General regression neural network

Generalized regression neural network (GRNN) is a variation to radial basis neural networks. 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 dynamical systems.

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

Mathematical representation

$Y(x)={\frac {\sum _{k=1}^{N}y_{k}e^{d_{k}/2\sigma }}{\sum _{k=1}^{N}e^{d_{k}/2\sigma }}},\qquad d_{k}=(x-x_{i})^{T}(x-x_{i})$

where $Y(x)$ is the prediction value of input $x$ and $d_{k}$ is the distance between the training samples $x_{i}$ and the input $x.$

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

Advantages and disadvantages

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 optimal method to improve it.