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I have a problem with continuous feature and outcome data. The features are weak predictors. I'd like to be able to cluster my features into $k$ classes. This is not semi-supervised learning so much as poorly-supervised learning---I want to cluster the feature data, with some influence from the known outcomes in the training data, but not take it as gospel.

Is there a nice way to cluster while incorporating the outcome training data in a single step?

I can think of regressing the data and then clustering the predicted outcomes (each a scalar); however, the regression is not very good so I don't want to rely on it heavily. I can also cluster the data unsupervised ($k$-means) and then rank them by the mean outcome of each cluster in the training data. The latter works surprisingly well, but doesn't taken into account the training data that I have available.

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There exist semi-supdrvised clustering (also referred to as constrained clustering) algorithms.

There you can specify "must link" and "cannot link" constraints for known objects. The algorithm then searches a solution that retains as much of these constraints as possible, clustering the remainder of the data.

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