Shapiro-Wilk index: discriminatory index

We propose to employ the Shapiro-Wilk statistic (W statistic) as discriminatory index in the best clustering basis algorithm. The original work on the best clustering basis requires a clustering algorithm to partition clusters of data in order to obtain discriminatory index associated to a wavelet packet. The use of the W statistic eliminates the need for a clustering algorithm and therefore reduces the computational complexity introduced by a clustering algorithm. The use of the W statistic is based on testing for normality of data projection. The relationship between the W statistic and distance between cluster centroids is provided empirically. The experiments performed show that the algorithm with the W statistic can find basis functions with large discriminatory powers.