Informative Oscillatory EEG Components and their Persistence in Time

and Frequency

Michael Tangermann and Andreas Meinel

Brain State Decoding Lab, Cluster of Excellence BrainLinks-BrainTools, Department of Computer Science,

Albert-Ludwigs-University of Freiburg, Albertstr. 23, Freiburg im Breisgau, Germany

Keywords:

Electroencephalogram, EEG, Oscillatory Component, Oscillatory Subspace, Hyperparameter Optimization,

Brain-Computer Interface, Common Spatial Patterns, CSP, Source Power Comodulation, SPoC, Visualization,

Characterization, Tracking.

Abstract:

Oscillatory brain activity measured by the electroencephalogram, local ﬁeld potentials or magnetoencephalo-

gram can reﬂect cognitive processes. It can be used to run brain-computer interfaces or to analyze information

processing, user learning and rehabilitation progress, e.g., after stroke. To extract oscillatory components,

which are informative about a users task and which show an enhanced signal-to-noise compared to raw mul-

tivariate recordings, data-driven spatial ﬁltering methods are widely applied. Some of these approaches can

learn spatial ﬁlters from labeled data. They typically require the data analyst to at least deﬁne a frequency

band of interest and time interval relative to the course of events in the experiment. These hyperparameters

are exploited by the ﬁltering method in order to extract informative oscillatory features. Their choice typically

is domain-speciﬁc and may require adaptations to individuals. Post-hoc data analysis, however, should not be

restricted to the initial hyperparameter ranges. Thus we present an approach, which allows to characterize a

given oscillatory component with respect to the frequency bands and the temporal windows for which it con-

tains task-relevant information. The approach allows to track task-informative persistence of components over

multiple experimental sessions and may be helpful to monitor motor learning and rehabilitation over time.

1 INTRODUCTION

Neurotechnological applications like brain-computer

interface (BCI) systems for patients or non-medical

use (Wolpaw and Wolpaw, 2012; H

ohne et al., 2014;

van Erp et al., 2012) tap into multivariate brain sig-

nals. Their goal is to either drive an online applica-

tion, or to monitor mental processes, which are in-

formative about the tasks executed by the user. But

also outside the ﬁeld of BCI, oscillatory signal com-

ponents of electrophysiological recordings like the

magnetoencephalogram, the electroencephalogram

(EEG), invasive recordings of the electrocorticogram

or local ﬁeld potentials have long been studied, as

they can contain information about the user task or

task performance (Klimesch, 1999). The exploita-

tion of these oscillatory signal components, however,

is not straight forward due to the low signal-to-noise

ratio especially with non-invasive recordings. Here,

sophisticated data driven machine learning meth-

ods (M

uller et al., 2008) proved helpful to extract sub-

spaces containing informative oscillations with en-

hanced signal-to-noise ratio. Among these methods,

common spatial patterns (CSP) (Ramoser et al., 2000;

Koles, 1991; Fukunaga, 1990) and variants thereof

are widely used (Tangermann et al., 2012; Lotte and

Guan, 2011). The algorithm allows to extract oscil-

latory components, which display contrastive behav-

ior, e.g. event-related de-synchronization (ERD) and

-synchronization (ERS) effects. These ERD/ERS ef-

fects are time-locked e.g. to the cueing time point

of discrete motor tasks (Pfutscheller et al., 1997),

and are extracted for a pre-selected frequency band.

More recently, source power comodulation (SPoC)

was proposed by D

ahne and colleagues (D

ahne et al.,

2014) as a regressing subspace ﬁltering approach.

SPoC allows to extract oscillatory components from

bandpass-ﬁltered EEG, which comodulate in their

band power amplitude with a known variable. This

variable in practice can be derived e.g. from a task-

wise behavioral metric or represent the intensity

of stimuli. At training time, when spatial ﬁlters

(they determine the oscillatory subspace components)

are derived, an optimization problem needs to be

solved. Depending on the algorithm, this can be time-

consuming as it typically involves an iterative gra-

Tangermann M. and Meinel A.

Informative Oscillatory EEG Components and their Persistence in Time and Frequency.

In NEUROTECHNIX 2017 - Extended Abstracts (NEUROTECHNIX 2017), pages 17-21

-2.0 -1.0 1.0 2.0

time t

test

relative to trial start (s)

frequency f

test

(Hz)

train

z-AUC

-0.63

-0.60

-0.58

-0.55

-0.53

-0.51

-0.47

-0.45

train

A B

Filter

Pattern

train

=28.8 Hz

subject S5

train

= -0.05 s

Figure 1: (a) Characterization of an exemplary oscillatory component (spatial ﬁlter and spatial pattern) derived by parameters

train

= -50 ms, f

train

= 28.8 Hz) using the source power comodulation (SPoC) method. (b) The z-AUC performance of this

SPoC component for varying pairs of hyperparameters (t

test

, f

test

) sampled at coordinates marked by single black dots is

interpolated and depicted in a color scheme. The chance level is provided by the blue-rimmed z-AUC values.

dient descent or the calculation of covariance matri-

ces and their inversion. At testing time, however, the

application of a known spatial ﬁlter usually is very

fast, as it can typically be realized by computing a

weighted linear combination of input channels.

No matter if supervised approaches like CSP,

SPoC or other subspace methods shall be used for

the analysis of multivariate brain signals, it usu-

ally is unclear a priori, in which exact task-related

time segment and in which frequency band the in-

formative oscillatory activity persists (Meinel et al.,

2016b). While knowledge about these method- and

task-speciﬁc hyperparameters would be desirable to

have already at training time, it provides valuable in-

sights also in the post-hoc analysis of experimental

data collected during repeated executions or sessions

of the task. For these reasons we present a method,

that allows to characterize an oscillatory component

in terms of its persistence over time and frequency

space. We are convinced, that this characterization

contributes valuable information which goes beyond

a description of ERD/ERS behavior and of the spatial

pattern.

2 METHODS

The decoding or even prediction of motor perfor-

mance from brain signal recordings is a recent re-

search topic (Meyer et al., 2014). In (Meinel et al.,

2016a), we studied the sequential visual isometric

pinch task (SVIPT, (Meinel et al., 2015)) as an ex-

ample of a repetitive hand force task. While we re-

fer the reader to (Meinel et al., 2015) for details on

this hand force training task, it is helpful to know,

that each repetitive trial required the user to control

the horizontal movement trajectory of a cursor on the

screen by applying varying levels of pinch force to

sensor. Per trial, behavioral performance metrics such

as the deviation from the optimal trajectory, reaction

time after the trial start etc. were measured. For de-

tails on SVIPT metrics and correlations among differ-

ent metrics please refer to (Tangermann et al., 2015).

The EEG activity of participants was recorded prior

and during the execution of SVIPT trials using d = 63

gel-based Ag/AgCl electrodes and BrainAmp ampli-

ﬁers. Thriving to ﬁnd an explanation for the observed

strong inter-trial variability of the motor performance,

we were able to identify robust pre-trial oscillatory

components, i.e. components whose band power was

informative to predict the single-trial motor perfor-

mance. For a discussion on robustness scores please

refer to (Casta

no-Candamil et al., 2015). Based on

the multichannel EEG recordings, spatial ﬁlters and

resulting oscillatory components were computed with

SPoC using trial-wise continuous performance labels

z. More precisely, the spatial ﬁlters were trained using

one epoch of EEG data per trial, which was extracted

as a 750 ms wide time segment. The segment’s posi-

tion within the trial is described by the hyperparam-

eter t

train

, which marks the end of the segment. In

addition, the data were ﬁltered prior to the training of

the spatial ﬁlter method to a passband of 1.5 Hz width

around a central frequency f

train

of this band. For

SPoC training, epochs of the EEG had been extracted

from trial-wise time segments located just before the

go-cue (t

train

= −50 ms).

For this short paper, we selected a single, representa-

tive spatial ﬁlter derived by SPoC, which was trained

on data of the beta frequency band f

train

= 28.8 Hz

and used the trial-wise reaction time as label z. In

Fig. 1A, we show an example of a derived spatial ﬁl-

ter w

train

∈ R

. The Figure shows the ﬁlter together

with the corresponding spatial pattern. For informa-

tion on the relation between ﬁlters and patterns in

spatial subspace decomposition methods we refer the

reader to (Haufe et al., 2014).

To obtain an estimate of the label z

est

for a novel

data epoch e, the trained spatial ﬁlter w

train

is applied

to the spatial covariance estimate Σ(e, t, f ) of the data

epoch:

est

(e) = w

train

Σ(e, t, f ) w

train

(1)

Please note, that the covariance estimate requires to

make an explicit choice of the hyperparameters (t, f ).

Equation 1 now allows to test the persistence

of a given oscillatory component on the same data

set. Therefore we evaluated the estimated labels z

est

according to Equation 1 with N = 500 novel, ran-

domly chosen time-frequency hyperparameter pairs

test

, f

test

) within the frequency range of 1 to 46 Hz

and for time segment endpoints within -2.5 s to +2.0 s

relative to the go-cue of each SVIPT trial.

For characterizing the sensitivity of the compo-

nent with respect to varying hyperparameters the z-

AUC performance is reported. Related to the area un-

der the receiver-operator characteristics curve (AUC),

the z-AUC describes how well the estimated labels

est

gathered by the band power of the SPoC compo-

nent are in accordance with the measured trial-wise

motor performance labels z. We decided to use z-

AUC rather than the correlation coefﬁcient r as an

evaluation score for the component’s persistance, as

it has shown to be less sensitive to varying training

set size. For further details see (Meinel et al., 2016a).

The interpolation and visualization of z-AUC re-

sulting from various hyperparameter pairs was per-

formed using using functional ANOVA toolbox (Hut-

ter et al., 2014).

3 RESULTS

An exemplary oscillatory component derived by

SPoC is characterized in Fig. 1A by the spatial ﬁl-

ter and pattern of the component. Its band power was

found to predict the trial-wise SVIPT reaction time.

The pattern could be interpreted such, that the com-

ponent reﬂects the status of the motor system.

As shown in Fig. 1B, its persistence has been

tested for many hyperparameter pairs, which go be-

yond the frequency of 28.8 Hz and the temporal seg-

ment of [-800 -50] ms relative to the go-cue, on which

the component had been trained. It can be observed,

that the component is able to extract information

about the task performance (reaction time in this ex-

ample) also in time intervals after the go-cue. This in-

formation subsides at around 800 ms after the go cue,

which is not unexpected, as most of the motor reac-

tions already have happened at this latency. Interest-

ingly, a second informative time interval around 1.5 s

after the go cue is observed, which may be caused by

the repetitive structure within each single SVIPT trial.

The information extracted by the component is

visible in a large beta band (approximately in the

range of 15 to 35 Hz and also in the the gamma band

above 35 Hz. In this gamma band, however, the in-

formative time intervals are shorter than in the beta

band. Interestingly, these frequency ranges and time

interval, i.e. the existance range of the component, by

large extends the original parameters (t

train

, f

train

) that

have been used to extract the component with SPoC.

4 DISCUSSION

In previous work with SPoC on data derived with the

SVIPT hand motor training, we had identiﬁed a num-

ber of oscillatory components, which allowed to pre-

dict trial-wise SVIPT reaction time (and other per-

formance metrics). We reported these components

in (Meinel et al., 2016a), but have not yet described

a method to characterize their stability in the time-

frequency domain.

Based upon an oscillatory EEG component that

has the ability to predict or decode behavioral perfor-

mance, we have introduced a method, which allows

to describe how the task-related information of this

component persists over time and in frequency space.

We have evaluated the method for an exemplary com-

ponent which had been found in our earlier study. The

method will open the door for an re-analysis of large

collections of informative components and may in the

future contribute to their functional interpretation.

A similar sensitivity analysis termed event-related

spectral pertubation analysis has recently been pro-

posed by Mousavi and colleagues for a motor im-

agery BCI paradigm. Comparing class-informative

information in the oscillatory domain along the time-

frequency space (Mousavi et al., 2017), their ap-

proach involves multiple training repetitions of the

CSP spatial ﬁltering method, while our proposed

method requires evaluations of a trained component

only, but does not require full re-training for every

hyperparameter pair.

The in-depth characterization of components with

our method clearly goes beyond a description based

on solely the ERD/ERS behavior or the corresponding

spatial patterns. While applied exemplarily to a SPoC

component, the proposed method is not restricted to

SPoC and can be utilized to characterize any type of

spatial ﬁlter / component.

We propose to use a component’s persistence in

the time- and frequency domain in order to track

changes over sessions and we argue that this is use-

ful in various scenarios. Examples are cognitive and

memory tasks (Klimesch, 1999), when changes of

oscillatory activity is induced by motor learning in

sports, or over the course of BCI-supported motor re-

habilitation after stroke — a ﬁeld which recently re-

ceived a lot of attention (Soekadar et al., 2015; Rem-

sik et al., 2016). In experimental scenarios with a re-

stricted, similar functional context, this form of anal-

ysis may even help to identify corresponding oscil-

latory components across users and can thus support

novel forms of group level analyses.

ACKNOWLEDGEMENTS

The authors are thankful for support by the Clus-

ter of Excellence BrainLinks-BrainTools, funded by

the German Research Foundation (DFG, grant num-

ber EXC 1086) and by state of Baden-W

urttemberg

through bwHPC and the German Research Founda-

tion (DFG) through grant no INST 39/963-1 FUGG.

Finally, we want to thank Katharina Eggensperger and

Frank Hutter for providing software on the hyperpa-

rameter analysis.

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