Bayes’ Rule in Probabilistic Neural Network
In PNNs, Bayes’ Rule is used to estimate the posterior probability of each class given the input data. The process involves the following steps:
- Probability Density Function (PDF) Estimation: The PNN approximates the probability density function (PDF) of each class using the Parzen window technique, which is a non-parametric method. This involves summing the kernel outputs (e.g., Gaussian functions) for all training samples belonging to a particular class.
- Class Probability Estimation: For a new input vector, the PNN calculates the probability of the input belonging to each class by evaluating the PDF for each class. This is done by summing the kernel outputs for the input vector across all training samples of that class.
Probabilistic Neural Networks: A Statistical Approach to Robust and Interpretable Classification
Probabilistic Neural Networks (PNNs) are a class of artificial neural networks that leverage statistical principles to perform classification tasks. Introduced by Donald Specht in 1990, PNNs have gained popularity due to their robustness, simplicity, and ability to handle noisy data. This article delves into the intricacies of PNNs, providing a detailed explanation, practical examples, and insights into their applications.
Table of Content
- What is Probabilistic Neural Network (PNN)?
- Bayes’ Rule in Probabilistic Neural Network
- How Does PNNs Work?
- Implementation of Probabilistic Neural Network
- Advantages and Disadvantages of PNNs
- Use-Cases and Applications of PNN