I am researching cluster analysis, and I am interested in variables that are both categorical and continuous, for which I have read that a Gower's similarity coefficient is a good proximity measure. I am interested in first using an average linkage algorithm, and have found that some have recommended looking for the 'elbow' in the sum of squared error (SSE) scree plot as a guideline for deciding how many clusters to retain. I was wondering if the Gower's similarity coefficient (being non-metric and non-Euclidean) would allow me to create an SSE scree plot, or if that didn't make sense statistically.
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$\begingroup$ SS of deviations ("error") from what? $\endgroup$– ttnphnsCommented Jul 18, 2013 at 14:42
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$\begingroup$ SSE being the squared distance between each member of a cluster and its cluster centroid. $\endgroup$– LauraCommented Jul 18, 2013 at 14:54
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$\begingroup$ No, centroids call for euclidean distance. They make little sense with Gower coefficient. Search this site for "clustering criterions" and "number of clusters" for further info. $\endgroup$– ttnphnsCommented Jul 18, 2013 at 15:04
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$\begingroup$ Ah, thank you, that was exactly what I was looking for. $\endgroup$– LauraCommented Jul 18, 2013 at 15:06
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1 Answer
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SSE is the measure optimized by k-means.
It doesn't make much sense for any other algorithm than k-means. And even there it suffers from the fact that increasing k will decrease SSE, so you can mostly look at which point further increasing k stops yielding a substantial increase in SSE - that is essentially the vague "elbow method".
There exist other criteria such as Silhouette, Davies-Bouldin index, BIC, AIC that can be used to get an "alternative view" of what is actually optimal.
But in the end, that is just a mathematical heuristic. It may not work for real data.
answered Jul 19, 2013 at 8:46