Wilk’s lambda

If the filter coefficients are to be used for discriminatory purposes, then the criterion function should strive to reflect differences among classes. In this section three suitable discriminant criterion functions are described. These discriminant criterion functions are Wilk s lambda (3a), entropy (3e), and the cross-validated quadratic probability measure (3cvqpm)-... 

For the Wilk s Lambda criterion, optimization was based on band(3,3), while the entropy criterion optimized over band(3,2). The CVQPM criterion optimized over the scaling band(3,0). Some features which we might expect from the adaptive wavelet algorithm, is that at termination, the band on which optimization was based would outperform the other bands, at least in... 

Table 3. The percentage of correctly classified spectra, using the coefficients X (t) for T = 0,..., 3 at initialization and at termination of the adaptive wavelet algorithm. The discriminant criterion functions were Wilk s Lambda, symmetric entropy and the CVQPM.

One reason why the CVQPM, maybe outperforming the other criterion functions could be due to the fact that optimization and hence classification is based on scaling coefficients. So that a fair comparison could be made, the optimization routine using the Wilk s Lambda, and symmetric criterion functions was repeated, this time forcing optimization over the scaling band. These results are summarized in Table 4. 

Optimization over the scaling band did improve the results slightly for the Wilk s Lambda and symmetric entropy criterion, but these criterion functions were not able to improve upon the results previously obtained with the CVQPM criterion function. 

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