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I implemented Isomap and I plan to use it as a feature extraction technique for a classification task.

My problem is that although I can map the training data into a lower dimensional space, how can I use the same mapping for a separate test dataset?

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Applying the mapping to test data is called the out-of-sample problem. Take a look at the following paper to see a solution for Isomap:

Bengio, Yoshua, et al. Out-of-sample extensions for lle, isomap, mds, eigenmaps, and spectral clustering. Advances in neural information processing systems 16 (2004): 177-184.

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As far as I know, the Isomap in scikit-learn implements out-of-sample isomap:

http://scikit-learn.org/stable/modules/generated/sklearn.manifold.Isomap.html

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I solved the problem like this; solve Train*W = Y for W, map using Test*W.

But other contributions are welcome.

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  • $\begingroup$ Glad you solved your problem! One of our goals here is to be a repository of information for future readers. Unfortunately this answer is unclear without more explanation, so it isn't helpful to anyone else. Moreover, other users can't even comment on this answer (maybe there's a problem with your technique and they want to warn you!) if they can't understand what you mean. $\endgroup$ – shadowtalker Dec 5 '15 at 13:09
  • $\begingroup$ @ssdecontrol: Not only is this answer unclear, it is also clearly wrong, because Isomap is not a linear method. -1. $\endgroup$ – amoeba says Reinstate Monica Dec 5 '15 at 14:31

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