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I know about embeddings for words, but I would like to know if it is possible to do something similar for curves. What I mean by curves is a curve of a function. Say I have 1000 points corresponding to a curve for 0% to 100% every 0.1 and I would like to use this in a ML model but I don't want to use those 1000 points, but rather embedded them into a smaller vector so that two curves that are 'close' will have a vector closer.

I don't know if I explained myself clearly, so tell me if it is not the case !

Note : I would like to do this in Python

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  • $\begingroup$ If you have a mathematical expression for the curves, you may also consider an approximation approach that can profit from that knowledge (e.g. Tailor expansion or Chebyshev polynomials) together with a custom distance function in coefficient space, instead of a black-box approximation. $\endgroup$
    – noe
    Jan 31, 2023 at 14:13

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Unlike word embedding, where you can get "for free" the embeddings of words, in your use case you'll need to derive the embeddings yourself.

I would try an approach based on autoencoders. An autoencoder is a neural network architecture based on an encoder and a decoder. The idea is that the encoder takes the input data (in your case a curve) and encodes it to a small vector (in your case a vector with dimensionality < 1000). Then, the decoder takes this small vector and tries to reproduce the original input (in your case the original curve). Once the network is trained you'll have a way of extracting embeddings from your curves using the encoder layer.

Here you have an example with images.

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  • $\begingroup$ Thank you very much, I will try this out ! $\endgroup$
    – WLD
    Feb 1, 2023 at 13:21

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