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Is there any function which could map the labeled clusters into a space where all clusters are away from each other as far as possible? Now I have many labeled clusters, but they may be mixed in low dimension space. So I want to find a function or algorithm that could do this. I think the problem in this way: First, there should be some function or algorithm with parameters. Second, By learning from those labeled clusters, I could get the parameters of the mapping function or mapping algorithm. Finally, I get the mapping method. However, I have no idea about what kinds of function or algorithm is suitable for my problem. Can someone help me please? Thank you!

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  • $\begingroup$ Since you have already identified (labeled) your clusters, this is not a clustering problem. Essentially you want to train a classifier, where each cluster is considered a separate class. For example SVM is a "maximum margin classifier", which is essentially your goal. $\endgroup$
    – GeoMatt22
    Commented Sep 13, 2016 at 3:37
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    $\begingroup$ It is really similar to classification problem but not. Let me tell more about my purpose. When I get the specific mapping function or algorithm, I use it transform my test data. In the transformed test data set, I will do clustering. The reason for not clustering on original test data set is that they may be mixed in a low dimension space and could be separate in high dimension space. Therefore, I need some good mapping method. The mapping method learned from current labeled clusters could be convincing. $\endgroup$
    – Jay Li
    Commented Sep 13, 2016 at 4:41

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Substitute "clusters" by "classes" and you will find many projection techniques.

For example Fisher's Linear Discriminant Analysis (the other LDA) tries to find the linear projection that best separates classes. And of course other approaches have been proposed since 1936.

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