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A Quantitative Discriminant Method of Elbow Point for the Optimal Number of Clusters in Clustering Algorithm
Congming Shi
Anyang Normal University
Corresponding Author
ORCiD: https://orcid.org/0000-0002-4666-553X
License:
This work is licensed under a CC BY 4.0 License. Read Full License
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.
Keywords
Machine Learning, Clustering, Elbow Method, Silhouette Coefficient, Cosine Law
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CURRENT STATUS: Under Review
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Received 06 Jan, 2021
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Reviewer #1 agreed
On 26 Dec, 2020
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On 26 Dec, 2020
Editor invited
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No comments provided
Editorial decision: Minor revision
On 24 Nov, 2020
Review #1 received
Received 22 Nov, 2020
Review #2 received
Received 18 Nov, 2020
Reviewer #3 agreed
On 17 Nov, 2020
Reviewer #2 agreed
On 17 Nov, 2020
Review #3 received
Received 17 Nov, 2020
Reviewers invited
Invitations sent on 11 Nov, 2020
Reviewer #1 agreed
On 11 Nov, 2020
Editor assigned
On 27 Oct, 2020
Submission checks complete
On 27 Oct, 2020
Editor invited
On 27 Oct, 2020
No comments provided
Editorial decision: Major revision
On 13 Sep, 2020
Review #3 received
Received 12 Sep, 2020
Review #2 received
Received 27 Aug, 2020
Review #1 received
Received 24 Aug, 2020
Reviewer #3 agreed
On 21 Aug, 2020
Reviewers invited
Invitations sent on 20 Aug, 2020
Reviewer #1 agreed
On 20 Aug, 2020
Reviewer #2 agreed
On 20 Aug, 2020
Editor assigned
On 19 Aug, 2020
Editor invited
On 18 Aug, 2020
Submission checks complete
On 15 Aug, 2020
First submitted
On 13 Aug, 2020
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This preprint is under consideration at EURASIP Journal on Wireless Communications and Networking. A preprint is a preliminary version of a manuscript that has not completed peer review at a journal. Research Square does not conduct peer review prior to posting preprints. The posting of a preprint on this server should not be interpreted as an endorsement of its validity or suitability for dissemination as established information or for guiding clinical practice.
Learn more about In Review
Research
A Quantitative Discriminant Method of Elbow Point for the Optimal Number of Clusters in Clustering Algorithm
Congming Shi
Anyang Normal University
Corresponding Author
ORCiD: https://orcid.org/0000-0002-4666-553X
Badges
Prescreen
This manuscript passed our Prescreen assessment
Complete author information
Appropriate declaration statements
Potential risks to human health
Prescreen
Peer Review Timeline
CURRENT STATUS: Under Review
Version 3
Posted 11 Jan, 2021
No community comments so far
Review #1 received
Received 06 Jan, 2021
Editor assigned
On 26 Dec, 2020
Reviewers invited
Invitations sent on 26 Dec, 2020
Reviewer #1 agreed
On 26 Dec, 2020
Submission checks complete
On 26 Dec, 2020
Editor invited
On 26 Dec, 2020
No comments provided
Editorial decision: Minor revision
On 24 Nov, 2020
Review #1 received
Received 22 Nov, 2020
Review #2 received
Received 18 Nov, 2020
Reviewer #3 agreed
On 17 Nov, 2020
Reviewer #2 agreed
On 17 Nov, 2020
Review #3 received
Received 17 Nov, 2020
Reviewers invited
Invitations sent on 11 Nov, 2020
Reviewer #1 agreed
On 11 Nov, 2020
Editor assigned
On 27 Oct, 2020
Submission checks complete
On 27 Oct, 2020
Editor invited
On 27 Oct, 2020
No comments provided
Editorial decision: Major revision
On 13 Sep, 2020
Review #3 received
Received 12 Sep, 2020
Review #2 received
Received 27 Aug, 2020
Review #1 received
Received 24 Aug, 2020
Reviewer #3 agreed
On 21 Aug, 2020
Reviewers invited
Invitations sent on 20 Aug, 2020
Reviewer #1 agreed
On 20 Aug, 2020
Reviewer #2 agreed
On 20 Aug, 2020
Editor assigned
On 19 Aug, 2020
Editor invited
On 18 Aug, 2020
Submission checks complete
On 15 Aug, 2020
First submitted
On 13 Aug, 2020
Metrics
Comments: 0
PDF Downloads: ...
HTML Views: ...
Subject Areas
Systems and Networking
License:
This work is licensed under a CC BY 4.0 License. Read Full License
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.
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Due to technical limitations, full-text HTML conversion of this manuscript could not be completed. However, the latest manuscript can be downloaded and accessed as a PDF.