ISNN 2010

Extraction of microsaccade-related signal from single-trial localfield potential by ICA with reference

Meng Hu • Hongmiao Zhang • Hualou Liang

Received: 8 March 2010 / Accepted: 18 October 2010 / Published online: 4 November 2010

� Springer-Verlag London Limited 2010

Abstract During visual fixation, we unconsciously make

tiny, involuntary eye movements or ‘microsaccades’,

which have been shown to have a crucial influence on

analysis and perception of our visual environment. Given

the small size and high irregularity of microsaccades, it is a

significant challenge to detect and extract the microsac-

cade-related neural activities. In this work, we present a

novel application of the independent component analysis

with reference algorithm to extract microsaccade-related

neural activity from single-trial local field potential (LFP).

We showed via extensive computer simulations that our

approach can be used to reliably extract microsaccade-

related activity. We then applied our method to real cortical

LFP data collected from multiple visual areas of monkeys

performing a generalized flash suppression task and dem-

onstrated that our approach has excellent performance in

extracting microsaccade-related signal from single-trial

LFP data.

Keywords LFP � Microsaccade � ICA-R

1 Introduction

Our eyes move continually. Even during visual fixation, we

unconsciously make small (generally\1�), involuntary eye

movements or ‘microsaccades’ at an average rate of

1–2 per second. These tiny eye movements, once disre-

garded as oculomotor noise with no useful purpose [1],

have recently received increasing attentions. For instance,

microsaccades are now thought to counteract visual fading

[2] and contribute to discriminate the high spatial fre-

quencies [3]. It has also been observed that microsaccades

modulate neural activities throughout the visual system

[4–10].

However, because of the small size and high irregularity

of microsaccades, it is a significant challenge to extract the

microsaccade-related neural activity from single-trial

recording. In previous studies, microsaccade-related signal

is estimated by simple average to achieve the microsac-

cade-triggered activity [7–9]. This approach, similar to the

traditional event-related potential (ERP) method, assumes

that there are no variations at all in amplitudes, latencies or

waveforms of the evoked potentials across many micro-

saccades. This is a strong assumption and may not be valid

in practice. To overcome this limitation, we apply the

independent component analysis with reference (ICA-R)

algorithm to single-trial LFP for extracting microsaccade-

related signal.

ICA-R algorithm aims to extract desired source signals

from observed mixtures without knowledge of mixing

coefficients [11]. It takes advantage of prior information

about the desired source signal as a reference to guide the

separation process. As a result, the ICA-R algorithm

extracts only the desired source signal, which is the closest

to the reference signal. The ICA-R algorithm has been

successfully used for speech processing, ECG, EEG and

fMRI data analysis [12–15]. In this paper, we use ICA-R to

extract microsaccade-related signal from single-trial LFP,

even with low signal-to-noise ratio (SNR).

The rest of the paper is organized as follows. In Sect. 2,

we describe the neural data used in this paper and ICA-R

algorithm. In Sect. 3, computer simulations are performed

to verify the effectiveness and robustness of our approach.

Our method is then applied to real cortical LFP data

M. Hu � H. Zhang � H. Liang (&)

School of Biomedical Engineering, Science and Health Systems,

Drexel University, Philadelphia, PA 19104, USA

e-mail: Hualou.Liang@drexel.edu

123

Neural Comput & Applic (2011) 20:1181–1186

DOI 10.1007/s00521-010-0469-2

collected from monkeys performing a generalized flash

suppression (GFS) task. Section 4 contains the conclusion.

2 Materials and methods

2.1 Experiment and data description

Generalized flash suppression [16, 17], in which a salient

visual stimulus could be rendered invisible despite contin-

uous retinal input, had provided a rare opportunity to study

neural mechanisms directly related to perception. In the GFS

task, monkeys were required to press the lever to initialize a

trial. As soon as a monkey gained fixation, the stimulus of a

red disk (target) was presented. At 1,400 ms after the target

onset, small random-moving dots appeared as the sur-

roundings. With the immediate presence of the surround-

ings, the red disk could be rendered invisible. If the stimulus

disappeared from perception, the monkey was trained to

release a lever; otherwise, monkey was to hold the lever.

Therefore, based on the responses of the animal, the trial was

classified as either ‘‘visible’’ or ‘‘invisible’’. Note that the

stimuli in these two conditions were physically identical.

Multi-electrode local field potential (LFP) recordings

were simultaneously collected from multiple cortical areas

V1, V2 and V4 while monkeys performed the GFS task.

The data were obtained by band-pass filtering the full

bandwidth signal between 1 and 500 Hz, and then resam-

pled at 1,000 Hz. Horizontal and vertical eye positions

were digitized at a sampling rate of 1,000 Hz. Microsac-

cades were detected by our previous developed algorithm

[18]. In this report, we use the LFP neural recordings of

totally 88 channels from area V1 to demonstrate the

effectiveness of our method.

2.2 Independent component analysis with reference

The ICA-R algorithm has been successfully used for signal

analysis and extraction. The goal of the ICA-R is to maxi-

mize the contrast function approximated by negentropy [19]

JðyÞ � k½EfZðyÞg � EfZðgÞg�2, subject to h(w) B 0, where

y ¼ wT �x, w is a weight vector, �x is the pre-whitened

observed signals, k is a positive constant, g is a Gaussian

variable having zero-mean and unity variance, Z(�) is a

nonquadratic function, h(w) is a constraint to the contrast

function indicating the closeness measure. This problem can

be formulated as an augmented Lagrangian function [11]:

Lðw; lÞ ¼ JðyÞ � 1

2s½max

2 flþ shðwÞ; 0g � l2�;

where s is a scalar penalty parameter, l is an initial value

for the Lagrange multiplier. In this paper, we solve the

problem with an efficient implementation of ICA-R [12],

which is used to extract microsaccade-related signal by

pre-whitening the observed signals and normalizing the

weight vector. Here, we provide a brief description of ICA-

R algorithm; more details can be found in [12].

1. Center the observed signals x to make its mean zero;

2. Whiten the observed signals x to give �x;

3. Take a random initial vector w0 of norm 1, or just let

w0 = 0;

4. Choose proper s, l and learning rate g. In this work,

they are set to 0.02, 10.8 and 0.08, respectively;

5. Compute the constant k ¼ jEfZðyÞg � EfZðgÞgj;6. Update the Lagrange multiplier l by lkþ1

maxf0; lk þ shðwkÞg;7. Update the weight vector w by wþkþ1 wk � gL0wk

=

eðwkÞ, where eðwÞ ¼ kEfZ 00ðyÞg � 0:5gEfh00ðwÞg;8. Normalize the weight vector w by wkþ1 wþkþ1

�

wþkþ1

�� ��;

9. Until wTk wkþ1

�� �� approaches 1 (up to a small error),

otherwise go back to the Step (5).

In our application, we use a leave-one-out approach to

obtain the average as a reference. Specifically, all the trials

but the one being considered are used to calculate the

reference signal. The reference signal is obtained by

averaging across trials, then across electrodes.

3 Result

In this section, we perform extensive computer simulations

to verify the effectiveness and robustness of our method,

then apply it to real LFP data.

3.1 Simulations

It has been shown that the characteristic of the microsac-

cade-related signal shows a dominant peak or trough [8]. In

the simulations, we hence use a one-cycle sine wave with

peak-to-peak value of 2 to model the desired target (mi-

crosaccade-related) signal as shown in Fig. 1a.

For the cortical LFP signal, the microsaccade-related

signal is typically inappreciable due to its small size,

especially in the single-trial neural recording. As such, in

our simulation, the simulated microsaccade, i.e., the target

signal, is buried in the background activity, which is sim-

ulated as a mixture of zero-mean white Gaussian noise

e2(n) with variance of 3 and colored noise e1(n) generated

by second-order random AR process [20, 21]:

e1ðnÞ ¼ 0:75e1ðn� 1Þ � 0:35e1ðn� 2Þ þ uðnÞ;

where u(n) is a zero-mean white Gaussian noise with

variance of 0.25. Figure 1b displays an example of

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simulated signal, which is constructed by a simple sum-

mation of the target signal and the simulated background

activity. In the simulation, it is set to 1,000 data samples

with sample rate of 1,000 Hz.

In what follows, we generate 50 realizations of simu-

lated data, each consisting of 20 channels. For each reali-

zation, the scaling factor of the target signal for each

channel is Gaussian distributed with mean of 1 and vari-

ance of 0.2, and the latency shifts across realizations are

uniformly distributed from -10 to 10 ms. Figure 2 shows

the results of a typical realization with -10 ms latency

shift after the ICA-R is applied. The scaling factors in

Fig. 2a–d are respectively 0.7, 1.1, 1.6 and 1.7. From these

results, we can see that the estimated target signal (dash-

dot) matches the true target signal (solid) well in each

panel, especially for the one-cycle sine part, which presents

the most relevant information of target signal.

Figure 3 shows the grand averages of true target signal

(solid) and estimated target signal (dash-dot), which are

obtained by averaging across all trials, then across all

channels. From Fig. 3, we can see that two average wave-

forms match well, especially for their one-cycle sine wave

portions. This result provides further support that our

approach is indeed capable to extract desired signals from

low SNR data. Together, these results demonstrate that our

method not only is able to recover the target signal at the

low SNR, but also works well at different latencies and the

scaling factors.

To quantify the performance of our algorithm, we use

the root mean square error (RMSE) between the true target

Fig. 1 The target signal

(a) and a typical example of

simulated signal (b)

Fig. 2 Simulated results for

-10-ms latency shift: a scaling

factor 0.7, b scaling factor 1.1,

c scaling factor 1.6, and

d scaling factor 1.7

Neural Comput & Applic (2011) 20:1181–1186 1183

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signal s(n) and the estimated target signal s_ðnÞ. The RMSE

is computed as

RMSE ¼ 1

N

XN

n¼1

ðsðnÞ � s_ðnÞÞ2

( )1=2

;

where N is the number of data samples. Our second

measure is the SNR, which is computed as

SNR ¼ 10 log10

PNn¼1 s2ðnÞ

PNn¼1 ðsðnÞ � s

_ðnÞÞ2

( )

ðdBÞ:

Figure 4a shows the RMSE as a function of SNR of

the simulated signal. From this figure, we can see that

when SNR of simulated signal is as low as -20 dB, RMSE

remains quite small (below 0.2), indicating that our

algorithm works well even in the low SNR. Figure 4b

shows the SNR of estimated signal as a function of SNR of

simulated signal. When SNR of simulated signal is -20 dB,

with our algorithm the SNR can be increased to 5 dB. These

results indicate that our algorithm can be used to extract the

desired signal from low SNR signal with different scaling

factors and latency shifts.

3.2 Application to monkey cortical LFP data

The LFP recording consists of data collected from many

sessions, each having many trials. In each trial, there are

a number of microsaccades occurring at different times.

For each microsaccade, multi-electrode LFP data is first

extracted from 50 ms prior to microsaccade onset to 350 ms

after microsaccade onset in each trial of a session. ICA-R is

then performed on these microsaccade-triggered segments to

extract microsaccade-related signal.

To appreciate the effectiveness of our method, we first

apply our approach to LFP recordings before surrounding

onset, in which the data are well controlled except the

microsaccade as the major influence. We then apply our

algorithm to the LFP recordings after surrounding onset,

where we compare the raw microsaccade-triggered signal

with the extracted microsaccade-related signal for both

visible and invisible conditions. The results demonstrate

that the microsaccade-related signal extracted by our

method has much clearer separation of two conditions

than those obtained by the simple microsaccade-triggered

average.

3.2.1 LFP data before surrounding onset

In this section, the microsaccade-triggered averages are

calculated for both raw LFP data and the ICA-R-extracted

LFP. These averages are compared after they are normal-

ized. As shown in the Fig. 5, both averages demonstrate the

consistent trend: LFP shows intensive strong suppression

from about 50 to 200 ms after microsaccade onset, fol-

lowed by a relatively weak suppression. These curves

provide a clear indication of influence of microsaccades on

neural activity.

On the other hand, we can see from Fig. 5 that the

standard error of mean for the extracted microsaccade-

related signal (solid) is smaller than those obtained by the

microsaccade-triggered average (dashed). This result sug-

gests that our method can be used to extract microsaccade-

related component.Fig. 3 Comparison of average of true target signals (solid) and of

estimated target signals (dash-dot)

Fig. 4 RMSE (a) and SNR

(b) of estimated signal as a

function of SNR of simulated

signal

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3.2.2 LFP data after surrounding onset

In this section, our approach is applied to LFP data after

surrounding onset. Figure 6 shows the extracted micro-

saccade-related signal in two conditions, in which there are

two curves that correspond to ‘visible’ (solid) and ‘invisi-

ble’ (dashed) condition, respectively, showing clearly the

microsaccade-modulated neural activity. From Fig. 6, we

can see that immediately after the microsaccade onset,

there is a strong suppression of neural activity for both the

visible and invisible conditions, followed by a clear sepa-

ration of these two conditions from about 90 to 250 ms

before the two curves merged.

In contrast, in Fig. 7, we show the microsaccade-trig-

gered average based on the raw LFP data. In general, there

is a good agreement between Figs. 6 and 7. However, there

are two discrepancies that merit our further comments.

First, the difference of the two conditions in Fig. 6 is sig-

nificantly larger than that in Fig. 7, as shown by statistic

test (p \ 10-8 vs. p \ 10-4), indicating that our method is

able to detect more subtle difference in neural activity

evoked by microsaccades. Second, around the microsac-

cade onset, the difference between two conditions in Fig. 7

disappears in the data obtained by our method, as shown in

Fig. 6. The difference between two conditions in Fig. 7 is

largely related to the separation of perceptual visibility

(visible vs. invisible), whereas in Fig. 6, the extracted LFP

is mostly due to the occurrence of microsaccades, This

discrepancy underscores that our method is able to reliably

extract the microsaccade-related activity.

4 Conclusion

Previous studies showed that the ICA-R has a potential to

extract the desired target signal by choosing a relevant ref-

erence signal. In this paper, we extracted microsaccade-

related signal from single-trial LFP data by the ICA-R algo-

rithm. By simulations, we have shown that our approach can

be used to extract the desired signal in the low SNR signal,

and it is not sensitive to the trial-by-trial variations. These

simulations validated the effectiveness and robustness of our

method. The applications to cortical LFP demonstrated that

our approach has excellent performance in extracting

microsaccade-related signal from single-trial LFP data.

Acknowledgments This work is partially supported by NIH. We

thank Dr Melanie Wilke for proving the data, which were collected at

the laboratory of Dr Nikos Logothetis at Max Planck Institute for

Biological Cybernetics in Germany.

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Fig. 5 Comparison of the ICA-R-extracted microsaccade-related

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