The objective of clustering is to find interesting groups in data. My question is, whether feature selection can substantially help with this objective.
I understand feature selection can remove redundant variables, which might help with interpretation. However, the feature selection finds a subset by optimizing for compactness/separation. Thus, it might find a subset, which has a higher compactness/separation but actually has lower association with the concept I am looking for.
Doesn't make more sense to manually select the features, because it is, in fact, defining the task I am interested in?
More clarification: In supervised learning there is a label, that defines a task. Then, I can remove features or do anything else, as long as it predicts the label. In clustering, on the other hand, the definition of a task are the unlabeled data itself. Thus, by changing the data (feature selection) I am changing the task and might searching for something not meaningful.