11-06-2012, 12:53 PM
Adaptive Network Based Fuzzy Inference Systems (ANFIS)
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ANFIS is an adaptive network. An adaptive network is network of nodes and directional links. Associated with the network is a learning rule - for example back propagation. It’s called adaptive because some, or all, of the nodes have parameters which affect the output of the node. These networks are learning a relationship between inputs and outputs.
Adaptive networks covers a number of different approaches but for our purposes we will investigate in some detail the method proposed by Jang known as ANFIS.
The ANFIS architecture is shown below. The circular nodes represent nodes that are fixed whereas the square nodes are nodes that have parameters to be learnt.
The Forward Pass
Present the input vector
Calculate the node outputs layer by layer
Repeat for all data and formed
Identify parameters in using Least Squares
Compute the error measure for each training pair
Backward Pass
Use steepest descent algorithm to update parameters in (backpropagation)
For given fixed values of the parameters in found by this approach are guaranteed to be the global optimum point.
