I have a data set that has an attribute(A) with 300 different nominal values. Attribute A has a lot of noise. I decide to cluster my data based on other attributes that related to A. I hope to reach clusters with high correlation to A.
Now, I would like to know, how successful I was. In my opinion, more correlation between A and the clusters means more success. I found chi-squared as a method to check the correlation between two nominal attributes. However, chi-squared gives a value (X-squared) that doesn't have a specific range.
So by different numbers of clusters, how can I recognize which clustering is better?
Can I use p-value?
Is there any better way to evaluate clusters for this problem?