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Any attempt to validate an artefact correction algorithm using actual data is second-guessing, but if appearances can be believed, the method used herein was adequate (figure 0). Some authors have asserted the presence of substantial phase shifts in transmission of EOG signals through tissue, but the imaginary parts of the correlation coefficients in this experiment were always smaller than the real parts (figure 1), most of them by an order of magnitude. This suggests that phase shifts in this application were not very important. The magnitudes of the correlations peaked between 9s-1 and 16s-1, depending on the subject, and decreased to a base level by about 25s-1. Average values of the single-trial Wiener coefficients peaked at the low end of the frequency range (figure 2). Standard deviations of the Wiener coefficients were comparable to the values themselves, suggesting substantial adaptation to varying blink morphologies.
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We began three-layer simulations using only two hidden units, and tested on selected individual data sets using progressively more hidden units, up to five. However, we found that networks incorporating more than two hidden units yielded no improvement in performance. Because of the computational expense of these simulations we therefore restricted our comprehensive tests to the two-unit case, and it is only those results that are reported here.
Most networks run on data sets from individuals reached at least 80% performance on the test set (table 0). Performances of the three-layer networks were neither consistently better nor consistently worse than those of the two-layer networks run on the same data sets. Presentation of input in the frequency domain led often to faster convergence and usually produced better peak performance than presentation in the time domain.
Before tackling the more complex architecture, it is instructive to examine the weights arrived at in the two-layer simulations, which correspond more directly and intuitively to features of the input vectors. We averaged ERPs separately for those correct target detections that were correctly predicted by the network, and for the remaining correct target detections which the network misclassified as misses. In the time domain, some peaks in the weights vector can be identified with ERP components by their corresponding latencies (figure 3). Brief bands of consistently negative or positive weights are visible at time steps corresponding to N1, P2, N2, P3a, P3b (when present), and positive slow-wave components. However, superimposed upon these bands are many isolated weights with no obvious correlates.
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Many of the differences between averages of correctly classified targets and averages of misclassified targets are latency changes. But this is not the case in the autistic auditory data set, in which the average of the misclassified detections contains prominent N270 and P700 components which are not at all apparent in the average of correctly classified detections. We supposed that the misclassifications may have arisen largely from the data of one or a few individuals who were outliers, and examined the network's input to confirm or to refute this hypothesis. We found that the misclassifiactions came from all six subjects, in the ratio 24:20:16:8:6:5. In comparison, the ratio for correct classifications was 57:46:49:27:26:52.
In addition to the faster convergence, presentation of the input in the frequency domain yielded more consistent weights. This tendency is most evident in the weights vectors calculated from individual data sets, but is also present in the weights calculated from pooled data (figure 4). In both the amplitude and the phase spectra, wider positive and negative bands of weights were produced than in the time-domain networks.
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The three-layer networks did not share any consistent pattern of utilisation of the hidden units. In some, a push-pull architecture emerged in which one hidden unit drove the output toward a negative answer and the other drove toward a positive answer. In others, both hidden units pulled the output in the same direction away from a strong bias, with differing degrees of potency. As in the case of the two-layer networks, some peaks in the incoming weights on each hidden unit corresponded to features of the averaged event-related potential, but an unintelligible pattern of peaks was superimposed on these.
