General regression neural network: Difference between revisions

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Generalized regression neural network (GRNN) is a variation to radial basis neural networks (RBFNN). GRNN was suggested by D.F. Specht in 1991.^[1] It 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^[2].

Mathematical represntion of the GRNN^[3]:

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

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 $x$ .

References

^ "A general regression neural network - IEEE Xplore Document". Ieeexplore.ieee.org. 2002-08-06. Retrieved 2017-03-13.
^ https://minds.wisconsin.edu/bitstream/handle/1793/7779/ch2.pdf?sequence=14
^ https://minds.wisconsin.edu/bitstream/handle/1793/7779/ch2.pdf?sequence=14

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[1] "A general regression neural network - IEEE Xplore Document". Ieeexplore.ieee.org. 2002-08-06. Retrieved 2017-03-13.

[2] ttps://minds.wisconsin.edu/bitstream/handle/1793/7779/ch2.pdf?sequence=14

[3] ttps://minds.wisconsin.edu/bitstream/handle/1793/7779/ch2.pdf?sequence=14

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@@ Line 7: / Line 7: @@
 GRNN represents an improved technique in the neural networks based on the [[Regression|non-paramertic regression]]. The basic idea is that every training sample will represents a mean to a radial basis [[Neuron|neuron]]<ref>https://minds.wisconsin.edu/bitstream/handle/1793/7779/ch2.pdf?sequence=14</ref>.
+Mathematical represntion of the GRNN<ref>https://minds.wisconsin.edu/bitstream/handle/1793/7779/ch2.pdf?sequence=14</ref>:
+<math>
+Y(x)=\frac{\sum_{k=1}^N y_k e^(d_k/2\sigma)}{\sum_{k=1}^N e^(d_k/2\sigma)}
+</math><br></br>
+where <math>Y(x)</math> is the prediction value of input <math>x</math>.<br></br>
+<math>
+d_k=(x-xi)^T(x-xi).
+</math><br></br>
+where <math>d_k</math> is the distance between the training samples <math>xi</math> and the input <math>x</math>.
 ==References==