Pretty much anything in classical linear algebra can be abstracted to something more powerful by taking a swig of the Axiom of Choice.
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The math looks a lot different, but it's basically PCA with an (infinite) orthogonal polynomial basis.
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It's used in CFD somewhat, that's about it. I've never met a data scientist or even a math professor who's heard of it.
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But it is incredibly powerful and parallelizable, particularly for simulation. Maybe I should write an open source python library someday..
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do it. I want to learn.
End of conversation
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