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I've about 60 samples divided in two predefined groups (group A, group B). We perform gene expression analysis on these samples and wanted to know if the predefined groups reflects well (or not) the current expression profiles (we perform some clustering on it). In other terms the 60 samples will be grouped using the predefined groups (A or B - based on multiple clinical factors independent of expression profile) and also using the expression data (a clustering based on a big 60x20000 expression matrix). How can I assess that the clustering using the expression profiles are in concordance with the predefined groups.

I thought at a permutation approach were I permute at each iteration the sample groups assignment but I'm not sure if it's the right direction to choose.. Any ideas ?

Thanks

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    $\begingroup$ I may just be being dense, but it's not clear what you're asking. Could you perhaps re-express your questions in terms that don't require knowledge of what a gene expression analysis is? $\endgroup$ – Ian_Fin Sep 16 '16 at 12:31
  • $\begingroup$ I added some details $\endgroup$ – Nicolas Rosewick Sep 16 '16 at 12:36
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    $\begingroup$ So, if I'm understanding correctly, your samples are organised according to two separate approaches. One is your predefined groups, which have two categories, A and B. The other approach is organising them via the gene expression analysis. How many categories does this produce? $\endgroup$ – Ian_Fin Sep 16 '16 at 12:41
  • $\begingroup$ Yes that's it. I did a kmeans with N=2 clusters. $\endgroup$ – Nicolas Rosewick Sep 16 '16 at 13:38
  • $\begingroup$ One final question so I can get a handle on your question. Imagine if you have cluster 1 and cluster 2. Is your goal to show that cluster 1 and cluster 2 map onto group A and group B, or is it to show that both groups are representative of the population (i.e., the proportion of 1s and 2s in the population should be the same as the proportions in groups A and B)? $\endgroup$ – Ian_Fin Sep 16 '16 at 13:54
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Read the Wikipedia article on clustering; in particular the section on external cluster validation.

I suggest you try the adjusted rand index first. If you have a value close to 1, then you have a high similarity. But if your value id close to 0, or below, you only have random correspondence between your clusters and labels.

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The problem you're facing is the cluster assignment problem. Although the Rand index mentioned by @Anony-Mousse is probably the most widely used method for such task, it was shown in this paper that the clustering error method is a more robust method that can achieve the same goal. In the same paper, the authors explain how to calculate it. Or you can take a look at this video.

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