02-06-2012, 11:58 AM
Adaptive Network Based Fuzzy Inference Systems (ANFIS)
[attachment=23962]
As we have already seen, fuzzy systems present particular problems to a developer:
• Rules. The if-then rules have to be determined somehow. This is usually done by ‘knowledge acquisition’ from an expert. It is a time consuming process that is fraught with problems.
• Membership functions. A fuzzy set is fully determined by its membership function. This has to be determined. If it’s gaussian then what are the parameters?
The ANFIS approach learns the rules and membership functions from data.
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.
This then is how, typically, the input vector is fed through the network layer by layer. We now consider how the ANFIS learns the premise and consequent parameters for the membership functions and the rules.
There are a number of possible approaches but we will discuss the hybrid learning algorithm proposed by Jang, Sun and Mizutani (Neuro-Fuzzy and Soft Computing, Prentice Hall, 1997) which uses a combination of Steepest Descent and Least Squares Estimation (LSE). This can get very complicated (!) so here I will provide a very high level description of how the algorithm operates.
It can be shown that for the network described if the premise parameters are fixed the output is linear in the consequent parameters.
[attachment=23962]
As we have already seen, fuzzy systems present particular problems to a developer:
• Rules. The if-then rules have to be determined somehow. This is usually done by ‘knowledge acquisition’ from an expert. It is a time consuming process that is fraught with problems.
• Membership functions. A fuzzy set is fully determined by its membership function. This has to be determined. If it’s gaussian then what are the parameters?
The ANFIS approach learns the rules and membership functions from data.
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.
This then is how, typically, the input vector is fed through the network layer by layer. We now consider how the ANFIS learns the premise and consequent parameters for the membership functions and the rules.
There are a number of possible approaches but we will discuss the hybrid learning algorithm proposed by Jang, Sun and Mizutani (Neuro-Fuzzy and Soft Computing, Prentice Hall, 1997) which uses a combination of Steepest Descent and Least Squares Estimation (LSE). This can get very complicated (!) so here I will provide a very high level description of how the algorithm operates.
It can be shown that for the network described if the premise parameters are fixed the output is linear in the consequent parameters.