# Exploring the EEG Correlates of Neurocognitive Lapse with Robust Principal Component Analysis

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## Abstract

Recent developments of brain-computer interfaces (BCIs) for driving lapse detection based on electroencephalogram (EEG) have made much progress. This study aims to leverage these new developments and explore the use of robust principal component analysis (RPCA) to extract informative EEG features associated with neurocognitive lapses. Study results showed that the RPCA decomposition could separate lapse-related EEG dynamics from the task-irrelevant spontaneous background activity, leading to more robust neural correlates of neurocognitive lapse as compared to the original EEG signals. This study will shed light on the development of a robust lapse-detection BCI system in real-world environments.

## Keywords

EEG BCI RPCA Drowsiness Lapse Driving Fatigue## 1 Introduction

The neurocognitive lapse has been known as a critical safety issue in vehicle driving. Such momentary lapse causes approximate 1.9 million drivers to fatal car accidents with injury or death [1]. Technologies that enable instant lapse detection and feedback delivery to rectify drivers from the occurrence of lapse are thus urgently required. For the past two decades, the noninvasive brain-sensing technology, namely electroencephalogram (EEG), has been adopted for this purpose because of its high temporal resolution of brain signals allowing a prompt response to a neurocognitive lapse. For example, studies have shown strong EEG correlates of behavioral lapses, including power spectra [2, 3, 4, 5, 6] and autoregressive features [7, 8]. These EEG features could then be used to develop various on-line/off-line neuroergonomic systems for monitoring drowsiness, fatigue, and behavioral lapse in task performance [2, 3, 9, 10, 11, 12]. It is believed that an effective computational approach that can further leverage EEG correlates of neurocognitive lapse is a crucial step for improving the practicability of BCI-based lapse detection system in real life, which is the main focus of this study.

Robust principal component analysis (RPCA) [13] has recently been shown to be able to separate task-relevant and sparse EEG dynamics from the spontaneous task-irrelevant background activity [14]. The study demonstrated that the RPCA could improve the characterization of emotion-related EEG patterns across different recording days, and in turn facilitate a more effective emotion-classification model. As such, the task-related EEG dynamics of interest could be extracted from the task-irrelevant spontaneous background activity using RPCA, and could alleviate the EEG variability across sessions [14]. Analogously, this study explores the applicability of the RPCA for assessing the EEG correlates of neurocognitive lapses during driving.

## 2 Materials and Methods

### 2.1 Experiment and EEG Recording

This proof-of-concept study employed an EEG dataset of eight subjects participating in a lane-keeping driving task (LKT) in which EEG data and human driving behavior were simultaneously recorded [15]. The experiments were conducted in a virtual-reality-based driving simulator. Each subject drove on a straight highway scene during the night with artificial lane-deviation events introduced every 6–10 s. In each lane-deviation event, the car would randomly drift toward to left or right, and the subject was instructed to steer the car back to the cruising position as soon as possible. The duration from the onset of lane-deviant to the onset of steering movement was defined as the reaction time (RT), which indexed the extent of neurocognitive lapse. Longer RT indicated poor driving performance at the given moment. The experiment started in early afternoon when afternoon slump often occurred and thus maximized the opportunity of collecting neurocognitive lapses. The entire session of LKT lasted about 90 min, which was long enough to collect sufficient data under both alertness and drowsiness.

The EEG data were recorded by a 32-channel Quik-Cap electrode system (Compumedics Neuroscan, Inc.). Thirty Ag/AgCl electrodes were deployed according to the modified international 10–20 system, and two reference electrodes were placed upon left and right mastoids. The EEG signals were sampled with 16-bit quantization and 500 Hz sampling rate.

### 2.2 Lapse Assessment

In this study, a lapse refers to momentary unresponsiveness to the lane-deviation event in the LKT, and its level was quantitatively estimated based on RT. This study empirically defined the RT as alertness if its value was below the 5th percentile of the RTs across entire session for each session. In order to calibrate the individual differences in the distributions of RT values, the RTs of each individual was further normalized into a range of 0 to 1, defined as follows [11, 12]:

*LI*is the normalized lapse index,

*τ*is the RT for a lane-deviant event, and

*τ*

_{ 0 }is the RT of alert trials. That is, the higher

*LI*value is, the more momentary lapse a subject is. This study used correlation analysis to investigate the relationship between the EEG dynamics and the changes of RT.

### 2.3 EEG Data Processing

The 30-channel EEG signals referenced to the arithmetic average of left and right mastoid were first submitted to a band-pass finite impulse response filter (2 to 30 Hz) to eliminate DC drift and high-frequency noise including 60 Hz powerline noise. Trials contaminated by artifacts or noise were manually inspected and removed. Next, the filtered 30-channel EEG data were down-sampled to 250 Hz for analysis.

Previous studies [2, 3] have reported significant EEG spectral correlates of RT in stereotype frequency bands, such as delta (2–5 Hz), theta (5–8 Hz), alpha (8–13 Hz), and beta (13–30 Hz) bands. This study thus examined the impact of RPCA processing on EEG spectral time series in the same EEG frequency bands. To assess the associations between EEG dynamics and cognitive lapses, this study first calculated the band power (logarithmic signal variance) of each channel within a 3-s window before the onsets of each lane-deviation events, and then correlated that with the corresponding RT values.

### 2.4 Robust Principal Component Analysis

*X*\( \in R^{m \times n} \) (

*m*: number of attributes,

*n*: number of observations), into a sparse matrix,

*S*, and a low-rank matrix,

*L*, followed by

*X*=

*S*+

*L*, which can be efficiently solved by a tractable convex optimization proposed in [13]:

*i.e.*, the sum of singular values, \( \left\| \cdot \right\|_{1} \) denotes the L1 norm,

*i.e.*, the sum of absolute values of matrix entries, \( S^{ + } \) is the optimized estimate of sparse component, \( L^{ + } \) is the optimized estimate of low-rank component, and \( \lambda \) is a positive regularizing parameter empirically defined as \( \lambda = 1/\sqrt {max(m,n)} \) [13]. This study formed the input matrix (

*m*: number of electrodes × number of time points in a 3-s epoch,

*n*: number of epochs in a session) for each subject. The method of augmented Lagrange multipliers [16] was adopted to perform RPCA decomposition. After the RPCA decomposition, the correlation coefficients between the normalized RTs (the lapse index) and the EEG spectral features estimated separately from the original band-passed EEG signals, sparse component, and low-rank component were compared using a statistical assessment of Wilcoxon signed-rank test. This study hypothesized that the sparse components,

*S*, would profitably extract lapse-related EEG dynamics, and therefore would be more correlated with the RTs, compared to the low-rank components,

*L*, and the original EEG signals,

*X*.

## 3 Results and Discussion

*p*-value) between RTs and band power at different scalp locations using the (the 1

^{st}row) band-passed EEG signals, (the 2

^{nd}row) sparse components, and (the 3

^{rd}row) low-rank components. Brightness in gray-scaled topographies represents the correlation was statistically significant (a strong correlation) between the band power and RTs. The 4

^{th}(5

^{th}) row plots the differences of

*p*-values between the 1

^{st}and the 2

^{nd}(3

^{rd}) rows. The red squares mark the channels whose correlations between the band power and RTs were significantly enhanced in terms of the

*p*-value over using the original EEG band power. Specifically, the ‘Original’ scalp map exhibited strong correlations in frontal delta, moderate correlations in frontal theta, and parietal-occipital theta and alpha, which were somewhat in line with previous studies [2, 3, 4]. The sparse components obtained by RPCA enhanced the extents of the correlations between the EEG power and RTs at several channels (marked in red), compared to the original scalp-EEG band power. The augmentations in the highlighted channels (see the 4

^{th}raw, Sparse - Original) were statistically significant. In contrast, the low-rank component did not provide any improvement in the correlations between EEG power and RTs (see the bottom row, Low-rank – Original).

The above findings evidently proved the posed hypothesis that the sparse EEG signals obtained by RPCA can profitably extract lapse-related EEG dynamics, and therefore carry more informative EEG spectral features accounting for behavioral lapses. In this preliminary proof-of-concept study, with such an improvement in feature extraction for EEG correlates of lapse, we believe that RPCA could boost the performance of a lapse detecting system.

While previous studies have applied independent component analysis (ICA) to extract highly informative EEG correlates of drowsiness [2, 9], a quantitative comparison between RPCA, ICA, and other related approaches on enhancing the quality of EEG features would be of interest to the researchers in this field and a natural next step of this study. Future work will also study to what extent the RPCA-enhanced EEG spectral correlates of neurocognitive lapse can improve the performance of lapse detection, which will increase the practicability of BCI-based lapse detection system in real life.

## 4 Conclusion

The present study empirically demonstrated the efficacy of RPCA for enhancing EEG correlates of neurocognitive lapse. Study results suggested that the RPCA could be used as a pre-processing step to extract the lapse-related EEG dynamics of interest from the spontaneous background activity, leading to a more robust lapse-detection BCI in real-world environments.

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