4 The Analysis of Event-Related Potentials
73
methods. Advanced spatial analysis has therefore become common practice in ERP
research.
In contrast to continuous EEG, ERP studies allow spatial analysis with hightemporal resolution, i.e., they allow the generation of topographical and/or tomographical maps for each time sample. This is due to the SNR gain engendered by
averaging across sweeps. Thus, as compared to continuous EEG, ERPs offer an analysis in the spatial domain with much higher temporal resolution. The SNR increases
with the number of averaged sweeps. One can further increase the SNR by using a
multivariate filtering method, as previously discussed. One can also increase the SNR
by averaging spatial information in adjacent samples. The spatial patterns observed
at all samples forming a peak in the global field power
2 can safely be averaged, since
within the same peak the spatial pattern is supposed to be constant [52].
When using a source separation method (see Fig. 4.2 for an example) the spatial
pattern related to each source component is given by the corresponding column vector
of the estimated mixing matrix, i.e., the pseudo-inverse of the estimated matrix B
T .
In fact, a source separation method decomposes the ensemble average in a number
of source components, each one having a different and fixed spatial pattern. These
patterns are analyzed separately as a topographic map and are fed individually to
a source localization method as input data vector. Source localization methods in
general perform well when the data is generated by one or two dipoles only, while
if the data is generated by multiple dipoles the accuracy of the reconstruction is
questionable [95]. BSS effectively decomposes the ensemble average in a number of
simple source components, typically generated by one or two dipoles each [25]. As a
consequence, spatial patterns decomposed by source separation can be localized with
high accuracy by means of source localization methods. Note that applying a generic
filtering method such as PCA and CSTP, the components given by the filter are still
mixed and so are the spatial patterns held as column vectors by the matrix inverse
of the spatial filter, that is, the pseudo-inverse of B
T . This prevents any physiological interpretation of the corresponding spatial patterns. Source separation methods
are therefore optimal candidates for performing high-resolution spatial analysis by
means of ERPs. An example of topographical analysis is presented in Figs. 4.2 and
4.8. For an example of tomographic analysis refer to Congedo et al. [24].
4.6 Inferential Statistics
As we have seen, in time-domain ERP studies it is of interest to localize experimental
effects along the dimension of space (scalp location) and time (latency and duration
of the ERP components). Analysis in the time-frequency-domain involves the study
of amplitude and phase in the time-frequency plane. The dimensions retained by
2 The global field power is defined for each time sample as the sum of the squares of the potential
difference at all electrodes. It is very useful in ERP analysis to visualize ERP peaks regardless their
spatial distribution [52].
73
methods. Advanced spatial analysis has therefore become common practice in ERP
research.
In contrast to continuous EEG, ERP studies allow spatial analysis with hightemporal resolution, i.e., they allow the generation of topographical and/or tomographical maps for each time sample. This is due to the SNR gain engendered by
averaging across sweeps. Thus, as compared to continuous EEG, ERPs offer an analysis in the spatial domain with much higher temporal resolution. The SNR increases
with the number of averaged sweeps. One can further increase the SNR by using a
multivariate filtering method, as previously discussed. One can also increase the SNR
by averaging spatial information in adjacent samples. The spatial patterns observed
at all samples forming a peak in the global field power
2 can safely be averaged, since
within the same peak the spatial pattern is supposed to be constant [52].
When using a source separation method (see Fig. 4.2 for an example) the spatial
pattern related to each source component is given by the corresponding column vector
of the estimated mixing matrix, i.e., the pseudo-inverse of the estimated matrix B
T .
In fact, a source separation method decomposes the ensemble average in a number
of source components, each one having a different and fixed spatial pattern. These
patterns are analyzed separately as a topographic map and are fed individually to
a source localization method as input data vector. Source localization methods in
general perform well when the data is generated by one or two dipoles only, while
if the data is generated by multiple dipoles the accuracy of the reconstruction is
questionable [95]. BSS effectively decomposes the ensemble average in a number of
simple source components, typically generated by one or two dipoles each [25]. As a
consequence, spatial patterns decomposed by source separation can be localized with
high accuracy by means of source localization methods. Note that applying a generic
filtering method such as PCA and CSTP, the components given by the filter are still
mixed and so are the spatial patterns held as column vectors by the matrix inverse
of the spatial filter, that is, the pseudo-inverse of B
T . This prevents any physiological interpretation of the corresponding spatial patterns. Source separation methods
are therefore optimal candidates for performing high-resolution spatial analysis by
means of ERPs. An example of topographical analysis is presented in Figs. 4.2 and
4.8. For an example of tomographic analysis refer to Congedo et al. [24].
4.6 Inferential Statistics
As we have seen, in time-domain ERP studies it is of interest to localize experimental
effects along the dimension of space (scalp location) and time (latency and duration
of the ERP components). Analysis in the time-frequency-domain involves the study
of amplitude and phase in the time-frequency plane. The dimensions retained by
2 The global field power is defined for each time sample as the sum of the squares of the potential
difference at all electrodes. It is very useful in ERP analysis to visualize ERP peaks regardless their
spatial distribution [52].