I am running isomap for feature reduction and I want to see what number of features are best for classification with experiments at different number of features. Do I need to run isomap for each try to get specified number of features or just run the algo. once and chose again and again the number of features I need? Is it like PCA? PCA gives possible new bases with their relative importance (eigenvalues) and you might choose the bases incrementally and test classification performance so you do not run PCA again and again for each experiment.
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2 Answers
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You can hold the configuration matrix Y and eigenvalues of the matrix Y*Y' to choose different number of features.
However, it is not like PCA, the configuration matrix itself holds the new features. So, I am also interested in finding out how to apply the same mapping to the test data.
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The eigenvalues of the kernel matrix in Isomap tell you about the relative importance of the components.
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.
