My professor mentioned that we may merge "close" clusters (those with relatively low sum of squared errors) after k-means clustering. However, I don't see the benefit in doing this. If a cluster has very small errors, then that knowledge is valuable, and merging that cluster with another cluster makes us lose information.
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2$\begingroup$ Clustering is descriptive. It is not used to produce small errors. Otherwise wouldn't you make the clusters consist of single points? $\endgroup$– Michael R. ChernickCommented Mar 30, 2017 at 16:44
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1$\begingroup$ If this relates to course work you should add the self-study tag. $\endgroup$– Michael R. ChernickCommented Mar 30, 2017 at 16:46
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$\begingroup$ @MichaelChernick This question relates to my course, but it's not a homework or quiz problem. I just was confused and wanted an explanation. $\endgroup$– ShuklaswagCommented Mar 30, 2017 at 17:55
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1 Answer
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You may want to merge close clusters if, for whatever context relevant reason, you want fewer clusters. Some plausible context relevant reasons would be parsimony in communication/interpretation or if you want to perhaps offer personalization on clusters and it's infeasible to do it on too many clusters.
Now, you may say that if you want fewer clusters then just rerun K-means with smaller K parameter! This may not work due to a drawback of K-means. K-means as an algorithm tends to lead to equal-sized groups. So, it's quite plausible that rerunning K-means with smaller K may not lead to the cluster merging you want (hierarchical clustering algorithms may work better here).
Merging cluster manually is a very hacky approach. Instead, I would argue that if K-means isn't working, try a different algorithm! Or, embed your knowledge of the problem into your algorithm/model prior to the results and not embeding ex post facto.
answered Mar 30, 2017 at 17:15
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$\begingroup$ This makes sense! So merging clusters isn't something that should be do algorithmically, but something a human analyst would do if he or she needed to do so for some particular domain. Is that right? $\endgroup$ Commented Mar 30, 2017 at 18:02
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$\begingroup$ I'm actually arguing the opposite - I edited my response to be clearer. $\endgroup$ Commented Mar 30, 2017 at 18:05
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$\begingroup$ Okay, so would it be correct to say that cluster-merging in K-Means is mostly useful when we want to algorithmically generate k clusters of unequal size (because of our knowledge of the domain) but don't know how to program that domain knowledge into the algorithm itself? And for some reason we insist on using K-Means rather than Hierarchical or another clustering algorithm? $\endgroup$ Commented Mar 30, 2017 at 18:10
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1$\begingroup$ That's a good takeaway. Just be careful on "insist on using k-means". It's a red-herring because I don't know why you'd insist on it but I suppose there may be some situation where that's the case. If you really want unequal clusters, go with a different algorithm. Unless, of course, it's insisted that you can't. $\endgroup$ Commented Mar 30, 2017 at 18:27