Can I use the Silhouette to measure quality of clusters in different dimensions?
For example, let's say we run kmeans for some $k$ using 6 features of the dataset. Mark the resulted silhouette as $s_A$.
Now run kmeans for some $k'$ ($k=k'$) using 3 features of the dataset. Mark the resulted silhouette as $s_B$.
Can I decide which clustering is better by the highest value between $s_A$,$s_B$?
Or in other words, will the dimension of the dataset effect my silhouette value? I'm worried since the Silhouette uses distance, but on the other hand it is normalised by the distance based on some heuristic.
Context: (Very condensed!) I want to evaluate the performance of some feature selection algorithm for unsupervised feature learning, and I want to measure the quality of my selected features against other algorithms (using kmeans for the clustering task)