Chapter 4
The Analysis of Event-Related Potentials
Marco Congedo
Abstract In this chapter, we provide an introduction to the major methods used
for the analysis and classification of Event-Related Potentials (ERPs). We start by
considering the problem of estimating ERP ensemble averages in the time domain.
An estimator allowing for weights and time shifts for each trial is discussed. Then
we consider spatial, temporal and spatio-temporal multivariate filters for improving
the estimation, including principal component analysis, the common spatial pattern
and blind source separation. Then, we review time-frequency analysis methods. The
reader is provided with definitions in order to understand the most commonly used
linear and non-linear measures used in the time-frequency domain. We continue with
a brief discussion on the importance of the analysis in the spatial domain, including topographic maps and tomographies. Next, we review procedures for applying
inferential statistics to ERP studies. Emphasis is given to procedures based on permutation tests, which account for the multiple comparison problem and adapt to
the form and degree of correlation between hypotheses. Finally, we consider the
problem of classifying ERP single-trials, pointing to recent literature covering the
most promising methods currently available, namely, Riemannian geometry, random
forests and neural networks.
4.1 Introduction
Event-Related Potentials (ERPs) are a fundamental class of phenomena that can be
observed by means of electroencephalography (EEG). They are defined as potential difference fluctuations that are both time-locked and phase-locked to a discrete
physical, mental, or physiological occurrence, referred to as the event. ERPs are
usually described as a number of positive and negative peaks characterized by their
polarity, shape, amplitude, latency and spatial distribution on the scalp. All these
M. Congedo (B)
GIPSA-Lab, Centre National de la Recherche Scientifique (CNRS), Grenoble-INP, Université
Grenoble Alpes, Grenoble, France
e-mail: marco.congedo@gmail.com
© Springer Nature Singapore Pte Ltd. 2018
C.-H. Im (ed.), Computational EEG Analysis, Biological and Medical Physics,
Biomedical Engineering, https://doi.org/10.1007/978-981-13-0908-3_4
55
The Analysis of Event-Related Potentials
Marco Congedo
Abstract In this chapter, we provide an introduction to the major methods used
for the analysis and classification of Event-Related Potentials (ERPs). We start by
considering the problem of estimating ERP ensemble averages in the time domain.
An estimator allowing for weights and time shifts for each trial is discussed. Then
we consider spatial, temporal and spatio-temporal multivariate filters for improving
the estimation, including principal component analysis, the common spatial pattern
and blind source separation. Then, we review time-frequency analysis methods. The
reader is provided with definitions in order to understand the most commonly used
linear and non-linear measures used in the time-frequency domain. We continue with
a brief discussion on the importance of the analysis in the spatial domain, including topographic maps and tomographies. Next, we review procedures for applying
inferential statistics to ERP studies. Emphasis is given to procedures based on permutation tests, which account for the multiple comparison problem and adapt to
the form and degree of correlation between hypotheses. Finally, we consider the
problem of classifying ERP single-trials, pointing to recent literature covering the
most promising methods currently available, namely, Riemannian geometry, random
forests and neural networks.
4.1 Introduction
Event-Related Potentials (ERPs) are a fundamental class of phenomena that can be
observed by means of electroencephalography (EEG). They are defined as potential difference fluctuations that are both time-locked and phase-locked to a discrete
physical, mental, or physiological occurrence, referred to as the event. ERPs are
usually described as a number of positive and negative peaks characterized by their
polarity, shape, amplitude, latency and spatial distribution on the scalp. All these
M. Congedo (B)
GIPSA-Lab, Centre National de la Recherche Scientifique (CNRS), Grenoble-INP, Université
Grenoble Alpes, Grenoble, France
e-mail: marco.congedo@gmail.com
© Springer Nature Singapore Pte Ltd. 2018
C.-H. Im (ed.), Computational EEG Analysis, Biological and Medical Physics,
Biomedical Engineering, https://doi.org/10.1007/978-981-13-0908-3_4
55