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Old 05-30-2013, 09:39 AM
Kais_M Kais_M is offline
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Join Date: Apr 2013
Posts: 3
Default Re: Gradient Descent on complex parameters (weights)

Originally Posted by Elroch View Post
z = x+iy \implies dz = dx + i dy
{\partial \over {\partial z}} = ({{\partial \over {\partial x}},{\partial \over {\partial y}}})
actually there is multiplication of complex numbers; one complex number is a parameter we are trying to optimize, the other is the data. The data is represented in the Fourier domain, that's why it's complex. When taking the derivative wrt the complex parameter and propagating it inside the formula for sum of squared errors you eventually have to take the derivative of the complex parameter multiplied by the complex data wrt the complex parameter... e.g. the complex parameters could be values in a transfer function, complex data is Fourier transform of real signal.
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