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I am fairly new to clustering data and all the indexes and distances that exists. I have experiemented with k-means and trying to pick the optimal number of clusters by hand, used hierarchical clustering as well, and lastly looked at the Bayesian Interface Criteron.

From those experiences, k-means is fairly arbitrary and we can use the elbow method, but it is not very repetitive it seems. This is because the number of clusters might differ. Likewise for hierarchical clustering.

Since then I have found packages like NbClust and mclust that test to find the optimal number of clusters.

NbClust looks at the frequency of number of clusters based on a distance and a method. Although I can read and understand what the distance is being calcualted formally, I am curious to know if anybody has any good rules of thumb or guidelines for picking the distance and method? Also, I am curious if I really should pick the number of clusters beased on the frequency of those number of clusters, as in follow the majority rule. Secondly, the Best.partition from NbClust. Which clustering index is that based on? Surely each index that was selected from the majority rule cannont always have the same items in each cluster?

Most of the work I have read, used BIC criteron, which is understandable based on the answer provided here. Re-quoted below:

Long answer: The purpose of using model based clustering over heuristic based clustering approaches such as k-means and hierarchical (agglomerative) clustering is to provide a more formal and intuitive approach to comparing and selecting an appropriate cluster model for your data.

My question should I use process like the Information Criteron or NbClust? What are the pros and cons or are they as simple as the answer provided above?

In applying the BIC method to my model, I only found 1 cluster, hence the results were not as riveting as I expected. Therefore, I explored NbClustbut now I am stuck on what distance and method I should use. How do others decide between BIC or NbClust or do they simply just pick one and do not bother discussing the validility of their choice?

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  • $\begingroup$ Majority, almost all of internal cluster validity indices can be used with results of K-means clustering. Most natural to use is criteria based on ANOVA ideology (read here), AIC/BIC are also frequently used. $\endgroup$ – ttnphns Oct 22 '18 at 15:30
  • $\begingroup$ The citation in the question is about clustering (model based or "heuristic"), but your question is about assessing the quality, validity of clustering results. These are a bit independent topics. $\endgroup$ – ttnphns Oct 22 '18 at 15:36
  • $\begingroup$ It is a bit of both I feel. You can cluster based on the results of the Information Criteron or cluster based on the majoriy rule. All of the different indcies in NbClust will test the validity of those clusters. The AHP process combines the results from the Information Criteron to select the optimal number of clusters. I think the question is about cluster validiity, but which process do you use? $\endgroup$ – Jack Armstrong Oct 23 '18 at 8:13
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One source I found was An Approach for Determining the Number of Clusters in a Model-Based Cluster Analysis. They used an Analytic Hierarchy Process that treated the various Information Criterion as the Criteria and the number of clusters as Alternatives. I found it extremly interesting, because it removes the issue of stating to use one criteron method over another.

For those that do not want to read it, here is the conclusion:

This paper has proposed to combine the AHP and some information criteria, namely AIC, AWE, BIC,CLC, and KIC,in determining the number of clusters of a data set in model-based clustering. It has been concluded that the proposed approach has been seen to be more accurate than the corresponding information criteria. The approach has thus been realized to be capable of application to a widespread number of clustering algorithms. To carry out this study, the decision matrix has been created by using the information criteria values for each case. To increase the successes of the information criteria, a pairwise comparison matrix has been suggested in this study. Note that the proposed method is strongly expected to be very effective in analyzing data come out in various of fields science such as economics, biology, engineering etc. For further studies, researchers can pay their attention to produce different decision and pairwise comparison matrices to deal with their problems.

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