K.j. Kim, H. Ahn Expert Systems with Applications 34(2008)1200-1209 1. Design the structure of chromosomes and define fitness function 3. Perform the K-means process according to the given initial seeds Calculate the intraclass inertia as fitness function for each chromosome 5. Apply genetic operators and produce a new generation No e stopping crite 7. Finish Fig 1. The overall framework of GA K-means. the stopping conditions are satisfe e repeated until values, they have to be coded on a chromosome, a form of binary strings. The structure of the chromosomes for GA K-means 3. 2. Chromosome encoding As shown in Fig. 2, the length of each chromosome for GA K-means depends on the types of features In the case The system searches the space to find optimal or near- of the binary selection variables whose value is 0 or l, the optimal values of the features that consist of the centroids length of each feature is just I bit. But, the features that for each cluster. To apply Ga to search for these optimal have continuous values require more bits to express them Types of the features consist of the data set Type 1. Binary selection(0 or 1) Type 2. Continuous values ranging from 0 to 1 baalislslziap o u a s u 1111234567891011121131412141 Cluster1[t。-011|1001 10110110 Cluster2[011011010011。04 Cluster3[101。1。1111-1 L。1o。1。1。o。11。。1 Cluster n[t1-1。010。11。11。1。。_10 Fig. 2. The structures of the chromosomes for GA K-means.duced. After that, Step (2) and (3) are repeated until the stopping conditions are satisfied. 3.2. Chromosome encoding The system searches the space to find optimal or near￾optimal values of the features that consist of the centroids for each cluster. To apply GA to search for these optimal values, they have to be coded on a chromosome, a form of binary strings. The structure of the chromosomes for GA K-means is presented in Fig. 2. As shown in Fig. 2, the length of each chromosome for GA K-means depends on the types of features. In the case of the binary selection variables whose value is 0 or 1, the length of each feature is just 1 bit. But, the features that have continuous values require more bits to express them 1. Design the structure of chromosomes 2. Generate the initial population and define fitness function 3. Perform the K-means process according to the given initial seeds 4. Calculate the intraclass inertia as fitness function for each chromosome 5. Apply genetic operators and produce a new generation 6. Satisfy the stopping criteria? 7. Finish User Data Base No Yes Fig. 1. The overall framework of GA K-means. 1 V1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 V2 Type 1. Binary selection (0 or 1) Type 2. Continuous values ranging from 0 to 1 Types of the features consist of the data set 1 V37 2 3 4 5 6 7 8 9 10 11 12 13 14 … … 1 V36 1 V42 1 2 … 14 V1 1 V2 … … Cluster 1 Cluster 2 Cluster 3 … Cluster n 1 0 … 0 1 0 1 1 0 0 1 0 0 1 0 1 1 0 … 1 1 … 0 0 1 … 1 01101001110011 … 0 1 … 0 1 1 … 0 11011100111101 … 1 1 … 1 1 0 … 1 11001011000111 … 0 0 … 1 1 1 … 1 00100110110100 … 1 0 … 0 Fig. 2. The structures of the chromosomes for GA K-means. K.-j. Kim, H. Ahn / Expert Systems with Applications 34 (2008) 1200–1209 1203