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Comparison of anfis and Neuro-Fuzzy Designer Functionality

This topic discusses the arguments and range components of the command-line function anfis and the analogous functionality of the Neuro-Fuzzy Designer.

You can configure the training options for the anfis command using an anfisOptions option set.

opt = anfisOptions;
[fismat1,trnError,ss,fismat2,chkError] = anfis(trnData,opt);
where trnData is the training data. To use default training options, omit opt. You can modify the default option set using dot notation. For more information on the available options and their default values, see the anfisOptions reference page. All output arguments other than fismat1, the tuned fuzzy system, are optional.

When you open the Neuro-Fuzzy Designer, only the training data set must exist before implementing anfis. In addition, the step-size is fixed when the adaptive neuro-fuzzy system is trained using this app.

Training Data

The training data, trnData, is a required argument to anfis, and to the Neuro-Fuzzy Designer. Each row of trnData is a desired input/output pair of the target system you want to model. Each row starts with an input vector and is followed by an output value. Therefore, the number of rows of trnData is equal to the number of training data pairs. Since there is only one output, the number of columns of trnData is equal to the number of inputs plus one.

Input FIS Object

You can define the FIS object to tune using the opt.InitialFIS training option. You can create this object using:

  • The Fuzzy Logic Designer

  • The Membership Function Editor

  • The Rule Editor from the Neuro-Fuzzy Designer (which allows an FIS object to be loaded from a file or the MATLAB® workspace)

  • The command-line function, genfis (for which you only specify numbers and types of membership functions)

The FIS object contains both the model structure (which specifies such items as the number of rules in the FIS and the number of membership functions for each input) and the parameters (which specify the shapes of membership functions).

There are two methods that anfis learning employs for updating membership function parameters, which you can select using the opt.OptimizationMethod training option:

  • Backpropagation for all parameters (a steepest descent method)

  • A hybrid method consisting of backpropagation for the parameters associated with the input membership functions, and least squares estimation for the parameters associated with the output membership functions

As a result, the training error decreases, at least locally, throughout the learning process. Therefore, the more the initial membership functions resemble the optimal ones, the easier it is for the model parameter training to converge. Human expertise about the target system to be modeled can aid in setting up these initial membership function parameters in the FIS object.

The genfis function, when used with grid partitioning, produces an FIS object based on a fixed number of membership functions. This object can cause an excessive number of rules when the number of inputs is moderately large; that is, more than four or five. Fuzzy Logic Toolbox™ software offers a method that provides for some dimension reduction in the fuzzy inference system: you can generate an FIS object using the clustering algorithm discussed in Subtractive Clustering. To use the clustering algorithm, you must select the Sub. Clustering option in the Generate FIS portion of the Neuro-Fuzzy Designer before the FIS is generated. This subtractive clustering method partitions the data into clusters, and generates an FIS with the minimum number of rules required to distinguish the fuzzy qualities associated with each clusters.

Training Options

The Neuro-Fuzzy Designer allows you to choose your desired error tolerance and number of training epochs.

For anfis command, you can specify training the training termination condition and gradient descent step size. To specify the following options, first create a default anfisOptions option set, opt. You can then modify the options using dot notation.

  • opt.EpochNumber — Number of training epochs (default = 10)

  • opt.ErrorGoal — Training error goal (default = 0)

  • opt.InitialStepSize — Initial step-size (default = 0.01)

  • opt.StepSizeDecreaseRate — Step-size decrease rate (default = 0.9)

  • opt.StepSizeIncreaseRate — Step-size increase rate (default = 1.1)

If you do not modify an option in opt, the default value is used. The training process stops if the designated epoch number is reached or the error goal is achieved, whichever comes first.

Usually, the step-size profile is a curve that increases initially, reaches some maximum, and then decreases for the remainder of the training. You achieve this ideal step-size profile by adjusting the initial step-size and the increase and decrease rates (opt.InitialStepSize, opt.StepSizeDecreaseRate, opt.StepSizeIncreaseRate). The default values are configured to cover a wide range of learning tasks. For any specific application, you can modify these step-size options to optimize the training. However, there are no user-specified step-size options for training the adaptive neuro-fuzzy inference system generated using the Neuro-Fuzzy Designer.

Display Options

Display options apply only to the command-line function anfis. You can specify what training progress information to display in the MATLAB Command Window. As with the training options, you specify the display options using the anfisOptions option set, opt . For each display option, if you specify a value of 1 (the default value), the corresponding data is displayed. Specifying a value of 0 suppresses the display:

  • opt.DisplayANFISInformation — Display ANFIS information at the start of training

  • opt.DisplayErrorValues — Display the training error at each epoch

  • opt.DisplayStepSize — Display the step-size each time it changes.

  • opt.DisplayFinalResults — Display the final training error and validation error

Method

Both the Neuro-Fuzzy Designer and the command-line anfis apply either a backpropagation form of the steepest descent method for membership function parameter estimation, or a hybrid combination of backpropagation and the least-squares methods. The choices for this argument are hybrid or backpropagation. To specify the training method for the anfis function, use the opt.OptimizationMethod training option as either 1 (hybrid) or 0 (backpropagation).

Output FIS Object for Training Data

fismat1 is the output FIS object corresponding to the minimum training error. This FIS object is the one that you use to represent the fuzzy system when there is no checking data used for model cross-validation. fismat1 corresponds to the FIS object that the Neuro-Fuzzy Designer saves when the checking data option is not used. For more information on cross-validation using checking data, see Checking Data.

Training Error

The training error is the difference between the training data output value, and the output of the fuzzy inference system corresponding to the same training data input value (the one associated with that training data output value). The training error trnError records the root mean squared error (RMSE) of the training data set at each epoch. fismat1 is the snapshot of the FIS object when the training error measure is at its minimum.

The Neuro-Fuzzy Designer plots the training error versus epochs curve as the system is trained.

Step-Size

You cannot control the step-size options with the Neuro-Fuzzy Designer. Using the command-line anfis, the step-size array ss records the step-size during the training. Plotting ss gives the step-size profile, which serves as a reference for adjusting the initial step-size (opt.InitialStepSize) and the corresponding decrease and increase rates. The step-size for the command-line function anfis is updated according to the following guidelines:

  • If the error undergoes four consecutive reductions, increase the step-size by multiplying it by a constant (opt.StepSizeIncreaseRate) greater than one.

  • If the error undergoes two consecutive combinations of one increase and one reduction, decrease the step-size by multiplying it by a constant (opt.StepSizeDecreaseRate) less than one.

The default value for the initial step-size is 0.01; the default values for opt.StepSizeIncreaseRate and opt.StepSizeDecreaserate are 1.1 and 0.9, respectively.

Checking Data

The checking data, opt.ValidationData, is used for testing the generalization capability of the fuzzy inference system at each epoch. The checking data has the same format as the training data, and its elements are distinct from those of the training data.

The checking data is important for learning tasks for which the input number is large or the data itself is noisy. A fuzzy inference system should track a given input/output data set well. Because the model structure used for anfis is fixed with a large number of parameters, there is a tendency for the model to overfit the data on which it is trained, especially for many training epochs. If overfitting does occur, the fuzzy inference system may not respond well to other independent data sets, especially if they are noisy. A validation or checking data set can be useful for these situations. This data set is used to cross-validate the fuzzy inference model. This cross-validation requires applying the checking data to the model and then seeing how well the model responds to this data.

When the checking data option is used with anfis, either via the command line, or using the Neuro-Fuzzy Designer, the checking data is applied to the model at each training epoch. When the command-line anfis is invoked, the model parameters that correspond to the minimum checking error are returned via the output argument fismat2. When both training and checking data are loaded, the FIS membership function parameters computed using the Neuro-Fuzzy Designer are associated with the training epoch that has a minimum checking error.

The use of the minimum checking data error epoch to set the membership function parameters assumes the checking data:

  • Is similar enough to the training data that the checking data error decreases as the training begins.

  • Increases at some point in the training after the data overfitting occurs.

For information on using checking data, see Checking Data Does Not Validate Model.

Output FIS Object for Checking Data

The output of the command-line anfis, fismat2, is the output FIS object with the minimum checking error. This FIS object is the one that you should use for further calculation if checking data is used for cross-validation. fismat2 is only returned if you specify validation data using opt.ValidationData.

fismat2 corresponds to the FIS object that the Neuro-Fuzzy Designer saves when the checking data option is used.

Checking Error

The checking error is the difference between the checking data output value, and the output of the fuzzy inference system corresponding to the same checking data input value, which is the one associated with that checking data output value. The checking error chkError records the RMSE for the checking data at each epoch. fismat2 is the snapshot of the FIS object when the checking error is at its minimum. chkError is only returned if you specify validation data using opt.ValidationData.

The Neuro-Fuzzy Designer plots the checking error versus epochs curve as the system is trained.

See Also

Apps

Functions

Related Topics