Spike Sorting Method Based on Two-Stage Radial Basis Function Networks - Advances in Computational Science and Engineering - page 101

N

∑

edyd CC =−=− ωϕ (|| − ||)

(5)

i i i i j i j

j = 1

Where d is the desired output of the i th training sample. y is the actual output of
RBF network, which is linear weighted sum of hidden units' output.

N

∑

edyd CC =−=− ωϕ (|| − ||) (6)

i i i i j i j

j = 1

Then calculate the total error E.

1
2

P

∑

E = e

2

(7)

i

i = 1

where P is the number of the training samples. If E is less than the error limit, the
procedure will terminate, else update the weights, and calculate the error again.

ωωω ←∆ +

(8)

i i i

∂ E

P

∑

∆=− ωη = η ϕ e XC (|| − ||)

(9)

i j j i

∂ ω

j = 1

i

X is

Where

η

is learning rate, which affects the convergence speed of the algorithm,

the j th training sample.

2.2 Testing Stage of RBF Networks

When using the ith sample as input vector, output of the jth hidden unit is
( )

ϕϕ = || XC i − || , = 1, 2,..., Pj ; = 1, 2,..., N . (10)

ij i j

So the output matrix of hidden layer is

Φ= ⎣ ⎦ ⎡ ⎤ ϕ

(11)

ij PN

×

The weights matrix between hidden layer and output layer is
[ ]

W = ωω , ,..., ω

(12)

12 N

Then the output vector of RBF network is
()

FX W =Φ

(13)

Actually, after training we get the weights matrix W and the function

()

￿ . Then
using X as the input of RBF networks, we can get the results by the above formula.

ϕ