Training & Test Set Dimensionality R...

  • Mike

    Mike - 2012-01-05


    I need to have the same parameters for the test set as were generated by the
    Isomap training set. How to do this? I'm not

    trying to be specific about the Isomap but any of the other dimensionality
    reduction transforms.


  • Mike Gashler

    Mike Gashler - 2012-01-05

    If I understand correctly, you want to do supervised learning. Since your data
    has high-dimensional features, you want to pre-process them with Isomap (or
    some other algorithm) to improve runtime performance with a small cost in
    predictive accuracy. Is that right?

    There is a subtle difference between dimensionality reduction algorithms and
    manifold learners. Manifold learners (such as PCA, Kernel-PCA, Nonlinear-PCA,
    and Autoencoders) train a model that maps from low-to-high (or high-to-low)
    dimensional space (or both). Many dimensionality reduction techniques (such as
    Isomap, LLE, MLLE, Manifold Sculpting, HLLE, LTSA, and MVU) reduce
    dimensionality without training a map or model of the manifold. Technically,
    these techniques are not "manifold learners" (, although the published
    literature is not always careful to make this distinction). If you want to
    generalize (that is, apply the same transformation to a test set), then a
    mapping is required.

    If you wish to use a dimensionality reduction algorithm that is not a manifold
    learner (such as Isomap), you can train a separate model to do the mapping. In
    other words, after you reduce the dimensionality of the training features, you
    can train a regression model to map from the high-dimensional features to the
    low-dimensional features. You can then use your trained regression model to
    apply a similar transformation to the test set.



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