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How to distance and to MDS-plot objects according their complex shape

Suppose I have four basal forms of signal (blue, purple, red, green). I also have created transition forms between each other. If you carefully look on the picture below, you can see that for example...

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How to prove that the manifold assumption is correct?

In machine learning, it is often assumed that a data set lies on a smooth low-dimensional manifold (the manifold assumption), but is there any way to prove that assuming certain conditions are...

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What's wrong with my derivation on stochastic neighbor embedding?

I’ve been reading the well-known stochastic neighbor embedding [

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