Spike Sorting Method Based on Two-Stage Radial Basis Function Networks - Advances in Computational Science and Engineering - page 99

2 Two-Stage Radius Basis Function Network

There are three layers in a typical RBF network, i.e. input layer, hidden layer and output
layer. Input layer is made up of conception units, which receive input from outside.
Hidden layer applies a nonlinear transformation between input layer and hidden layer.
Output layer calculates the linear weighted sum of hidden units' output and provides
the result after a linear trans-formation. The scheme of RBF networks is depicted in
Figure 1.
It actually implements a mapping

n

fR R : → as follows:

n

()

∑

( )

fx = ωϕ || xC − ||

(1)

i i

i = 1

xR ∈

n

()

is a transform function from Rn to R, ||

||

￿

Where is the input vector, ϕ is

￿

the Euclidean norm.

ω ,1 i in ≤≤

, are weights of each hidden unit.

i CR i n

∈≤

n

,1 ≤

, are called RBF centers, and n is the number of centers.

Because theoretical investigation and practical results suggest that the choice of
()

￿ is not crucial to the performance of RBF network. In this paper, we adopt
Gaussian function as

ϕ

()

￿ .

ϕ

2

r

ϕ ( ) r =− exp( )

(2)

2

2 σ

σ

Where is the width of the receptive field.

Fig. 1. Scheme of RBF network