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With PCA, one can use the explained variance ratio and keep the number of components that explain 95% of the dataset.

How does one do the same for manifold learning methods for dimensionality reduction? For example, isomap or MDS etc. in python sci-kit learn. Thanks

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Maximizing retained variance in PCA is equivalent to minimizing reconstruction error, that is, difference between original and reduced data pairwise distances.

This has natural generalization to other methods, since you can also calculate reconstruction error for them (although you need to note that nonlinear dimensionality reduction shouldn't be judged by raw reconstruction error - their point is to reduce data so that distances between close points are preserved while not caring for distant ones).

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