Achim, A, & Bouchard, S, 1997: Toward a dynamic topographic components model, Electroencephalography & Clinical Neurophysiology, 103(3):381-385.

Möcks' topographic component model (TCM) (Möcks, J, Topographic components model for event-related potentials and some biophysical considerations. IEEE Trans. Biomed. Eng., 1988a, 35: 482-484; Möcks, J, Decomposing event-related potentials: a new topographic components model. Biol. Psychol., 1988b, 26:199-215) decomposes event-related potentials into components uniquely determined by their respective amplitude profiles across replicates, assuming a constant topography and wave shape for each component. To accommodate possible changes in the component expression across conditions, a dynamic version of TCM is investigated which further admits component modulation in time scale. Twenty test problems were synthesized, incorporating two arbitrary topographies each activated with its own arbitrary wave shape modified, across two conditions, in amplitude, onset and duration. Seventeen problems were perfectly solved, with substantial success on the remaining three, confirming that component jitter or stretching can even help component identification.

Galán, L, Biscay, R, Rodríguez, J L, Pérez-Abalo, M C, & Rodríguez, R, 1997: Testing topographic differences between event related brain potentials by using non-parametric combinations of permutation tests, Electroencephalography & Clinical Neurophysiology, 102(3):240-247.

MANOVA and repeated measures ANOVA approaches have provided evidence of a number of limitations in several event-related potential (ERP) studies due to violations of their statistical assumptions and the typically moderate size of the available sample. Alternative, computer-intensive methods based on permutation principles have recently been developed. Up to now this methodology has focused mostly on magnitude differences between scalp distributions as measured by t statistics. In this paper the scope of permutation techniques in ERP analysis was widened. A new statistic (D statistic) is introduced to compare the shapes of scalp distributions of ERPs. Additionally a general non-parametric combinatory technique is introduced to evaluate, by means of multivariate permutation tests, several time points and/or recording sites in ERP data. The methodology described here was used to test if two ERP components elicited during word-pair matching tasks to semantic or phonological incongruences had different scalp distributions.

Jackson, C, & Sherratt, M, 2004: A novel spatio-temporal decomposition of the EEG: derivation, validation and clinical application, Clinical Neurophysiology, 115(1):227-237.

Objective: To obtain clinically useful graphical and numerical data on the distribution of activities in the EEG using a novel type of spatiotemporal decomposition.
Methods: The EEG is divided into 1/4 s epochs. An approximation to the spatial distribution of the locally dominant activity in each epoch is represented as a point in a spatial component space. Points representing epochs dominated by activity from the same source form a cluster. The centres of these clusters represent the global spatial component of each source. As each spatial component is identified, its corresponding temporal activity is removed from the record, allowing activity from sources with smaller amplitude to become dominant in the reduced record. Successive components are identified in the reduced record. The method was applied to 40 normal EEGs and features were identified, which were common to them all. The method was also applied to 4 separate records with different forms of focal abnormality.
Results: The method successfully separated components from the EEG representing alpha rhythm, eye artefact, electrode artefact and EEG. In 40 normal EEGs the method isolated spatial components that were common to all EEGs, and in 4 abnormal EEGs it achieved a high degree of mutual separation of alpha rhythm, focal spikes, focal theta and focal delta activities.
Conclusions: The method achieved a high degree of mutual separation of the EEG components and successfully differentiated the artefacts due to eye movement, ECG and electrode faults. The clinical implications are discussed.

Lal, T N, Schröder, M, Hinterberger, T, Weston, J, Bogdan, M, Birbaumer, N, & Schölkopf, B, 2004: Support vector channel selection in BCI, IEEE Trans. Biomed. Eng., 51(6):1003-1010.

Designing a brain computer interface (BCI) system one can choose from a variety of features that may be useful for classifying brain activity during a mental task. For the special case of classifying electroencephalogram (EEG) signals we propose the usage of the state of the art feature selection algorithms Recursive Feature Elimination [3] and Zero-Norm Optimization [13] which are based on the training of support vector machines (SVM) [11]. These algorithms can provide more accurate solutions than standard filter methods for feature selection [14].
We adapt the methods for the purpose of selecting EEG channels. For a motor imagery paradigm we show that the number of used channels can be reduced significantly without increasing the classification error. The resulting best channels agree well with the expected underlying cortical activity patterns during the mental tasks.
Furthermore we show how time dependent task specific information can be visualized.

Maris, E, 2004: Randomization tests for ERP topographies and whole spatiotemporal data matrices, Psychophysiology, 41:142-151.

In ERP studies, the comparison of topographies (multichannel measurements) or whole spatiotemporal data matrices (multichannel time series of measurements), the classical statistical tests very often cannot be used. It is argued that, for these comparisons, randomization tests are an excellent alternative. It is also argued that the randomization test is superior to another resampling method, the bootstrap, because exact probability statements (e.g., p values) can be made. A review is given of the literature on randomization tests designed for electrophysiological data. New randomization tests are presented and applied to two data sets, one coming from a psychopharmacological experiment and the other from an ERP experiment in visual word recognition.

McFarland, D J, McCane, L M, David, S V, & Wolpaw, J R, 1997: Spatial filter selection for EEG-based communication, Electroencephalography & Clinical Neurophysiology, 103(3):386-394.

Individuals can learn to control the amplitude of mu-rhythm activity in the EEG recorded over sensorimotor cortex and use it to move a cursor to a target on a video screen. The speed and accuracy of cursor movement depend on the consistency of the control signal and on the signal-to-noise ratio achieved by the spatial and temporal filtering methods that extract the activity prior to its translation into cursor movement. The present study compared alternative spatial filtering methods. Sixty-four channel EEG data collected while well-trained subjects were moving the cursor to targets at the top or bottom edge of a video screen were analyzed offline by four different spatial filters, namely a standard ear-reference, a common average reference (CAR), a small Laplacian (3 cm to set of surrounding electrodes) and a large Laplacian (6 cm to set of surrounding electrodes). The CAR and large Laplacian methods proved best able to distinguish between top and bottom targets. They were significantly superior to the ear-reference method. The difference in performance between the large Laplacian and small Laplacian methods presumably indicated that the former was better matched to the topographical extent of the EEG control signal. The results as a whole demonstrate the importance of proper spatial filter selection for maximizing the signal-to-noise ratio and thereby improving the speed and accuracy of EEG-based communication.

Montgomery Jr., E B, Huanga, H, & Assadic, A, 2005: Unsupervised clustering algorithm for N-dimensional data, J. Neuroscience Methods 144(1):19-24.

Cluster analysis is an important tool for classifying data. Established techniques include k-means and k-median cluster analysis. However, these methods require the user to provide a priori estimations of the number of clusters and their approximate location in the parameter space. Often these estimations can be made based on some prior understanding about the nature of the data. Alternatively, the user makes these estimations based on visualization of the data. However, the latter is problematic in data sets with large numbers of dimensions. Presented here is an algorithm that can automatically provide these estimates without human intervention based on the inherent structure of the data set. The number of dimensions does not limit it.

Tandonnet, C, Burle, B, Hasbroucq, T, & Vidal, F, 2005: Spatial enhancement of EEG traces by surface Laplacian estimation - comparison between local and global methods, Clinical Neurophysiology, 116(1):18-24.

Objective: Surface Laplacian estimation enhances EEG spatial resolution. In this paper, we compare, on empirical grounds, two computationally different estimations of the surface Laplacian.
Methods: Surface Laplacian was estimated from the same monopolar data set with both Hjorth's method [local; Electroenceph Clin Neurophysiol 39 (1975) 526] as modified by MacKay [Electroenceph Clin Neurophysiol 56 (1983) 696] and with spherical spline interpolation [global; Electroenceph Clin Neurophysiol 72 (1989) 184].
Results: The grand averages computed with the two methods proved to be very similar but differed markedly from the monopolar ones. The two different computations were highly correlated, presented low relative errors and allowed to evidence comparable experimental effects.
Conclusions: These results suggest that Hjorth's method and spherical spline interpolation convey similar topographic and chronometric informations.
Significance: We provide empirical evidence that local and global methods of surface Laplacian estimation are equivalent to improve the spatial resolution of EEG traces. Global methods allow to explore the scalp topography and local methods allow to spare time in electrode setting that can be useful for studies on special populations (i.e. children, aged subjects) and for clinical purposes.