Ideal PCA replaces the square kernel matrix k(X,X) in kernel PCA with a non-square kernel matrix k(X,Z) - the cross-kernel matrix - where Z are points different from the data input.
(a) Cross-kernels scale more favourably in the number of data points, allowing to obtain PCA-like components more quickly (in linear time).
(b) The right singular values of a cross-kernel-like matrix can be used for manifold learning with kernels.
The IPCA package allows extraction of both kind of features (left/right) and also implements several derived ones which can then be used in further learning tasks. See
Franz J. Király, Martin Kreuzer, Louis Theran. Learning with Cross-Kernels and IPCA. http://arxiv.org/abs/1406.2646
- Changes to previous version:
Initial Announcement on mloss.org.
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