EFFECTIVE SELECTION OF ELECTRODE SUBSETS IN BCI

EXPERIMENTS

Andrey Eliseyev

1,2,3

, Cecile Moro

, Jean Faber

1,2

, Alexander Wyss

, Napoleon Torres

Corinne Mestais

, Tetiana Aksenova

1,2

and Alim-Louis Benabid

2,3

Foundation Nanosciences, Grenoble, France

CEA/LETI/CLINATEC, MINATEC Campus, Grenoble, France

Joseph Fourier University of Grenoble, Grenoble, France

Keywords: Tensor Factorization, Partial Least Squares, L1-Regularization, Multi-Way Analysis, Brain-Computer

Interface, Self-Paced.

Abstract: Recently N-way Partial Least Squares (NPLS) were reported as an effective tool for neuronal signal

decoding and BCI system calibration. This method simultaneously analyses data in several domains. It is

based on the projection of a data tensor to a low dimensional space using all variables to create a final

model. In the present paper the L1-Penalized NPLS is proposed for sparse BCI system calibration allowing

to combine the projection technique with an effective selection of subset of features. The L1-Penalized

NPLS was applied for binary self-paced BCI system calibration providing a subset of electrodes selection.

Our BCI system is designed for animal research in particular for research in non-human primates.

1 INTRODUCTION

Based on neuronal activity recordings from the

brain, Brain Computer Interface (BCI) aims to

provide an alternative non-muscular communication

pathway to send commands to the external world.

Over the last decades several approaches and

methods have been developed to improve neuronal

signal decoding. Amongst others, recently multi-way

analysis was reported as an effective tool for

neuronal signal processing (Eliseyev et al., 2011;

Fatourechi et al, 2008; Müller-Putz et al., 2010;

Bashashati et al., 2007). Data from several domains

are treated simultaneously (e.g. space, frequency and

time modalities). In particular, the multi-way

analysis was applied in a binary self-paced BCI

designed to function in animals (rats) (Eliseyev et

al., 2011). In the above mentioned study rats were

trained to push a pedal to activate a food dispenser

without any cue or external stimulus. Neuronal

activity was monitored and intentional control

patterns were recognized by the BCI system. To map

the neuronal recordings to the spatial-temporal-

frequency space, continuous wavelet transform

(CWT) was applied to form a tensor of observation.

To identify the predictive model N-way Partial Least

Squares (NPLS) (Bro, 1996) was applied. It projects

the feature tensor into a low dimensional feature

space of latent variables. In parallel, a regression

model predicting the intentional control was created.

As opposed to other tensor-based methods which

recently have been applied in BCI studies

(Nazarpour et al., 2006; Zhao et al., 2009; Mørup et

al., 2008) the N-way PLS involves class information

to perform the tensor decomposition which

significantly increases the efficiency of the model.

As the NPLS works without any prior knowledge, it

can efficiently be applied to automatically generate a

model predicting BCI events from recordings of the

neuronal brain activity. That is why this method has

been chosen as a basic approach in the present study.

Note that the NPLS is a projection based method. It

involves all variables generating the final model.

Throughout BCI experiments neuronal signals of the

brain are processed in real-time. Thus computational

efficiency of the BCI system is of crucial

importance. Selecting an effective subset of features

optimizes the computational efficiency and improves

the quality of control. In the present article we

propose

 -Penalized NPLS to directly include

feature selection in the modelling process. While

generic NPLS lead to a linear combination of all

437

Eliseyev A., Moro C., Faber J., Wyss A., Torres N., Mestais C., Aksenova T. and Benabid A..

EFFECTIVE SELECTION OF ELECTRODE SUBSETS IN BCI EXPERIMENTS.

DOI: 10.5220/0003724304370443

In Proceedings of the International Conference on Neural Computation Theory and Applications (Special Session on Challenges in Neuroengineering-

2011), pages 437-443

ISBN: 978-989-8425-84-3

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

features the

 -Penalized NPLS provide a sparse

solution in different directions of analyses (e.g.

space, frequencies, or time modalities). In the

present study the

 -Penalized NPLS was applied in

binary self-paced BCI system calibration providing

at the same time, a subset of electrodes selection.

Corresponding BCI experiments were done in

nonhuman primates.

2 METHODS

2.1 Generic NPLS

The N-way PLS algorithm is based on the data

projection to a low dimensional feature space (the

space of latent variables), with further construction

of a linear regression. This method was introduced

by Bro, 1996 as a generalization of the ordinary

Partial Least Squares (PLS) (Geladi and Kowalski,

1986) to multi-way data sets (tensors). The PLS

regression models a linear relationship between a

vector of output variables and a vector of input

variables on the basis of observation matrices

and

Y : VXCY += , where V and C are noise

and coefficient matrices. To build the model, the

observations are projected into the low dimensional

spaces in such a way that the maximum variances of

X and Y are explained simultaneously. The PLS

approach is an iterative procedure. First, the matrices

X and Y are represented as

EptX +=

FquY +=

where

t and

u are the latent variables (score

vectors), whereas



and

are the loading vectors.

and

are the matrices of residuals. The score

vectors are calculated to maximize the covariance

between

and

(Geladi and Kowalski, 1986). The

coefficient

of a regression 1111

rtu

= b

calculated to minimize the norm of the residuals

r .

The procedure is iteratively applied to the residual

matrices.

Similar to the PLS, the NPLS projects the tensor

of data into the space of latent variables. Tensors

(multi-way arrays) are a higher-order generalization

of vectors and matrices. Elements of a tensor

×××

∈

…

are denoted as

iii

…

. Here,

the order of the tensor, i.e., the number of

dimensions (ways or modes). The number of the

variables

in the mode i shows the dimensionality

of this mode (Kolda and Bader, 2007). Let us

consider the case of a fourth-order tensor of

observations

321

∈

which contains n

samples

321

∈

...

. Each samples

321

∈

is the tensor of the third-order (cube).

This case corresponds to simultaneous analysis of

neuronal activity in three domains (e.g. space,

frequency and time). As an output a vector



R∈y

observations of scalar variables is considered. The

particular case of binary

R∈y corresponds to

binary self-paced BCI experiments.

The NPLS method decomposes the tensor

X as:

EwwwtX +=  ,

(1)

where the operation “



” is called the outer product

(see Kolda and Bader, 2007). The latent variable

R∈

t is extracted from the first mode of the

tensor

providing maximum of covariance between

and

. In parallel, the algorithm forms the factor,

i.e. the set of projectors

},,{

RRR ∈∈∈ www

||||



3,2,1

related to the second, the third, and the fourth modes

, respectively, in such a way that the projection

of the tensor

X on these vectors results in

t . The

projectors correspond to each modality of analyses

(e.g. space, frequency and time). To build the

projectors, a tensor of correlation



yXZ

×=

calculated (

× is the first-mode vector product of the

tensor

X and the vector y ). Then the vectors

321

,, www are estimated by the tensor Z

decomposition:

EwwwZ

321



321

→−

wwwZ 

, where



⋅

is the

Frobenius norm, which is the generalization of the

Euclidean norm for tensors (Kolda and Bader,

2007). To solve the optimization problem the

Alternating Least Squares (ALS) (Yates, 1933)

algorithm can be applied. It fixes all the projectors

except one, which is estimated in a least square

sense. The procedure is repeated for all projectors

until convergence. A coefficient

b of a regression

111

fty += b is calculated with the Minimal Least

Squares (MLS). Next, factors are calculated

decomposing the residuals. After the stop of

iterations all the particular regressions

bTy =

Ff ,1=

are summarized into a final

model

bTy ==

∑

. Vector b summarized the

NCTA 2011 - International Conference on Neural Computation Theory and Applications

438

regression coefficients for whole set of latent

variables

[

]

ttT ||

…=

. Latent variables

,1=

correspond to projectors

),,

(

321

www

2.2 L1-Penalized N-PLS Algorithm

The NPLS can be generalized to include additional

opportunities of feature selection. For this purpose,

the Alternating Least Squares algorithm can be

substitute for its penalized version decomposing

tensor

yXZ

×= . In this case the optimization

problem has the form:

{}

),),,(P

(minarg

321

zzz

zzzZzzz

zzz

+−=



(2)

where,

()

⋅P is a penalization term,

is a

nonnegative parameter of penalization. Depending

on the penalization operator

()

⋅P , several

optimization tasks can be considered: The Least

Absolute Shrinkage Selection Operator (LASSO),

)( AA =P , (Tibshirani, 1996); the Fusion Lasso

)( AA DP = , where D is a difference operator,

(Land and Friedman, 1996); the Elastic Net (Enet)

(Zou and Hastie, 2005) which includes weighted

 -

norm and

 -norm penalisations etc.

To obtain a sparse solution, the

 -norm penalty

(LASSO) is often used. The LASSO can be

implemented easily providing a sufficient level of

selectivity. In the present study, to solve the problem

the

 -penalty was integrated into the ALS

algorithm. At each step of the algorithm all the

projectors are fixed except one leading to the

optimization:

(

)

.3,2,1

minarg

321

+−=

zzzzZz



(3)

Considering the particular case

1=i :

(

)

3211

minarg

zzzzZz

+−=



(4)

The optimization problem (4) can be rewritten as

matrix:

⎟

⎠

⎞

⎜

⎝

⎛

+−=

3,211

minarg

zzzZz

(5)

where

)1(

ZZ =

is unfolding of the tensor Z , and

()

323,2

vect zzz = .

One of the approaches to solve an optimization

problem with the

1 -penalization is the Gauss-

Seidel algorithm (Shevade and Keerthi, 2003;

Schmidt, 2005). The advantages of this algorithm

are its simplicity and low iteration cost, as well as

low memory consumption. We have applied this

approach to solve the optimization task (5). Namely,

the anti-gradient of

3,21

zzzZ

+−=

RSS

was

considered:

(

)

TTT

2)( zzZzz −=

−

)(sign

−

For the first iteration,

is set equal to zero

consequently the anti-gradient

1Zz0

−

2)(

Then, the elements of

z with the largest magnitude

of the anti-gradient are added to a set of ‘free’

variables. These ‘free’ variables are optimized in a

‘one at a time’ way. For details see Shevade and

Keerthi, 2003. Note, that if

(

)

3,2

max

2max=≥

the method returns as a solution

0z =

Penalized decomposition of tensor

yXZ

×=

results in factor

{

}

{

}

321

zzzwww = .

To automatically select the optimal value of

different approaches can be used: Cross-validation

(Devijver and Kittler, 1982), generalized cross-

validation (Golub et al., 1979), Akaike’s Information

Criterion (Akaike, 1974), or Schwartz’s Bayesian

Information Criterion (Schwartz, 1978). The L1-

Penalized NPLS algorithm combines computational

simplicity and moderate memory consumption with

sufficient selectivity. This method was applied for

binary self-paced BCI system calibration and for a

subset of electrodes selection in the context of BCI

experiments in non-human primates.

2.3 Influence Analysis

The elements of the input data have an implicit

impact on the NPLS regression model through the

latent variables. The Modality Influence (MI)

analysis (Cook and Weisberg, 1982) allows

estimating the relative importance of the elements of

each mode for the final model. In case of tensor

input and scalar output variables, the MI procedure

is as follows. Latent variables are normalized

and the regression model takes the

form:

fff

bb t=

,1=

. Then for

chosen modality

3,2,1

i coefficients

b and

components of all factors related to this modality

{

}

w form the matrix

[

]

bb wwA

|| …= .

EFFECTIVE SELECTION OF ELECTRODE SUBSETS IN BCI EXPERIMENTS

439

Figure 1: BCI system calibration results in a decision rule; )(ty characterizes the position of the pedal at the moment

;

contains the signal from the brain, recorded during the experiment;

X is used for internal representation of the signal in the

system.

The vector of leverages



()

⎟

⎠

⎞

⎜

⎝

⎛

iii

diag AAh

shows the

summarized influence of elements of this modality

on the predicted output.

The MI analysis can be applied to estimate the

importance of electrodes, frequency bands, and time

intervals related to control events (Eliseyev, 2011).

3 RESULTS

3.1 Data Description

Data was collected from behavioral experiments in

non-human primates based on a simple reward-

oriented task. During the experiment the monkey is

sitting in a custom made primate chair minimally

restrained, its neck collar hooked to the chair. The

monkey has to push a pedal which can be mounted

in for different positions (‘left’, ‘right’, ‘up’, and

‘down’) on a vertical panel facing the monkey.

Every correct push event activates a food dispenser.

We used no cue or conditioning stimulus to tell the

monkey when to push the pedal. A set of ECoG

recordings was collected from 32 surface electrodes

chronically implanted in the monkeys brain.

Simultaneously, information about the state of the

pedal was stored. One recording of each position

was used to calibrate the BCI system. Training data

sets included all event-related epochs and randomly

selected ‘non-event’ epochs.

3.2 BCI System Calibration

To calibrate the BCI system the brain activity signal

of the training recording was mapped to the

temporal–frequency–spatial space to form a tensor

of observation. For each epoch

j (determined by its

final moment

), electrode c , frequency f and

time shift

, elements

cfj

,,,

of the tensor X were

calculated as norm of CWT of ECoG signal (see

Fig. 1). Frequency band

]300,10[ Hz with step

Hz and sliding windows

[]

tt ,

− ,

5.0

s with step 01.0

s were considered

for all electrodes

23 ,1=c . The resulting dimension

of a point is

(

)

3251146

. Meyer wavelet was

chosen as the mother wavelet taking into account its

computational efficiency (Sherwood and

Derakhshani, 2009). The binary dependent variable

was set to one,

, if the pedal was pressed at

the moment

, and

, otherwise.

The resulting tensor and the binary vector,

indicating the pedal position, were used for

calibration. Five factors (the number is defined by

the cross-validation procedure) and the

corresponding latent variables

t 5,1=i were

extracted by the NPLS algorithm for each pedal

position. Due to computational restrictions, the L1-

penalized version of the NPLS algorithm

(

max

9.0

) was applied to find a subset of

electrodes impacting most the final model. The

coefficients

b , of the normalized predictive model

bbty

∑

correspond to weights of the

related factors in the ﬁnal decomposition:

‘left’: 0.346, 0.273, 0.232, 0.111, 0.038;

‘right’: 0.346, 0.217, 0.195, 0.138, 0.104;

NCTA 2011 - International Conference on Neural Computation Theory and Applications

440

‘up’: 0.383, 0.263, 0.158, 0.151, 0.045;

‘down’: 0.278, 0.210, 0.194, 0.182, 0.138.

Resulting predictive models are based on subsets

of few electrodes: 6, 6, 7, and 9 for ‘left’, ‘right’,

‘up’, and ‘down’ positions of the pedal, respectively.

MI analysis revealed the leverages of the elements

of each modality (Fig. 2).

3.3 Comparison to Generic NPLS

To compare the L1-Penalized NPLS method with

the generic NPLS recordings corresponding to one

of positions of the pedal (‘up’ position) were used.

The BCI system was calibrated with both

algorithms. Resulted models were applied to the test

recording. The computational experiment has

demonstrated that the L1-Penalized NPLS

outperformed the generic NPLS approach for all

tested number of factors from 1 to 5 (Fig. 3).

4 DISCUSSION

Clinical application of BCI is one of the most

challenging tasks in neuroengineering. Over the last

decades, promising results were obtained both in

animal (Chapin et al., 1999; Wessberg et al., 2000)

and in human (Leuthardt et al., 2004; Wolpaw et al.,

2002) studies. Nevertheless, an effective solution

does not exist yet. Most BCI experiments were made

in the context of cue-paced (synchronized)

approaches where subjects wait for an external cue

that drives the interaction (Wolpaw et al., 2002). As

a consequence, users are supposed to generate

commands only during specific periods. Only the

last years an increasing number of laboratories

started to apply self-paced BCI paradigms (Leeb et

al., 2007; Scherer et al., 2008; Fatourechi et al.,

2008; Müller-Putz et al., 2010, Qian et al., 2010).

Users control a self-paced BCI at their own intention

making these devices more suitable for real-life

applications. However, the BCI performances

reported by the authors are still not suited for

practical application. Our study addresses the

problem of neuronal signal decoding in self-paced

BCI experiments.

A common approach in brain signal processing

intended for event detection/prediction consists in

extraction of event related features from neuronal

activity. Information from spatial (Rakotomamonjy

et al., 2005), frequency (Schlögl et al., 2005), and

temporal (Vidaurre et al., 2009) domains is

analysed. Note that standard methods are designed

for vector input variables which generally represent

only one domain (modality) of analysis. However,

using only one domain often does not provide

satisfactory results. In most cases two or

three ways of analyses are applied sequentially.

From the other hand, a tensor-based approach allows

simultaneous treatment of several domains. Recently

this approach was reported as a prospective tool for

neuronal signal processing.

However simultaneous signal processing in several

domains increases the dimension of feature space.

Reported methods of the multimodal analysis are

based on tensor factorization and projection of the

data into the low dimensional feature space. They

keep all the variables in a final model. Sparse

solutions, excluding non-informative electrodes

and/or frequency bands will provide better

computational efficiency and quality of control. This

was the particular objective of the present study.

To do so, we have applied the Penalized NPLS

which combines the advantages of the projection

technique, the variable selection as well as the

advantage of the integrated regression model. The

penalized version NPLS was applied to real data

collected during BCI experiments in non-human

primates to calibrate the self-paced BCI system.

Penalization was applied to the spatial modality

only. BCI system calibration resulted in predictive

models based on subsets of few electrodes (6 - 9

electrodes among 32) in all experimental protocols.

The Modality Influence analysis indicates that the

electrode #22 located in the primary motor cortex

has the highest impact on the decision rule (84%,

97%, 89%, and 75% of extracted information for

‘left’, ‘right’, ‘up’, and ‘down’ positions of the

pedal, respectively). High frequencies (

100≥ Hz)

significantly contribute to the decision in the

frequency modality, however, the influence of the

lower frequencies (

100

Hz) is also considerable,

especially for the ‘left’ position of the pedal. In the

time domain the interval [−0.2, 0] s before the event

is the most signiﬁcant for all positions of the pedal.

Comparison of the L1-Penalized NPLS with the

generic NPLS algorithm demonstrated that the

proposed method outperformed the generic

approach. This

advantage can be explained by the

overfitting effect suppression. Additional

computational experiments including different tasks

will allow better comparison of methods.

Application of sparse predictive models in on-

line real-time experiments will be the next step of

this study.

EFFECTIVE SELECTION OF ELECTRODE SUBSETS IN BCI EXPERIMENTS

441

Figure 2: Impact on the predictive model of the components of different modalities (weights) according to the MI analysis

for each pedal position; spatial modalities are represented by the graphs and the corresponding color map.

Figure 3: Comparison of prediction errors (root mean

squared error, RMSE) for the NPLS and the PNPLS

algorithms on the test set for different number of factors.

ACKNOWLEDGEMENTS

This work was partially supported by project CE

ICoBI, Nanosciences Foundation RTRA; Edmond J.

Safra Philanthropic Foundation; Fondation de

l’Avenir, CEA, France.

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