinemic phenotype.ConclusionDifferent HOMA2-based approaches did not classify patients with T2D in a consistent manner. The T2D classes characterized by high insulin resistance/hyperinsulinemia appeared most distinct.
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Zhao, Chao, Junchuang Yang, and Kexin Wen. "An Improved Clustering Algorithm Based on Density Peak and Nearest Neighbors." Mathematical Problems in Engineering 2022 (August 10, 2022): 1–10. http://dx.doi.org/10.1155/2022/5499213.
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Aiming at the problems that the initial cluster centers are randomly selected and the number of clusters is manually determined in traditional clustering algorithm, which results in unstable clustering results, we propose an improved clustering algorithm based on density peak and nearest neighbors. Firstly, an improved density peak clustering method is proposed to optimize the cutoff distance and local density of data points. It avoids that random selection of initial cluster centers is easy to fall into the local optimal solution. Furthermore, a K-value selection method is presented to choose the optimal number of clusters, which is determined by the sum of the squared errors within the clusters. Finally, we employ the idea of the K-nearest neighbors to carry out the assignment for outliers. Experiments on the UCI real data sets indicate that our proposed algorithm can achieve better clustering results compared with several known algorithms.
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Пастухов, Владимир, and Vladimir Pastuhov. "Technopark of High Technologies as a Coordinator of the Cluster Economy Development of Khanty-Mansiisk Autonomous District." Scientific Research and Development. Economics of the Firm 8, no. 4 (December 2, 2019): 45–46. http://dx.doi.org/10.12737/2306-627x-2019-43-47.
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The author considers the basics of clustering a foreign economy, the priorities of the cluster policy of the Russian Federation. The activity of the Center for Cluster Development “Technopark of High Technologies” as a coordinating center for the development of a cluster economy of Khanty-Mansiisk Autonomous District is analyzed. The Center adheres to the unshakable foundations of cluster policy, based on the organization of interaction between government bodies and local self-government, business structures and scientific and educational institutions in order to increase the innovativeness of production and the service sector of the district clusters. The role of the Center for Cluster Development in interacting with other district clusters and partners is estimated. The author believes that mutual cooperation will help to find optimal ways for the further effective development of clusters of Khanty-Mansiisk Autonomous District in the long term. The introduction of innovative technologies in the district clusters (oil and gas and oil and gas processing clusters, forestry and mining, medical, tourist and recreational clusters, the Technics and Technologies for the North cluster, and the scientific and innovative cluster) will ensure a synergistic effect of the economic activity of a wide range of regional territorial enterprises.
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Pasichnyy, M., A. Shirinyan, and J. Schmelzer. "Evolution of New Phase Clusters at the Initial Stages of Binary Alloy Decomposition Described in Terms of a Modified Theory of Nucleation." Ukrainian Journal of Physics 56, no. 2 (February 16, 2022): 192. http://dx.doi.org/10.15407/ujpe56.2.192.
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The work considers the thermodynamics and the kinetics of initial decomposition stages in a supersaturated binary solid solution inthe framework of the modified nucleation theory. The specific surface energy is considered as a function of intensive state parameters of both the cluster and the matrix, which allows one to uniformly describe clusters of critical, subcritical, and supercritical size. The analysis was performed in two stages. On the first one, the optimal size dependences of the compositions of new phase clusters were determined by analyzing the macroscopic equations of growth of nuclei. On the second stage, we solved akinetic equation to describe the evolution of the size distribution function of new-phase clusters along this optimal composition line.The effect of various kinetic factors on the behavior of the distribution function and characteristics of new-phase clusters was studied. The obtained distributions demonstrate a possibility of the existence of bimodal size distributions of new-phase clusters.