Hidden Layer Structure

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Predictive and Specialized Modeling • Neural Networks • Launch the Neural Platform • Hidden Layer Structure

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Hidden Layer Structure

Note: The standard edition of JMP uses only the TanH activation function, and can fit only neural networks with one hidden layer.

The Neural platform can fit one or two-layer neural networks. Increasing the number of nodes in the first layer, or adding a second layer, makes the neural network more flexible. You can add an unlimited number of nodes to either layer. The second layer nodes are functions of the X variables. The first layer nodes are functions of the second layer nodes. The Y variables are functions of the first layer nodes.

The functions applied at the nodes of the hidden layers are called activation functions. An activation function is a transformation of a linear combination of the X variables. The following activation functions are available:

The hyperbolic tangent function is a sigmoid function. TanH transforms values to be between -1 and 1, and is the centered and scaled version of the logistic function. The hyperbolic tangent function is:

where x is a linear combination of the X variables.

The identity function. The linear combination of the X variables is not transformed.

The Linear activation function is most often used in conjunction with one of the non-linear activation functions. In this case, the Linear activation function is placed in the second layer, and the non-linear activation functions are placed in the first layer. This is useful if you want to first reduce the dimensionality of the X variables, and then have a nonlinear model for the Y variables.

For a continuous Y variable, if only Linear activation functions are used, the model for the Y variable reduces to a linear combination of the X variables. For a nominal or ordinal Y variable, the model reduces to a logistic regression.

The Gaussian function. Use this option for radial basis function behavior, or when the response surface is Gaussian (normal) in shape. The Gaussian function is:

where x is a linear combination of the X variables.

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Help created on 7/12/2018