General regression neural network

Intoduction

Generalized regression neural network (GRNN) is a variation to radial basis neural networks (RBFNN). GRNN was suggested by D.F. Specht in 1991.

GRNN can be used for regression, prediction, and classification. GRNN can also be a good solution for online dynamic systems.

GRNN represents an improved technique in the neural networks based on the non-paramertic regression. The basic idea is that every training sample will represents a mean to a radial basis neuron.

Mathematical represntion of the GRNN:

$Y(x)={\frac {\sum _{k=1}^{N}y_{k}e^{(}d_{k}/2\sigma )}{\sum _{k=1}^{N}e^{(}d_{k}/2\sigma )}}$

where $Y(x)$ is the prediction value of input $x$.

$d_{k}=(x-xi)^{T}(x-xi).$

where $d_{k}$ is the distance between the training samples $xi$ and the input $x$.

GRNN has been implemented in many software including Matlab and R- programming language.

Advantages and Disadvatnages of GRNN:

Similar to RBFNN GRNN has the following advantages:

• single pass learning so no backpropagation is required.
• high accuracy in the estimation since it uses gaussian functions.
• it can handle noises in the inputs.

The main disadvantages of GRNN are:

• Its size can grow to huge size which computationally expensive.
• There is no otimal methods to improve it.