A '''probabilistic neural network (PNN)''' <ref name="pnn-book">{{cite book |last1=Mohebali |first1=Behshad |last2=Tahmassebi |first2=Amirhessam |last3=Meyer-Baese |first3=Anke |last4=Gandomi |first4=Amir H. |title=Probabilistic neural networks: a brief overview of theory, implementation, and application |date=2020 |publisher=Elsevier |pages=347–367 |doi=10.1016/B978-0-12-816514-0.00014-X |s2cid=208119250 }}</ref> is a [[feedforward neural network]], which is widely used in classification and pattern recognition problems. In the PNN algorithm, the parent probability distribution function (PDF) of each class is approximated by a [[Kernel density estimation|Parzen window]] and a non-parametric function. Then, using PDF of each class, the class probability of a new input data is estimated and Bayes’ rule is then employed to allocate the class with highest posterior probability to new input data. By this method, the probability of mis-classification is minimized.<ref>{{Cite journal|url=https://www.researchgate.net/publication/312519997|title=Competitive probabilistic neural network|year=2017|doi=10.3233/ICA-170540|last1=Zeinali|first1=Yasha|last2=Story|first2=Brett A.|journal=Integrated Computer-Aided Engineering|volume=24|issue=2|pages=105–118}}</ref> This type of ANN was derived from the [[Bayesian network]]<ref>{{cite web |url=http://herselfsai.com/2007/03/probabilistic-neural-networks.html |title=ArchivedProbabilistic copyNeural Networks |access-date=2012-03-22 |url-status=dead |archive-url=https://web.archive.org/web/20101218121158/http://herselfsai.com/2007/03/probabilistic-neural-networks.html |archive-date=2010-12-18 }}</ref> and a statistical algorithm called [[Kernel Fisher discriminant analysis]].<ref>{{cite web |url=http://www.psi.toronto.edu/~vincent/research/presentations/PNN.pdf |title=Archived copy |access-date=2012-03-22 |url-status=dead |archive-url=https://web.archive.org/web/20120131053940/http://www.psi.toronto.edu/~vincent/research/presentations/PNN.pdf |archive-date=2012-01-31 }}</ref> It was introduced by D.F. Specht in 1966.<ref>{{Cite journal|last=Specht|first=D. F.|date=1967-06-01|title=Generation of Polynomial Discriminant Functions for Pattern Recognition|journal=IEEE Transactions on Electronic Computers|volume=EC-16|issue=3|pages=308–319|doi=10.1109/PGEC.1967.264667|issn=0367-7508}}</ref><ref name=Specht1990>{{Cite journal | last1 = Specht | first1 = D. F. | doi = 10.1016/0893-6080(90)90049-Q | title = Probabilistic neural networks | journal = Neural Networks | volume = 3 | pages = 109–118 | year = 1990 }}</ref> In a PNN, the operations are organized into a multilayered feedforward network with four layers:
* Input layer
* Pattern layer
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==Layers ==
PNN is often used in classification problems.<ref>{{cite web |url=http://www.mathworks.in/help/toolbox/nnet/ug/bss38ji-1.html |title=ArchivedProbabilistic copyNeural Networks :: Radial Basis Networks (Neural Network Toolbox™) |website=www.mathworks.in |access-date=6 June 2022 |archive-url=https://archive.today/20120804150441/http://www.mathworks.in/help/toolbox/nnet/ug/bss38ji-1.html |archive-date=4 August 2012 |url-status=dead}}</ref> When an input is present, the first layer computes the distance from the input vector to the training input vectors. This produces a vector where its elements indicate how close the input is to the training input. The second layer sums the contribution for each class of inputs and produces its net output as a vector of probabilities. Finally, a compete transfer function on the output of the second layer picks the maximum of these probabilities, and produces a 1 (positive identification) for that class and a 0 (negative identification) for non-targeted classes.
=== Input layer ===
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== Advantages==
There are several advantages and disadvantages using PNN instead of [[multilayer perceptron]].<ref>{{cite web |url=http://www.dtreg.com/pnn.htm |title=ArchivedProbabilistic copyand General Regression Neural Networks |access-date=2012-03-22 |url-status=dead |archive-url=https://web.archive.org/web/20120302075157/http://www.dtreg.com/pnn.htm |archive-date=2012-03-02 }}</ref>
* PNNs are much faster than multilayer perceptron networks.
* PNNs can be more accurate than multilayer perceptron networks.
