Radial Basis Function Training (RBF NN)
Weight Update Function
\[\mathbf w=(\phi^T\phi+\lambda\mathbf I_{M\times M})^{-1}\phi^T\mathbf y\]where:
- $\lambda$ if the user-defined regularisation parameter:
- $\lambda=0$ indicates that the input data is completely trustworthy.
- $\lambda=\infty$ indicates that the dataset needs significant smoothing.
Radial Basis Functions vs. Multi-Layer Perceptrons
- Universal Approximators
- Given any function $f(x)=y$, we can approximate such a function using either network type.
- Radial Basis Functions Require a Matrix inverse to be taken. This is slow and doesn’t scale well.
- Despite the lengthy weight update process in MLP, they are preferred as it can be parallelised for large datasets.