Using a Clustering Genetic Algorithm to Support Customer Segmentation 411 1)Initialize the weights as the random small number. 2)An input sample, X,, is provided into the SOM network and the distances be- tween weight vectors, W,=(wu, was.,wm), and the input sample, X, is calcu- ated. Then, select the neuron whose distance with X is the shortest. The se- lected neuron would be called winne MmDO)=∑(n-x)2 (1) 3)When a is assumed to be the learning rate, the weights of the winner as well as of its neighbors are updated by following equation. NEW=w 4)Iterate Step 2)and 3)until the stop criterion is satisfied. In spite of several excellent applications, SOM has some limitations that hinder its performance. Especially, just like other neural network based algorithms, SOM has no mechanism to determine the number of clusters, initial weights and stopping con- 2.3 Criteria for Performance Comparison of Clustering Algorithms We compare the performances of the clustering algorithms using intraclass inertia Intraclass inertia is a measure of how compact each cluster is in the m-dimensional space of numeric attributes. It is the summation of the distances between the means and the observations in each cluster. Eq. (3)represents the equation for the intraclass neria for a given k clusters [8] F(k)=∑n1k=∑∑∑(xp-xk (3) where n is the number of total observations, c is set of the Kth cluster and Xrp is the mean of the Kth cluster that is Xxp=2Xp 3 GA-Based K-Means Clustering Algorithm As indicated in Section 2.1, K-means algorithm does not have any mechanism to choose appropriate initial seeds. However, selecting different initial seeds may gener ate huge differ of the clustering results, especially when the target sample con- tains many outliers. In addition, random selection of initial seeds often causes the clustering quality to fall into local optimization [1]. So, it is very important to select appropriate initial seeds in traditional K-means clustering method. To overcome this critical limitation, we propose GA as the optimization tool of the initial seeds in K means algorithm.Using a Clustering Genetic Algorithm to Support Customer Segmentation 411 1) Initialize the weights as the random small number. 2) An input sample, Xi , is provided into the SOM network and the distances be￾tween weight vectors, ( , ,..., ) Wj = wj1 wj2 wjm , and the input sample, Xi , is calcu￾lated. Then, select the neuron whose distance with Xi is the shortest. The se￾lected neuron would be called ëwinnerí. 2 ( ) = ∑( − ) i ji i Min D j w x (1) 3) When α is assumed to be the learning rate, the weights of the winner as well as of its neighbors are updated by following equation. j i j NEW Wj = W +α X −W (2) 4) Iterate Step 2) and 3) until the stop criterion is satisfied. In spite of several excellent applications, SOM has some limitations that hinder its performance. Especially, just like other neural network based algorithms, SOM has no mechanism to determine the number of clusters, initial weights and stopping con￾ditions. 2.3 Criteria for Performance Comparison of Clustering Algorithms We compare the performances of the clustering algorithms using ëintraclass inertiaí. Intraclass inertia is a measure of how compact each cluster is in the m-dimensional space of numeric attributes. It is the summation of the distances between the means and the observations in each cluster. Eq. (3) represents the equation for the intraclass inertia for a given k clusters [8]. ∑ ∑∑∑∈ = = − K KC i P K K P KP K X X n n I n F k ( ) 1 1 ( ) (3) where n is the number of total observations, CK is set of the Kth cluster and X KP is the mean of the Kth cluster that is ∑∈ = CK i P K KP X n X 1 . 3 GA-Based K-Means Clustering Algorithm As indicated in Section 2.1, K-means algorithm does not have any mechanism to choose appropriate initial seeds. However, selecting different initial seeds may gener￾ate huge differences of the clustering results, especially when the target sample con￾tains many outliers. In addition, random selection of initial seeds often causes the clustering quality to fall into local optimization [1]. So, it is very important to select appropriate initial seeds in traditional K-means clustering method. To overcome this critical limitation, we propose GA as the optimization tool of the initial seeds in K￾means algorithm