Predicting Cardiovascular Risks using Pattern Recognition and Data ...

d(C , Q)is minimized.ci1d(X , Q)i(4.16)According to the theory in Huang (1998), the Equation (4.16) is minimized if the frequency of value q kin data set C, for k th attribute, is equal or greater than the frequency of all different x ik such that x ik q k .Therefore, we can choose the mode vectors of m-p attributes as the highest frequency values in theseattributes. Their forms can be seen as follows:{q jk } = mode k= {“max freq” Val Ck }, k=p+1,.., m. (4.17)Accuracy MeasureThe accuracy (Acc) for measuring the quality of clustering algorithm is given by:Acc Ki1nai(4.18)where n is the number of samples in the dataset, a i is the number of data samples occurring in bothcluster i and its corresponding class, and K is number of clusters.Consequently, the clustering error (err) is defined as:err 1Acc(4.19).4.3.2.2 KMIX AlgorithmStep 1: Initialise K clusters according to K partitions of data set.Step 2: Update K centre vectors in the new data set ( in the first time, the centre vectors are calculated)Q j = (q N j1, q N j2, …, q N jp, q C jp+1, …, q C jm), j = 1, 2, …, kwhere {q N ji} i=1,2..p = {mean N ji } (mean of i th attribute in cluster j),and {q C ji} i=p+1,..m ={mode C ji} (max freq value in attribute i th in cluster j).Step 3: Update clusters as the following tasks:Calculate the distance between X i in i th cluster to K centre vectors:d(X i ,Q j ) = d N (X i ,Q j ) + d C (X i, Q j ); j=1,2,..k53