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I am struggling to understand how RBF (radial basis functions) work. My first question concerns the weights: are the learnable weights the same as the centres? So, is the algorithm essentially learning the centres? Furthermore, the slides of my deep learning class say that also the SD of the activation function is learned. Does this mean that the SD of each centre is learned or the overall SD for all centres? And as a follow up question, does this mean there are two different weights, one for the position of the centres and one for the SD of the activation functions?

And secondly, how would you initialise good weights? Should you look at the data and guess the centres for a starting point?

Thanks for your help.

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For each RBF node, you learn both its center and its SD, thus, for each center the belonging SD (as many SDs as there are centers). And those are your "weights", the parameters of your model, in the sense that while in ordinary NNs you fit the linear weights, in RBF NNs you fit the centers and SDs.

And yes, if you can guess the centers roughly beforehand, you would initialize RBF NNs by placing them there. If you can roughly guess a clustering, you would try to approximate the clusters with the centers with appropriate SDs for each.

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    $\begingroup$ That helps a lot! Thanks! $\endgroup$
    – DLTS
    Jun 16, 2022 at 10:25

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