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Radial Basis Function Net (RBFN)


The Radial Basis Function Network (or RBFN) is a 3-layer, feed-forward network, whose middle layer uses a multi-variate Gaussian function. It is especially useful for classification problems. The RBFN is best for choosing which class out of many classes an item belongs to. In general, RBFNs take less time to train but more time to execute than BPNs and Autoassociative Networks.

An RBFN contains exactly 3 layers. The first layer and the input vector must be the same size. The last layer and the output vector must be the same size. The middle or hidden layer can be any size.

Each node in a layer is connected to all other nodes in the layers before it and after it. The connections between the input and hidden layers are unweighted. However, RBFNs weight the connections between the hidden layer and output layer normally, like a BPN or an Autoassociative network.

The transfer function of the input and output layer is linear. You can choose whether the transfer functions of the hidden layer are spherical or elliptical Gaussians.

Note: NeurOn-Line does not use G2 objects to represent the nodes and connections in a neural network. Instead, NeurOn-Line stores the network internally and lets you change the network's architecture with the configure menu item.
An RBFN can take a vector of any length as an input value, and it passes an output vector and an output scalar. The vector is the same size as the last layer in the network. The scalar is the maximum hidden node activation, which indicates how well the hidden layer covers the input vector. This number is between 0.0 and 1.0. If it is close to zero, for example less than 0.2, the hidden layer does not cover the input well, indicating that the network possibly predicted inaccurately due to extrapolation.

Configuring

When you choose configure from the block's menu, it displays the dialog below.


To configure the Network Architecture, specify the number of nodes in the input, hidden, and output layers, the overlap between the nodes, and the shapes of the hidden nodes.

Caution: If you change the architecture for a trained network by reducing the size of any layer, you will need to retrain the network.
To set the number of nodes in the input layer, enter a number in the Input Nodes field. To set the number of nodes in the hidden layer, enter a number in the Hidden Nodes field. To set the number of nodes in the output layer, enter a number in the Output Nodes field.

To set the unit overlap, choose whether the overlap is automatic or fixed by selecting the toggle button next to the Unit Overlap attribute. If the overlap is automatic, the network chooses the best unit overlap for you automatically. Generally, you will use an automatic overlap. If the overlap is fixed, enter a positive value in the Unit Overlap attribute edit box. The unit overlap affects how smoothly the trainer fits the function to the data. A larger unit overlap creates a smooth, slowly changing fit. A smaller unit overlap allows rapid changes in the fit.

To choose the function shape for the hidden layer, select one of the options under Hidden Unit Shapes: spherical or elliptical. When data is sparse or the input values are not correlated to each other, spherical units may perform better. When more data is available or the input values are correlated to each other, elliptical units may perform better. If the input dimension is 1, there is no difference between spherical and elliptical nodes, and the network selects Spherical by default. To choose the option for other cases, you may need to perform cross-validation with the Train and Test block or the Five-Fold CV block.

Saving and Loading Weights

You can save the network's weights to a text file so you can load them later. For information on how to do this, see "Saving and Loading Weights" for the BPN block.

Making Values Permanent

When you choose make permanent from the block's menu, it saves the network's internal configuration and weights.

See Also

For more information on how to use this block, see the pages below.

Click here for more information...
Basic Block Behavior
Saving a Block's Data After Resetting G2
Rho Net

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