Ann

Purpose

Predictions based on Artificial Neural Network (ANN) regression models.

Synopsis

ann - Launches an Analysis window with ANN as the selected method.

[model] = ann(x,y,options);

[model] = ann(x,y, nhid, options);

[pred] = ann(x,model,options);

[valid] = ann(x,y,model,options);

Description

Build an ANN model from input X and Y block data using the specified number of layers and layer nodes. Alternatively, if a model is passed in ANN makes a Y prediction for an input test X block. The ANN model contains quantities (weights etc) calculated from the calibration data. When a model structure is passed in to ANN then these weights do not need to be calculated.

There are two implementations of ANN available referred to as 'BPN' and 'Encog'.

BPN is a feedforward ANN using backpropagation training and is implemented in Matlab.

Encog is a feedforward ANN using Resilient Backpropagation training. See Rprop for further details.

Encog is implemented using the Encog framework Encog provided by Heaton Research, Inc, under the Apache 2.0 license. Further details of Encog Neural Network features are available at Encog Documentation. BPN is the ANN version used by default but the user can specify the option 'algorithm' = 'encog' to use Encog instead. Both implementations should give similar results but one may be faster than the other for different datasets. BPN is currently the only version which calculates RMSECV.

Inputs

• x = X-block (predictor block) class "double" or "dataset", containing numeric values,
• y = Y-block (predicted block) class "double" or "dataset", containing numeric values,
• nhid = number of nodes in a single hidden layer ANN, or vector of two two numbers, indicating a two hidden layer ANN, representing the number of nodes in the two hidden layers. (this takes precedence over options nhid1 and nhid2),
• model = previously generated model (when applying model to new data).

Outputs

• model = a standard model structure model with the following fields (see Standard Model Structure):
  • modeltype: 'ANN',
  • datasource: structure array with information about input data,
  • date: date of creation,
  • time: time of creation,
  • info: additional model information,
  • pred: 2 element cell array with
    • model predictions for each input block (when options.blockdetail='normal' x-block predictions are not saved and this will be an empty array)
  • detail: sub-structure with additional model details and results, including:
    • model.detail.ann.W: Structure containing details of the ANN, including the ANN type, number of hidden layers and the weights.

• pred a structure, similar to model for the new data.

Training Termination

The ANN is trained on a calibration dataset to minimize prediction error, RMSEC. It is important to not overtrain, however, so some some criteria for ending training are needed.

BPN determines the optimal number of learning iteration cycles by selecting the minumum RMSECV based on the calibration data over a range of learning iterations values (1 to options.learncycles). The cross-validation used is determined by option cvi, or else by cvmethod. If neither of these are specified then the minumum RMSEP using a single subset of samples from a 5-fold random split of the calibration data is used. This RMSECV value is based on pre-processed, scaled values and so it is not saved in the model.rmsecv field. Apply cross-validation (see below) to add this information to the model.

Encog training terminates whenever either a) RMSE becomes smaller than the option 'terminalrmse' value, or b) the rate of improvement of RMSE per 100 training iterations becomes smaller than the option 'terminalrmserate' value, or c) time exceeds the option 'maxseconds' value (though results are not optimal if is stopped prematurely by this time limit). Note these RMSE values refer to the internal preprocessed and scaled y values.

Cross-validation

Cross-validation can be applied to ANN when using either the ANN Analysis window or the command line. From the Analysis window specify the cross-validation method in the usual way (clicking on the model icon's red check-mark, or the "Choose Cross-Validation" link in the flowchart). In the cross-validation window the "Maximum Number of Nodes" specifies how many hidden-layer 1 nodes to test over. Viewing RMSECV versus number of hidden-layer 1 nodes (toolbar icon to left of Scores Plot) is useful for choosing the number of layer 1 nodes. From the command line use the crossval method to add crossvalidation information to an existing model.

Options

options = a structure array with the following fields:

• display : [ 'off' |{'on'}] Governs display
• plots: [ {'none'} | 'final' ] governs plotting of results.
• blockdetails : [ {'standard'} | 'all' ] extent of detail included in model. 'standard' keeps only y-block, 'all' keeps both x- and y- blocks.
• waitbar : [ 'off' |{'auto'}| 'on' ] governs use of waitbar during analysis. 'auto' shows waitbar if delay will likely be longer than a reasonable waiting period.
• algorithm : [{'bpn'} | 'encog'] ANN implementation to use.
• nhid1 : [{2}] Number of nodes in first hidden layer.
• nhid2 : [{0}] Number of nodes in second hidden layer.
• learnrate : [0.125] ANN backpropagation learning rate (bpn only).
• learncycles : [20] Number of ANN learning iterations (bpn only).
• terminalrmse : [0.05] Termination RMSE value (of scaled y) for ANN iterations (encog only).
• terminalrmserate : [1.e-9] Termination rate of change of RMSE per 100 iterations (encog only).
• maxseconds : [{20}] Maximum duration of ANN training in seconds (encog only).
• preprocessing: {[] []} preprocessing structures for x and y blocks (see PREPROCESS).
• compression: [{'none'}| 'pca' | 'pls' ] type of data compression to perform on the x-block prior to calculaing or applying the ANN model. 'pca' uses a simple PCA model to compress the information. 'pls' uses a pls model. Compression can make the ANN more stable and less prone to overfitting.
• compressncomp: [1] Number of latent variables (or principal components to include in the compression model.
• compressmd: [{'yes'} | 'no'] Use Mahalnobis Distance corrected.
• cvmethod : [{'con'} | 'vet' | 'loo' | 'rnd'] CV method, OR [] for Kennard-Stone single split.
• cvsplits : [{5}] Number of CV subsets.
• cvi : M element vector with integer elements allowing user defined subsets. (cvi) is a vector with the same number of elements as x has rows i.e., length(cvi) = size(x,1). Each cvi(i) is defined as:

cvi(i) = -2 the sample is always in the test set.

cvi(i) = -1 the sample is always in the calibration set,

cvi(i) = 0 the sample is always never used, and

cvi(i) = 1,2,3... defines each test subset.

Additional information on the ‘BPN’ ANN implementation

The “BPN” implementation of ANN is a conventional feedforward back-propagation neural network where the weights are updated, or ‘trained’, so as to reduce the magnitude of the prediction error, except that the gradient-descent method of updating the weights is different from the usual “delta rule” approach. In the traditional delta-rule method the weights are changed at each increment of training time by a constant fraction of the contributing error gradient terms, leading to a reduced prediction error. In this “BPN” implementation the search for optimal weights by gradient-descent is treated as a continuous system, rather than incremental. The evolution of the weights with respect to training time is solved as a set of differential equations using a solver appropriate for systems where the solution (weights) may involve very different timescales. Most weights evolve slowly towards their final values but some weights may have periods of faster change. A reference paper for the BPN implementation is:

Owens A J and Filkin D L 1989 Efficient training of the back propagation network by solving a system of stiff ordinary differential equations Proc. Int. Joint Conf. on Neural Networks vol II (IEEE Press) pp 381–6.

Algorithm parameters: learncycles and learnrate

This BPN technique results in much faster training that with the traditional delta-rule approach. The training is governed by two parameters, ‘learncycles’ and ‘learnrate’. The learnrate parameter specifies the training time duration of the first learncycle. Each subsequent learncycle’s time duration is twice the previous learncycle’s duration. The performance of the ANN is evaluated at the end of each learncycle interval by calculating the cross-validation prediction error, RMSECV. The RMSECV initially decreases rapidly with training time but eventually starts to increase again as the ANN begins to overfit the data. The number of training cycles which yields the minimum RMSECV therefore provides an estimate of the optimal ANN training duration, for the given learnrate value. The ANN model contains these RMSECV values in model.detail.ann.rmsecviter, and the optimal, minimum RMSECV occurs at index model.detail.ann.niter, which will be smaller than or equal to the learncycles value. It is useful to check rmsecviter to see if a minimum RMSECV has been attained, but also to see if you are using too many learn cycles. Reducing the number of learncycles can significantly speed up ANN training. Note, the model.detail.ann.rmsecviter values are only used to pick the optimal number of learncycles. These rmsecviter values are calculated using scaled y and should not be compared to the reported RMSEC, RMSECV or RMSEP.

Usage from ANN Analysis window

The command line function “ann” has input parameter “nhid” specifying the number of nodes in the hidden layer(s) and builds the optimal model for that network. When using the ANN Analysis window, however, it is possible to specify a scan over a range of hidden layer nodes to use. This is enabled by setting the “Maximum number of Nodes” value in the cross-validation window. This only works for BPN ANNs having a single hidden layer. This causes ANN models to be built for the range of hidden layer nodes up to the specified number and the resulting RMSECV plotted versus the number of nodes is shown by clicking on the “Plot cross-validation results” plot icon in the ANN Analysis window’s toolbar. This can be useful for deciding how many nodes to use. Note that this plot is only advisory. The resulting model is built with the input parameter number of nodes, ‘nhid’, and its model.detail.rmsecv value relates to this number of nodes. It is important to check for the optimal number of nodes to use in the ANN but this feature can greatly lengthen the time taken to build the ANN model and should be be set = 1 once the number of hidden nodes is decided.

Summary of model building speed-up settings

From the Analysis window:

ANN in PLS_Toolbox or Solo version 8.2 can be very slow if you use cross-validation (CV). This is mostly due to the CV settings window also specifying a test to find the optimal number of hidden layer 1 nodes, testing ANN models with 1, 2, …,20 nodes, each with CV. This is set by the top slider field “Maximum Number of Nodes L1”. For example, if you want to build an ANN model with 4 layer 1 nodes (using the “ANN Settings” field) but leave the CV settings window’s top slider set = 20, then you will actually build 20 models, each with CV, and save the RMSECV from each. This can be very slow, especially for the models with many nodes.

To make ANN perform faster it is recommended that you drag this CV window’s “Maximum Number of Nodes L1” slider to the left, setting = 1, unless you really want to see the results of such a parameter search over the range specified by this slider. This is the default in PLS_Toolbox and Solo versions after version 8.2. The RMSECV versus number of Layer 1 Nodes can be seen by clicking on the “Plot cross-validation results” icon (next to the Scores Plot icon).

Summary: To make ANN perform faster:

1. Move the top CV slider to the left, setting value = 1.

2. Turning CV off or using a small number of CV splits.

3. Choose to use a small number of L1 nodes in the ANN settings window.

4. Don't use 2 hidden layers. This is very slow.

From the command line

1. Initially build ANN without cross-validation so as to decide on values for learnrate and learncycles by examining where the minimum value of model.detail.ann.rmscviter occurs versus learncycles. Note this uses a single-split CV to estimate rmsecv when the ANN cross-validation is set as "None". It is inefficient to use a larger than necessary value for option "learncycles".

2. Determine the number of hidden layer nodes to use by building a range of models with different number of nodes, nhid1, nhid2. If using the ANN Analysis window and the ANN has a single hidden layer then this can be done conveniently by using the “Maximum number of Nodes L1” setting in the cross-validation settings window. It is best to use a simple cross-validation at this stage, with a small number of splits and iterations at this survey stage.

See Also

analysis, crossval, lwr, modelselector, pls, pcr, svm