12-12-2012, 01:13 PM
Radial Basis Function (RBF) Networks
Radial Basis Function.ppt (Size: 137 KB / Downloads: 26)
RBF network
This is becoming an increasingly popular neural network with diverse applications and is probably the main rival to the multi-layered perceptron
Much of the inspiration for RBF networks has come from traditional statistical pattern classification techniques
The basic architecture for a RBF is a 3-layer network, as shown in Fig.
The input layer is simply a fan-out layer and does no processing.
The second or hidden layer performs a non-linear mapping from the input space into a (usually) higher dimensional space in which the patterns become linearly separable.
Output layer
The final layer performs a simple weighted sum with a linear output.
If the RBF network is used for function approximation (matching a real number) then this output is fine.
However, if pattern classification is required, then a hard-limiter or sigmoid function could be placed on the output neurons to give 0/1 output values.
Clustering
The unique feature of the RBF network is the process performed in the hidden layer.
The idea is that the patterns in the input space form clusters.
If the centres of these clusters are known, then the distance from the cluster centre can be measured.
Furthermore, this distance measure is made non-linear, so that if a pattern is in an area that is close to a cluster centre it gives a value close to 1.
Beyond this area, the value drops dramatically.
The notion is that this area is radially symmetrical around the cluster centre, so that the non-linear function becomes known as the radial-basis function.
Gaussian function
The most commonly used radial-basis function is a Gaussian function
In a RBF network, r is the distance from the cluster centre.
The equation represents a Gaussian bell-shaped curve, as shown in Fig.
Training hidden layer
These become the new values for the centre corresponding to class 1.
Repeated for all data found to be in class 2, then class 3 and so on until class k is dealt with - we now have k new centres.
Process of measuring the distance between the centres and each item of data and re-classifying the data is repeated until there is no further change – i.e. the sum of the distances monitored and training halts when the total distance no longer falls.