A probabilistic neural network (PNN) is a

feedforward neural network A feedforward neural network (FNN) is an artificial neural network wherein connections between the nodes do ''not'' form a cycle. As such, it is different from its descendant: recurrent neural networks. The feedforward neural network was the ...

, 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 In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method to estimate the probability density function of a random variable based on ''kernels'' as wei ...

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. This type of

artificial neural network Artificial neural networks (ANNs), usually simply called neural networks (NNs) or neural nets, are computing systems inspired by the biological neural networks that constitute animal brains. An ANN is based on a collection of connected unit ...

(ANN) was derived from the

Bayesian network A Bayesian network (also known as a Bayes network, Bayes net, belief network, or decision network) is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). Bay ...

and a statistical algorithm called

Kernel Fisher discriminant analysis In statistics, kernel Fisher discriminant analysis (KFD), also known as generalized discriminant analysis and kernel discriminant analysis, is a kernelized version of linear discriminant analysis (LDA). It is named after Ronald Fisher. Linear di ...

. It was introduced by D.F. Specht in 1966. In a PNN, the operations are organized into a multilayered feedforward network with four layers: * Input layer * Pattern layer * Summation layer * Output layer

Layers

PNN is often used in classification problems. 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

Each neuron in the input layer represents a predictor variable. In categorical variables, ''N-1'' neurons are used when there are ''N'' number of categories. It standardizes the range of the values by subtracting the median and dividing by the

interquartile range In descriptive statistics, the interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data. The IQR may also be called the midspread, middle 50%, fourth spread, or H‑spread. It is defined as the difference ...

. Then the input neurons feed the values to each of the neurons in the hidden layer.

Pattern layer

This layer contains one neuron for each case in the training data set. It stores the values of the predictor variables for the case along with the target value. A hidden neuron computes the

Euclidean distance In mathematics, the Euclidean distance between two points in Euclidean space is the length of a line segment between the two points. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, therefor ...

of the test case from the neuron's center point and then applies the

radial basis function kernel In machine learning, the radial basis function kernel, or RBF kernel, is a popular kernel function used in various kernelized learning algorithms. In particular, it is commonly used in support vector machine classification. The RBF kernel on two s ...

using the sigma values.

Summation layer

For PNN there is one pattern neuron for each category of the target variable. The actual target category of each training case is stored with each hidden neuron; the weighted value coming out of a hidden neuron is fed only to the pattern neuron that corresponds to the hidden neuron’s category. The pattern neurons add the values for the class they represent.

Output layer

The output layer compares the weighted votes for each target category accumulated in the pattern layer and uses the largest vote to predict the target category.

Advantages

There are several advantages and disadvantages using PNN instead of

multilayer perceptron A multilayer perceptron (MLP) is a fully connected class of feedforward artificial neural network (ANN). The term MLP is used ambiguously, sometimes loosely to mean ''any'' feedforward ANN, sometimes strictly to refer to networks composed of mu ...

. * PNNs are much faster than multilayer perceptron networks. * PNNs can be more accurate than multilayer perceptron networks. * PNN networks are relatively insensitive to outliers. * PNN networks generate accurate predicted target probability scores. * PNNs approach Bayes optimal classification.

Disadvantages

* PNN are slower than multilayer perceptron networks at classifying new cases. * PNN require more memory space to store the model.

Applications based on PNN

* probabilistic neural networks in modelling structural deterioration of stormwater pipes. * probabilistic neural networks method to gastric endoscope samples diagnosis based on FTIR spectroscopy. * Application of probabilistic neural networks to population pharmacokineties. * Probabilistic Neural Networks to the Class Prediction of Leukemia and Embryonal Tumor of Central Nervous System. * Ship Identification Using Probabilistic Neural Networks. * Probabilistic Neural Network-Based sensor configuration management in a wireless ''ad hoc'' network. * Probabilistic Neural Network in character recognizing. * Remote-sensing Image Classification.

References

{{Reflist Neural network architectures