Spike Sorting Method Based on Two-Stage Radial Basis Function Networks - Advances in Computational Science and Engineering - page 100

So in training stage of RBF network, we should determine the RBF cen-
ters,

n

i CR i n

∈≤ ,1 ≤ σ ∈≤≤

i R in

,1

, the width of receptive field, ,and the

ω ∈≤≤

i R in

,1

weights of each hidden unit, .

2.1 Training Stage of RBF Networks

fR R :

n

→

In a typical two-stage RBF network, the mapping is established in two

stages. In the first stage, RBF centers are determined by K-means cluster, and then the
width of the receptive field is calculated. In the second stage, the weights are deter-
mined by gradient descent algorithm.

Determine RBF centers using K-means method. K-means algorithm is a type of
self-organizing algorithm. It performs the clustering task by iteratively decreasing
distance between members of each cluster and the corresponding cluster centers. Here
an improved K-means method is used to determine centers of RBF to capture more
knowledge about the distribution of input patterns[4]. The method is illustrated as
follows:
Firstly, we initialize cluster centers. We use 'Farthest points' as initial cluster cen-
ters. To get these farthest points, we have initially that A

=∅ and B is the whole data
set to cluster. At first, two patterns which are farthest to each other are removed from B
and added to A. Then iteratively move pattern x from B to A, whose minimum distance
from any pattern in A is maximum. The iteration will continue until the number of
patterns in A equals the intended number of clusters.
Secondly, we should determine which cluster each point belongs to. Calculate dis-
tance between each input vector and its corresponding cluster center. The input vector x
is added to the cluster from whose center the distance is shortest. Then, update centers
of each cluster using the following formula.

∑

C = x

(3)

i

xS ∈

i

i Si n

,1 ≤≤

Where , is samples of the i th cluster.

At last, we should judge if termination conditions is satisfied. If all clusters remain
the same after this iteration, or the maximum iteration number is reached, the iteration
will terminate

Calculate the width of receptive field. The width of receptive field can be calculated
according to distances between each RBF center gotten above.

σλ λ == d min (|| C C − ||)

(4)

i i j i j

λ Where is the overlapping coefficient. It is an important parameter of K-means RBF

networks which effects how much the receptive fields overlap each other.

Determine the weights of hidden units using gradient descent algorithm. First,
initialize the weights randomly. For each training sample, calculate its error from the
corresponding target.