Batch Processing and Evaluation
4.4 DISCUSSION
The feature selection histogram s for b o th optim ization m ethods in Figures 19(a) and 19(b), respectively, indicate the optim al features for lower N-class conditions come from lower frequencies. In b o th figures, there is a distinct change in selected features from the 6-9 Hz range to th e 15-20 Hz range as the N-class condition increases from 8 to 9, which is also near the perform ance inflection point. This can be explained by examining the CCA plot in Figure 14. This plot shows th a t th e frequencies from 6- 10 Hz have a higher CCA coefficient across this entire b and com pared to the diagonals a t higher frequencies. This is partly due to the higher power and SNR in this low frequency range, particularly in th e alpha band. It should be noted th a t th e alpha ban d and its second harm onic are generally avoided in th e frequency selection due to th e innate n atu re of this rhythm , independent of stim ulation in this range.
Classification Error • Feature Histogram
tsm ssm M
2 4 6 6 10 12 14 16 18 20 22 24 26 28 30 32 34 36 # of C la s se s (a) 0 1 2 3 4 5 6 7 8 9 10ECM Norm - F eature Histogram
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 38
# of C la s se s
(b)
FIG. 19: 2-D histogram s of optim ized feature sets for each N-class condition. Each column is a different N-class condition th a t spans th e possible feature range (6-33.5 Hz). For a given N-class condition, the features from th e best optim ized solution are superim posed as white circles indicating th e selected feature. Each column has N dots corresponding to each N-class condition. The 9 next-best solutions are plotted as histogram s where the color corresponds to th e occurrence ra te of the selected feature, (a) shows the feature distributions for the classification error optim ization and (b) shows the feature distributions for the ECMN optim ization.
any low frequency features in th e final optim ized set. For th e classification error optim ization, Figure 19(a) shows a bias towards the middle frequency range (15-19.5 Hz) which gradually includes higher frequencies as the N-class condition increases. However, for the ECMN optim ization, Figure 19(b) shows another sharp change in selected features from th e mid range (15-19.5 Hz) to th e higher range (22-32 Hz) at the 10-class condition. This is likely due to the fact th a t these ranges of frequencies have more similar SNRs. This would result in a more balanced classification (i.e., minimizing the ECM norm), which is desirable for practical BCIs.
The contiguous n atu re of the m ajority of th e selected feature sets can also be, in p art, explained by th e relative SNR across particular frequency bands. For the classification error, it is observed th a t th e features are generally contiguous and after the inflection point, the added features come from the next highest frequency (i.e., next highest SNR). The ECMN optim ization follows a similar contiguous p attern , except the initial range after the inflection point is (22-28 Hz) and roughly alternating lower and higher frequency contiguous features are included to m aintain the class balance. A nother contributing factor to the observed contiguous ranges is th a t the harm onic frequencies play a role in the CCA as depicted in Figure 14. Particular frequency features, especially in the lower frequencies, will tend to dom inate the CCA a t th e respective harm onic frequencies. Thus, it is unlikely for frequencies to be selected th a t have com peting harmonics. Future work will examine the inclusion of harm onic frequencies in th e CCA and its im pact of on th e selected feature sets.
In term s of maximizing th e IT R across the population, the results indicate th a t a peak IT R near 40 b its/m in u te is achieved for the seven-class condition for b oth optim ization schemes. Additionally, b o th optim ization schemes selected contiguous frequency features from 6-9 Hz (0.5 Hz increm ent) for this condition. Aside from the inflection point, the IT R is generally fiat above the 10-class condition due to the steady decrease in accuracy for higher classes. It should be noted th a t a fixed inter-stim ulus interval was used across N-class conditions to com pute the sim ulated ITRs. It is likely th a t longer inter-stim ulus intervals would be needed for adequate scanning tim e in the higher-class conditions, which would further degrade th e IT R
as th e num ber of classes increases. Figure 17 shows the expected improvement in balanced classification across targ et frequencies for the ECMN optim ization for class sizes 9-34. Ultimately, if all targ et frequencies should be equi-probable for a given interface design, the ECMN optim ization will provide a more balanced scheme for more th a n 8 classes w ith m arginal decreases in overall classification performance.
T he proposed approach has some lim itations in term s of generalizing to an online BCI. The SSVEP responses were collected serially using a fairly large single-stimulus LED array. For an actual multi-class online im plem entation, simultaneous stim uli at different frequencies would be presented, generally w ith smaller physical dimensions. T he present analysis does no t account for th e potential simultaneous interference or atten tio n al issues present in a practical online scenario. A nother lim itation is th a t th e chirp signal, while slowly varying over th e selected tim e windows, is not of a fixed frequency and had a lim ited duration. Thus, there may not have been adequate tim e to fully entrain certain frequencies, and the CCA may have a slight bias due to the variation in frequency over the tim e windows. A nother consideration is th a t the selected features may be specific to the CCA approach and may be suboptim al if other SSVEP feature extraction and classification schemes are employed. Through exam ination of th e sensitivity of th e IT R and selected features to the near-optim al solutions shown in Figure 18, the selected next-best feature histogram s generally have overlapping densities w ith th e best solutions, and slight changes in the selected features lead to com parable IT R performances. Nevertheless, it is believed th a t th e present analysis provides a comprehensive evaluation of the m ost discriminable frequency feature sets for a given num ber of classes, which should serve as a reference and a guide for standardization of generalized SSVEP stim ulus frequencies.