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The point in radial basis function networks they're usually abbreviated as RBF networks is that we want to use different first layer, so we still want to use basis functions in the original parameter space, but they should be more spatially localized and the way it works is that your prediction is given by some bias plus number of parameters and the summations now over your weight functions so Would be the number of weight functions is now a scalar this time times in analogy to what we saw before let recall this SJ of X and SJ of X is e tithe minus X minus mu J where mu J is the center of the j DH basis function then the covariance functions are typically assumed to be isotropic and the even the variances are often fixed in advance soil#39’m not putting a parameter J here on the Sigma IN#39’m assuming that the same has been used for all basis functions there you go and in this type of networks the Centers of the basis functions the Murray are fixed in advance for instance by some clustering algorithm such as k-means which we very briefly discussed a week ago or two weeks ago and then the only thing that needs to be learned are the B and the Wand if the new J are fixed then these are learned easily by solving a linear system of equations which you derive simply by minimizing the sum of squared residuals, so it's, and it's an in essence aggression problem that you are solving here now for the fun of it we can bring this actually in the kind of funny graphical notation that we saw before for the perceptrons I am showing this for a single basis function only and doesn't#39’t make it doesn't make much sense, but I just want to show that it#39;possible in principle, so these are the original features, and you can then say that we have a perceptron that trivial perceptron that takes the first coordinate and subtracts the first element of the normal vector, and you have a trivial perceptron that takes your second coordinates your second coordinate and subtracts the second element of your mean vector and each then has an activation function which is this the square so the operation of squaring a number and these can then be summed up in a new perceptron which has Gaussian activation function and allow that would now be so all of that would be your first output let#39’s say alone of your first percent perceptron solar these mean vectors I give subscript 1 to say it belongs to the first RBF to the first radial basis function and the second index means IN#39;talking about the first component Randall of this would give s 1, and I can now replicate this entire structure to give me an S 2 I'm not drawing it now and Can replicate the structure again to give me an S 3, so you can see that if you can plot it as a kind of network awe did before, but the analogy yeah is little superficial and then at that point you can multiply with these weights W 1 W 2 W 3 and have a summation unit that takes as input your bias handout comes your prediction Y hat of X OK#39’ve...
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