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Radial Basis Function (RBF) Networks and Their Applications

Radial Basis Function (RBF) Networks are a type of artificial neural network used for classification and regression tasks. They rely on radial basis functions as activation functions, making them well-suited for function approximation, pattern recognition, and interpolation.

Architecture of an RBF Network

1. Input Layer: Passes input features to the hidden layer.

2. Hidden Layer:

   • Contains RBF neurons, each centered at a prototype point.

   • Computes the distance between input and the neuron’s center.

   • Uses a Gaussian function to transform inputs:

     $$\phi(x) = e^{-\frac{{||x - c||^2}}{2\sigma^2}}$$

     where $c$ is the neuron’s center and $\sigma$ is the spread parameter.

3. Output Layer:

   • Combines hidden layer outputs using linear weights to produce the final result.

How RBF Networks Are Used

1. Classification

• Computes similarity between input and class centers.

• Assigns a class label based on the highest activation.

• Example: Handwriting recognition, face detection.

2. Regression

• Learns function mapping from input to output.

• Used for time series forecasting, financial modeling.

Advantages of RBF Networks

• Fast training compared to deep networks.

• Good generalization for smooth decision boundaries.

• Handles non-linear relationships effectively.

RBF networks are widely used in real-time classification, function approximation, and robotics control due to their efficiency and ability to model complex patterns.