Trains a multilayered feedforward neural network.

The type double function is imsls_d_mlff_network_trainer.

An array of length 5 containing the summary statistics from the network training, organized as follows:

This space can be released by using the imsls_free function.

If training is unsuccessful, NULL is returned.

Function imsls_f_mlff_network_trainer trains a multilayered feedforward neural network returning the forecasts for the training data, their residuals, the optimum weights and the gradients associated with those weights. Linkages among perceptrons allow for skipped layers, including linkages between inputs and perceptrons. The linkages and activation function for each perceptron, including output perceptrons, can be individually configured. For more details, see optional arguments IMSLS_LINK_ALL, IMSLS_LINK_LAYER, and IMSLS_LINK_NODE in imsls_f_mlff_network.

Neural network training patterns consist of the following three types of data:

The first data type contains the encoding of any nominal input attributes. If binary encoding is used, this encoding consists of creating columns of zeros and ones for each class value associated with every nominal attribute. If only one attribute is used for input, then the number of columns is equal to the number of classes for that attribute. If more columns appear in the data, then each nominal attribute is associated with several columns, one for each of its classes.

Each column consists of zeros, if that classification is not associated with this case, otherwise, one if that classification is associated. Consider an example with one nominal variable and two classes: male and female (male, male, female, male, female). With binary encoding, the following matrix is sent to the training engine to represent this data:

Continuous input and output data are passed to the training engine using two double precision arrays: continuous and output. The number of rows in each of these matrices is n_patterns. The number of columns in continuous and output, corresponds to the number of input and output variables, respectively.

The network configuration consists of the following:

This description is passed into imsls_f_mlff_network_trainer using the structure Imsls_f_NN_Network. See imsls_f_mlff_network.

The training efficiency determines the time it takes to train the network. This is controlled by several factors. One of the most important factors is the initial weights used by the optimization algorithm. These are taken from the initial values provided in the structure Imsls_f_NN_Network, network‑>links[i].weight. Equally important are the scaling and filtering applied to the training data.

In most cases, all variables, particularly output variables, should be scaled to fall within a narrow range, such as [0, 1]. If variables are unscaled and have widely varied ranges, then numerical overflow conditions can terminate network training before an optimum solution is calculated.

Output from imsls_f_mlff_network_trainer consists of scaled values for the network outputs, a corresponding forecast array for these outputs, a weights array for the trained network, and the training statistics. The Imsls_f_NN_Network structure is updated with the weights and bias values and can be used as input to imsls_f_mlff_network_forecast.

The trained network can be saved and retrieved using imsls_f_mlff_network_write and imsls_f_mlff_network_read.

This example trains a two-layer network using 100 training patterns from one nominal and one continuous input attribute. The nominal attribute has three classifications which are encoded using binary encoding. This results in three binary network input columns. The continuous input attribute is scaled to fall in the interval [0,1].

The network training targets were generated using the relationship:

where X1, X2, X3 are the three binary columns, corresponding to the categories 1‑3 of the nominal attribute, and X4 is the scaled continuous attribute.

The structure of the network consists of four input nodes and two layers, with three perceptrons in the hidden layer and one in the output layer. The following figure illustrates this structure:

There are a total of 15 weights and 4 bias weights in this network. The activation functions are all linear.

Since the target output is a linear function of the input attributes, linear activation functions guarantee that the network forecasts will exactly match their targets. Of course, the same result could have been obtained using multiple regression. Printing is turned on to show progress during the training session.