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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.

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  • $\begingroup$ It is not clear what you mean. First of all feature selection is not about removing correlated features. Blindly removing correlated features may be a very bad idea in many cases. Second, feature selection is usually used for supervised algorithms, not unsupervised. Third, if you can select features manually based on some kind expert knowledge, you wouldn't use automated solutions. $\endgroup$
    – Tim
    Commented Jun 17, 2020 at 9:32
  • $\begingroup$ The objective of clustering is to find interesting groups in data. My question is, whether feature selection can substantially help with this goal. 1) Not sure about if the "correlated" part is precise, but for sure, one of the goals with feature selection for clustering is to remove redundant features. [1] $\endgroup$
    – sitnarf
    Commented Jun 17, 2020 at 14:48
  • $\begingroup$ 2) Yeah, but there are many methods for clustering too (e.g. [1]), thus I am asking about those methods. 3) Not necessary. It is possible you might select features based on expert knowledge and do the feature selection afterward to improve the clustering (again, it is core of my question). [1] link.springer.com/article/10.1007/s11222-016-9670-1 $\endgroup$
    – sitnarf
    Commented Jun 17, 2020 at 14:48

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The objective of clustering is given the data to group it into several groups. If you change the data, the results also could change. There is no feature selection methods for cluster analysis because the point of cluster analysis is to find groups in the data you have. It is your decision what kind of data you want to use to find the groups.

For example, you could have a data on patients from some hospital. You could cluster this data based on many different features. It is a completely different problem if you group those patients by demographics, as compared to grouping them based on their medical conditions. Surely, there may be overlap and the overlap may be interesting by itself, but those are answering two different research questions.

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  • $\begingroup$ Actually, there are at least several methods. For example link.springer.com/article/10.1007/s11222-016-9670-1 $\endgroup$
    – sitnarf
    Commented Jun 17, 2020 at 16:33
  • $\begingroup$ Free access link: researchgate.net/publication/… $\endgroup$
    – sitnarf
    Commented Jun 17, 2020 at 16:35
  • $\begingroup$ @sitnarf I didn’t read the paper, but it seems to describe regularization, so this is slightly different problem and solution. $\endgroup$
    – Tim
    Commented Jun 17, 2020 at 16:38

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