scholarly journals A Quantitative Discriminant Method of Elbow Point for the Optimal Number of Clusters in Clustering Algorithm

2020 ◽  
Author(s):  
Congming Shi ◽  
Bingtao Wei ◽  
Shoulin Wei ◽  
Wen Wang ◽  
Hai Liu ◽  
...  
Keyword(s):  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Optimal Number ◽  
Machine Learning Method ◽  
Learning Method ◽  
Cluster Number ◽  
Number Of Clusters ◽  
Optimal Cluster ◽  
Better Than ◽  
Optimal Number Of Clusters

Abstract Clustering, as a traditional machine learning method, is still playing a significant role in data analysis. The most of clustering algorithms depend on a predetermined exact number of clusters, whereas, in practice, clusters are usually unpredictable. Although elbow method is one of the most commonly used methods to discriminate the optimal cluster number, the discriminant of the number of clusters depends on manual identification of the elbow points on the visualization curve, which will lead to the experienced analysts not being able to clearly identify the elbow point from the plotted curve when the plotted curve being fairly smooth. To solve this problem, a new elbow point discriminant method is proposed to work out a statistical metric estimating an optimal cluster number when clustering on a dataset. Firstly, the average degree of distortion obtained by Elbow method is normalized to the range of 0 to10; Secondly, the normalized results are used to calculate Cosine of intersection angles between elbow points; Thirdly, the above calculated Cosine of intersection angles and Arccosine theorem are used to compute the intersection angles between elbow points; Finally, the index of the above computed minimal intersection angles between elbow points is used as the estimated potential optimal cluster number. The experimental results based on simulated datasets and a public well-known dataset (Iris Dataset) demonstrated that the estimated optimal cluster number output by our newly proposed method is better than widely used Silhouette method.

scholarly journals A Quantitative Discriminant Method of Elbow Point for the Optimal Number of Clusters in Clustering Algorithm

2020 ◽  
Author(s):  
Congming Shi ◽  
Bingtao Wei ◽  
Shoulin Wei ◽  
Wen Wang ◽  
Hai Liu ◽  
...  
Keyword(s):  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Optimal Number ◽  
Machine Learning Method ◽  
Learning Method ◽  
Cluster Number ◽  
Number Of Clusters ◽  
Optimal Cluster ◽  
Better Than ◽  
Optimal Number Of Clusters

Abstract Clustering, as a traditional machine learning method, is still playing a significant role in data analysis. The most of clustering algorithms depend on a predetermined exact number of clusters, whereas, in practice, clusters are usually unpredictable. Although elbow method is one of the most commonly used methods to discriminate the optimal cluster number, the discriminant of the number of clusters depends on manual identification of the elbow points on the visualization curve, which will lead to the experienced analysts not being able to clearly identify the elbow point from the plotted curve when the plotted curve being fairly smooth. To solve this problem, a new elbow point discriminant method is proposed to work out a statistical metric estimating an optimal cluster number when clustering on a dataset. Firstly, the average degree of distortion obtained by Elbow method is normalized to the range of 0 to10; Secondly, the normalized results are used to calculate Cosine of intersection angles between elbow points; Thirdly, the above calculated Cosine of intersection angles and Arccosine theorem are used to compute the intersection angles between elbow points; Finally, the index of the above computed minimal intersection angles between elbow points is used as the estimated potential optimal cluster number. The experimental results based on simulated datasets and a public well-known dataset demonstrated that the estimated optimal cluster number output by our newly proposed method is better than widely used Silhouette method.

scholarly journals A Quantitative Discriminant Method of Elbow Point for the Optimal Number of Clusters in Clustering Algorithm

2021 ◽  
Author(s):  
Congming Shi ◽  
Bingtao Wei ◽  
Shoulin Wei ◽  
Wen Wang ◽  
Hai Liu ◽  
...  
Keyword(s):  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Optimal Number ◽  
Machine Learning Method ◽  
Cluster Number ◽  
Number Of Clusters ◽  
Public Dataset ◽  
Optimal Cluster ◽  
Better Than ◽  
Optimal Number Of Clusters

Abstract Clustering, a traditional machine learning method, plays a significant role in data analysis. Most clustering algorithms depend on a predetermined exact number of clusters, whereas, in practice, clusters are usually unpredictable. Although the Elbow method is one of the most commonly used methods to discriminate the optimal cluster number, the discriminant of the number of clusters depends on the manual identification of the elbow points on the visualization curve. Thus, experienced analysts cannot clearly identify the elbow point from the plotted curve when the plotted curve is fairly smooth. To solve this problem, a new elbow point discriminant method is proposed to yield a statistical metric that estimates an optimal cluster number when clustering on a dataset. First, the average degree of distortion obtained by the Elbow method is normalized to the range of 0 to 10. Second, the normalized results are used to calculate the cosine of intersection angles between elbow points. Third, this calculated cosine of intersection angles and the arccosine theorem are used to compute the intersection angles between elbow points. Finally, the index of the above computed minimal intersection angles between elbow points is used as the estimated potential optimal cluster number. The experimental results based on simulated datasets and a well-known public dataset (Iris Dataset) demonstrated that the estimated optimal cluster number obtained by our newly proposed method is better than the widely used Silhouette method.

scholarly journals A quantitative discriminant method of elbow point for the optimal number of clusters in clustering algorithm

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Congming Shi ◽  
Bingtao Wei ◽  
Shoulin Wei ◽  
Wen Wang ◽  
Hai Liu ◽  
...  
Keyword(s):  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Optimal Number ◽  
Machine Learning Method ◽  
Cluster Number ◽  
Number Of Clusters ◽  
Public Dataset ◽  
Optimal Cluster ◽  
Better Than ◽  
Optimal Number Of Clusters

AbstractClustering, a traditional machine learning method, plays a significant role in data analysis. Most clustering algorithms depend on a predetermined exact number of clusters, whereas, in practice, clusters are usually unpredictable. Although the Elbow method is one of the most commonly used methods to discriminate the optimal cluster number, the discriminant of the number of clusters depends on the manual identification of the elbow points on the visualization curve. Thus, experienced analysts cannot clearly identify the elbow point from the plotted curve when the plotted curve is fairly smooth. To solve this problem, a new elbow point discriminant method is proposed to yield a statistical metric that estimates an optimal cluster number when clustering on a dataset. First, the average degree of distortion obtained by the Elbow method is normalized to the range of 0 to 10. Second, the normalized results are used to calculate the cosine of intersection angles between elbow points. Third, this calculated cosine of intersection angles and the arccosine theorem are used to compute the intersection angles between elbow points. Finally, the index of the above-computed minimal intersection angles between elbow points is used as the estimated potential optimal cluster number. The experimental results based on simulated datasets and a well-known public dataset (Iris Dataset) demonstrated that the estimated optimal cluster number obtained by our newly proposed method is better than the widely used Silhouette method.

scholarly journals Role of Cluster Validity Indices in Delineation of Precipitation Regions

Water ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 1372
Author(s):  
Nikhil Bhatia ◽  
Jency M. Sojan ◽  
Slobodon Simonovic ◽  
Roshan Srivastav
Keyword(s):  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Optimal Number ◽  
Ratio Test ◽  
Cluster Validity ◽  
Number Of Clusters ◽  
Cluster Validity Indices ◽  
Validity Indices ◽  
Point Data ◽  
Optimal Number Of Clusters

The delineation of precipitation regions is to identify homogeneous zones in which the characteristics of the process are statistically similar. The regionalization process has three main components: (i) delineation of regions using clustering algorithms, (ii) determining the optimal number of regions using cluster validity indices (CVIs), and (iii) validation of regions for homogeneity using L-moments ratio test. The identification of the optimal number of clusters will significantly affect the homogeneity of the regions. The objective of this study is to investigate the performance of the various CVIs in identifying the optimal number of clusters, which maximizes the homogeneity of the precipitation regions. The k-means clustering algorithm is adopted to delineate the regions using location-based attributes for two large areas from Canada, namely, the Prairies and the Great Lakes-St Lawrence lowlands (GL-SL) region. The seasonal precipitation data for 55 years (1951–2005) is derived using high-resolution ANUSPLIN gridded point data for Canada. The results indicate that the optimal number of clusters and the regional homogeneity depends on the CVI adopted. Among 42 cluster indices considered, 15 of them outperform in identifying the homogeneous precipitation regions. The Dunn, D e t _ r a t i o and Trace( W − 1 B ) indices found to be the best for all seasons in both the regions.

scholarly journals A New Fuzzy Clustering Algorithm Based on Clonal Selection for Land Cover Classification

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Yanfei Zhong ◽  
Liangpei Zhang
Keyword(s):  
Land Cover ◽  
Clustering Algorithm ◽  
Clonal Selection ◽  
Land Cover Classification ◽  
Optimal Number ◽  
Cluster Number ◽  
Number Of Clusters ◽  
Clonal Selection Theory ◽  
Fuzzy Clustering Algorithm ◽  
Optimal Number Of Clusters

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.

scholarly journals A novel bidirectional clustering algorithm based on local density

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Baicheng Lyu ◽  
Wenhua Wu ◽  
Zhiqiang Hu
Keyword(s):  
Clustering Algorithm ◽  
Local Density ◽  
Clustering Algorithms ◽  
Cluster Number ◽  
Denoising Method ◽  
Number Of Clusters ◽  
Data Points ◽  
Cutoff Distance ◽  
Large Clusters ◽  
Small Clusters

AbstractWith the widely application of cluster analysis, the number of clusters is gradually increasing, as is the difficulty in selecting the judgment indicators of cluster numbers. Also, small clusters are crucial to discovering the extreme characteristics of data samples, but current clustering algorithms focus mainly on analyzing large clusters. In this paper, a bidirectional clustering algorithm based on local density (BCALoD) is proposed. BCALoD establishes the connection between data points based on local density, can automatically determine the number of clusters, is more sensitive to small clusters, and can reduce the adjusted parameters to a minimum. On the basis of the robustness of cluster number to noise, a denoising method suitable for BCALoD is proposed. Different cutoff distance and cutoff density are assigned to each data cluster, which results in improved clustering performance. Clustering ability of BCALoD is verified by randomly generated datasets and city light satellite images.

scholarly journals Combination of clustering algorithms to maximize the lifespan of distributed wireless sensors

2016 ◽  
Vol 5 (1) ◽  
pp. 63-72 ◽  
Author(s):  
Derssie D. Mebratu ◽  
Charles Kim
Keyword(s):  
Wireless Sensors ◽  
Clustering Algorithms ◽  
Optimal Number ◽  
Sensor Nodes ◽  
Wireless Sensor ◽  
Wireless Sensor Nodes ◽  
Adaptive Clustering ◽  
Combination Approach ◽  
Better Than ◽  
Optimal Number Of Clusters

Abstract. Increasing the lifespan of a group of distributed wireless sensors is one of the major challenges in research. This is especially important for distributed wireless sensor nodes used in harsh environments since it is not feasible to replace or recharge their batteries. Thus, the popular low-energy adaptive clustering hierarchy (LEACH) algorithm uses the “computation and communication energy model” to increase the lifespan of distributed wireless sensor nodes. As an improved method, we present here that a combination of three clustering algorithms performs better than the LEACH algorithm. The clustering algorithms included in the combination are the k-means+ + , k-means, and gap statistics algorithms. These three algorithms are used selectively in the following manner: the k-means+ +  algorithm initializes the center for the k-means algorithm, the k-means algorithm computes the optimal center of the clusters, and the gap statistics algorithm selects the optimal number of clusters in a distributed wireless sensor network. Our simulation shows that the approach of using a combination of clustering algorithms increases the lifespan of the wireless sensor nodes by 15 % compared with the LEACH algorithm. This paper reports the details of the clustering algorithms selected for use in the combination approach and, based on the simulation results, compares the performance of the combination approach with that of the LEACH algorithm.

scholarly journals A novel bidirectional clustering algorithm based on local density

2021 ◽  
Author(s):  
BAICHENG LV ◽  
WENHUA WU ◽  
ZHIQIANG HU
Keyword(s):  
Clustering Algorithm ◽  
Local Density ◽  
Clustering Algorithms ◽  
Cluster Number ◽  
Denoising Method ◽  
Number Of Clusters ◽  
Data Points ◽  
Cutoff Distance ◽  
Large Clusters ◽  
Small Clusters

Abstract With the widely application of cluster analysis, the number of clusters is gradually increasing, as is the difficulty in selecting the judgment indicators of cluster numbers. Also, small clusters are crucial to discovering the extreme characteristics of data samples, but current clustering algorithms focus mainly on analyzing large clusters. In this paper, a bidirectional clustering algorithm based on local density (BCALoD) is proposed. BCALoD establishes the connection between data points based on local density, can automatically determine the number of clusters, is more sensitive to small clusters, and can reduce the adjusted parameters to a minimum. On the basis of the robustness of cluster number to noise, a denoising method suitable for BCALoD is proposed. Different cutoff distance and cutoff density are assigned to each data cluster, which results in improved clustering performance. Clustering ability of BCALoD is verified by randomly generated datasets and city light satellite images.

GIVING FUZZINESS TO SPATIAL CLUSTERS: A NEW INDEX FOR CHOOSING THE OPTIMAL NUMBER OF CLUSTERS

2013 ◽  
Vol 22 (03) ◽  
pp. 1350009 ◽  
Author(s):  
GEORGE GREKOUSIS
Keyword(s):  
Fuzzy Clustering ◽  
Spatial Clustering ◽  
Clustering Algorithms ◽  
Optimal Number ◽  
Fuzzy Cluster ◽  
Cluster Validation ◽  
Number Of Clusters ◽  
A Value ◽  
Membership Value ◽  
Optimal Number Of Clusters

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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