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A '''probabilistic neural network (PNN)''' 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 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 web|url=https://www.researchgate.net/publication/312519997_Competitive_probabilistic_neural_network|title=Competitive probabilistic neural network (PDF Download Available)|website=ResearchGate|language=en|access-date=2017-03-16}}</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=Archived copy |accessdate=2012-03-22 |deadurl=yes |archiveurl=https://web.archive.org/web/20101218121158/http://herselfsai.com/2007/03/probabilistic-neural-networks.html |archivedate=2010-12-18 |df= }}</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 |accessdate=2012-03-22 |deadurl=yes |archiveurl=https://web.archive.org/web/20120131053940/http://www.psi.toronto.edu/~vincent/research/presentations/PNN.pdf |archivedate=2012-01-31 |df= }}</ref> It was introduced by D.F. Specht in the 1966.<ref>{{Cite journal|last=Specht|first=D. F.|date=1967-06-01|title=Generation of Polynomial Discriminant Functions for Pattern Recognition|url=http://ieeexplore.ieee.org/document/4039069/|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 | pmid = | pmc = }}</ref> In a PNN, the operations are organized into a multilayered feedforward network with four layers:
* Input layer
*
*
* Output layer
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