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JuliaStats / MultivariateStats.jl

A Julia package for multivariate statistics and data analysis (e.g. dimension reduction)
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reconstruct for kernel PCA #125

Open mateuszbaran opened 4 years ago

mateuszbaran commented 4 years ago

Where the idea for code for kernel PCA reconstruct in MultivariateStats.jlhttps://github.com/JuliaStats/MultivariateStats.jl/blob/30aea0c2832f5a0a0574641433774eecc57aba92/src/kpca.jl#L61 is taken from? I've found some papers that state that reconstruction in kernel PCA is quite difficult and suggest solving it as an optimization problem: https://arxiv.org/pdf/1207.3538.pdf which is not what MultivariateStats.jl does.

wildart commented 4 years ago

The optimization problem you've mentioned is solved by a kernel ridge regression. See "3.1 Estimation of the Pre-Image Map" from "Learning to find pre-images", Bakır, 2004.

mateuszbaran commented 4 years ago

Thanks, it may be worth adding to documentation.