Radial Basis Function Network - Training

Training

RBF networks are typically trained by a two-step algorithm. In the first step, the center vectors of the RBF functions in the hidden layer are chosen. This step can be performed in several ways; centers can be randomly sampled from some set of examples, or they can be determined using k-means clustering. Note that this step is unsupervised. A third backpropagation step can be performed to fine-tune all of the RBF net's parameters.

The second step simply fits a linear model with coefficients to the hidden layer's outputs with respect to some objective function. A common objective function, at least for regression/function estimation, is the least squares function:

where

.

We have explicitly included the dependence on the weights. Minimization of the least squares objective function by optimal choice of weights optimizes accuracy of fit.

There are occasions in which multiple objectives, such as smoothness as well as accuracy, must be optimized. In that case it is useful to optimize a regularized objective function such as

where

and

where optimization of S maximizes smoothness and is known as a regularization parameter.

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