John Maddock said: (by the date of Fri, 6 Oct 2006 10:04:56 +0100)
Janek Kozicki wrote:
Mathematical Special Functions how about sigmoid, double sigmoid and their derivatives? Used for neural networks. Those are new ones to me.
yes, actually there is a wide family of sigmoid functions, they all have a similar shape. However there is one function called "sigmoid" and unless otherwise specified what sigmoid function is used, this one is assumed: sigmoid(x)=1/(1+exp(-x)) Theodore, please note that: (tanh(x/2)+1)/2 = 1/(1+exp(-x)) It's the same function, only written in different way. First parameter to tweak here, is the steep: sigmoid(x,s)=1/(1+exp(-x/s)) But there are other sigmoid functions. Double sigmoid is this: double_sigmoid(x,d,s) = sign(x-d)(1-exp(-((x-d)/s)^2)) d - function centre s - steep factor Actually it's all here: http://en.wikipedia.org/wiki/Sigmoid_function http://en.wikipedia.org/wiki/Gaussian_curve Both sigmoid functions and bell curves (e.g. gaussian) are useful in neural networks. But also it is necessary to have their first derivative. The most popular learning algorithm (called backpropagation) uses a gradient descent in n-dimensional space, and there the derivatives are necessary. Please note that it's the function shape that is important, not its exact vaules at any point. So if you know a 'faster' function that has similar shape and has a first derivative I'd like to know about it too! -- Janek Kozicki |