# How to compare two different clustering approaches?

I'm making a project connected with identifying the dynamics of sales. My database concerns 26 weeks (so equally in 26 time-series observations) after launching the product, 126 time-series=126 different products.

I used clustering to group products with similar dynamics of sales. I applied two different approaches to pam() = k-medoids clustering. First one groupes time-series - 3 clusters, second one groupes S-curve parameters, counted before by curve fitting to each time-series - 6 clusters.

Now I would like to compare these two methods, but have no idea how to compare the quality of two clustering methods if I have different number of clusters.

I would be grateful for any suggestions.

• There exist a lot of "internal clustering criterions" which, generally speaking, compare clustering solutions obtained on the same data but with different clustering methods or different number of clusters, - compare cluster articulatedness. Yet you should know that these criterions are biased: 1) each criterion tends toward a specific definition of cluster shape and density; 2) some criterions are idiosyncratic towards small number of clusters. – ttnphns Apr 17 '14 at 9:50
• So far, I used silhouette measure to examine cluster accuracy. Is there any unbiased way to compare it? and is there any possibility that I could countr 'correlation' for example between cluster1_method1 and cluster4_method2 to see if two methods create similar clusters (for example it will occur that cluster1_method1 consists of cluster2_method2 and cluster4_method2). Or even is there possibility to measure the distance between medoids of different clusters from method1 and method2 to see if they are close to each other? – peterpeter Apr 17 '14 at 10:15
• 1) Silhouette statistic is popular and quite good clustering criterion. Its standard formula defines cluster density as average within-cluster distance. 2) Identifying similar clusters across various solutions is a different task, it's not about "validity" (articulatedness) of clusters; use crosstabulations for that. – ttnphns Apr 17 '14 at 10:23
• In addition to statistical methods, I would urge you to look at the substantive meaning: Which clustering is more useful to you? – Peter Flom Apr 17 '14 at 10:44
• what does it mean 'more useful' for clustering? what's more crosstabulations say to me only, if cluster from different methods concur, thats all? Cause if I count how many time-series concur in method1_cluster1, method2_cluster one etc there is a random distribution so the only interpretation is that the methods are not similar and we cannot see any rule in matching time series between those two methods? – peterpeter Apr 17 '14 at 10:50