Computational Intelligence and Neuroscience

Volume 2018, Article ID 4278782, 11 pages

https://doi.org/10.1155/2018/4278782

## Sinc-Windowing and Multiple Correlation Coefficients Improve SSVEP Recognition Based on Canonical Correlation Analysis

Department of Electrical, Electronic and Information Engineering (DEI), University of Bologna, Cesena, Italy

Correspondence should be addressed to Valeria Mondini; ti.obinu@3inidnom.airelav

Received 9 August 2017; Revised 21 February 2018; Accepted 5 March 2018; Published 12 April 2018

Academic Editor: Jean-Pierre Bresciani

Copyright © 2018 Valeria Mondini et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Canonical Correlation Analysis (CCA) is an increasingly used approach in the field of Steady-State Visually Evoked Potential (SSVEP) recognition. The efficacy of the method has been widely proven, and several variations have been proposed. However, most CCA variations tend to complicate the method, usually requiring additional user training or increasing computational load. Taking simple procedures and low computational costs may be, however, a relevant aspect, especially in view of low-cost and high-portability devices. In addition, it would be desirable that the proposed variations are as general and modular as possible to facilitate the translation of results to different algorithms and setups. In this work, we evaluated the impact of two simple, modular variations of the classical CCA method. The variations involved (i) the number of canonical correlations used for classification and (ii) the inclusion of a prefiltering step by means of sinc-windowing. We tested ten volunteers in a 4-class SSVEP setup. Both variations significantly improved classification accuracy when they were used separately or in conjunction and led to accuracy increments up to 7-8% on average and peak of 25–30%. Additionally, variations had no (variation (i)) or minimal (variation (ii)) impact on the number of algorithm steps required for each classification. Given the modular nature of the proposed variations and their positive impact on classification accuracy, they might be easily included in the design of CCA-based algorithms that are even different from ours.

#### 1. Introduction

A Brain-Computer Interface (BCI) is a system enabling direct communication between the brain and the outside, as it directly translates the recorded neural activity into a control signal for an external device (e.g., a computer, a machine, or a speller) [1]. Among noninvasive systems, electroencephalography- (EEG-) based BCIs are the most widespread [2], and they can rely on four possible electrophysiological sources: slow cortical potentials (SCPs), event-related desynchronization/synchronization (ERD/ERS), event-related potentials (as P300), or Steady-State Visually Evoked Potentials (SSVEPs) [3]. Among these, SSVEP-based BCIs are appealing for their high accuracies and information transfer rate (ITR), thanks to the high signal-to-noise ratio of SSVEPs even without user training [4]. For this reason, SSVEP-based BCIs have been raising increasing attention over the years [5, 6].

SSVEPs are periodic brain signals elicited over the occipital cortex by visual stimulations with frequencies higher than 6 Hz [7]. In case different flickering objects (LEDs, symbols, and squares) are simultaneously presented, an analysis of the SSVEP spectral content permits to reconstruct which stimulus the user is focusing on.

Traditionally used methods perform SSVEP recognition based on power spectral density analysis (PSDA) [7]. In PSDA-based approaches, spectral powers are estimated from the EEG spectrum at the target stimulation frequencies and used as a feature for classification [8–10]. However, PSDA-based methods can suffer from noise sensitivity if few channels are acquired, besides requiring relatively long signal portions (e.g., >3 s) to estimate the spectrum with a sufficient frequency resolution [11–13]. A promising and increasingly used approach, which has recently attracted the interest of researchers [14–17], is the one based on Canonical Correlation Analysis (CCA) [7].

CCA is a multivariate statistical method able to reveal the underlying correlation between two sets of data [18]. For SSVEP recognition, CCA is performed several times between the considered EEG segment and a set of sine-cosine reference signals modeling the pure SSVEP responses to each stimulation frequency [7]. The frequency response showing highest correlation with the analyzed EEG portion is finally recognized as the observed one.

The efficacy of the CCA approach has been widely proven, and its superiority to PSDA in terms of speed, accuracy, and computational load has been shown [19, 20]. For this reason, several CCA variations have been proposed over the years [11–13, 15, 21–26].

Some CCA variations, as [11–13, 15, 21, 23], modified the SSVEP reference signals by including subject-specific features from each user’s EEG. The work in [24] enriched the algorithm with incorporating intersubject information from the signals of multiple subjects. In [25], an effort was made towards compensating the natural decrease in signal-to-noise ratio of SSVEPs at higher stimulation frequencies by correcting classification gains based on the shape of individual background EEG. Finally, in [22, 26], CCA was repeated multiple times for each stimulation frequency, each time processing the signal with a different IIR band-pass filter, to combine different aspects of the same EEG response.

Although each introduced variation produced significant increments of classification accuracy, all of them tended to increase the complexity of the algorithm. They indeed either required additional user training, to incorporate information from individual EEG data [11–13, 15, 21, 23], or increased computational load by multiplying the number of CCAs to assess each stimulation frequency [22, 26]. However, we believe that even taking simple procedures and low computational costs may be relevant, especially to favor the spread of low-cost and high-portability devices. In addition, it would be desirable that variations are as general or scalable as possible to facilitate the translation of results to different setups.

Given these premises, this work presents two simple and modular variations based on the classical CCA method. The variations regard (i) the number of correlations considered for classification and (ii) the preprocessing of the signals. We show that both modifications can significantly improve classification accuracy but still leaving the whole procedure training-free and with no (variation (i)) or minimal (variation (ii)) impact on the number of steps required for each SSVEP identification.

#### 2. Materials and Methods

##### 2.1. The Standard CCA Method for SSVEP Recognition

Canonical Correlation Analysis (CCA) is a multivariate statistical method [18] used to reveal the underlying correlation between two sets of data. Given two sets of random variables** X ** and** Y **, CCA finds the two corresponding sets** U **=** AX ** and** V** =** BY ** (linear combination of the original ones through** A ** and** B **), called* canonical variables*, so that the correlation between each pair or rows is maximized: with leaving , , and uncorrelated if . Each CCA leads to a number of solutions equal to the minimum between the numbers of rows in** A ** and** B **. The solutions , sorted in descending order, are called* canonical correlations* and are a measure of the similarity between the two sets of original data.

The use of CCA in the field of SSVEP recognition was first proposed by Lin et al. in [7]. Given stimulation frequencies to be distinguished, CCA is performed times, one for each stimulation frequency , between the multichannel EEG signal in** X ** ( acquired channels, time samples) and a set of sine-cosine reference signals in modeling the pure SSVEP responses. Each set is composed as follows:where is the stimulation frequency, is the sampling rate, and is the number of harmonics included in the analysis.

Every CCA generates a vector of canonical correlations , of which only the first and largest one, , is used as a feature for classification. The analyzed EEG segment in** X** is indeed assigned to the stimulation frequency leading to the maximum correlation :

##### 2.2. Variation 1: Number of Considered Canonical Correlations

Although the efficacy of the CCA method for SSVEP recognition has been widely proven [14, 16] and many variations have been proposed [11–13, 15, 21–27], the majority of approaches consider only the first canonical correlation as a feature for classification. Nevertheless, as already noted by Lin et al. [7], since real EEG signals may be contaminated by noise and show phase transitions, the information might be spread over more than one correlation coefficient.

As a first variation of the algorithm, we evaluated the impact of taking a combination of more than one correlation coefficient as a feature for classification, following preliminary results in [28]. Since the canonical variables in** U** and** V** are estimated so that each couple and are uncorrelated for and the sine-cosine waves in the reference signals are orthogonal between each other, the information contained in each set of canonical variables will always be in quadrature with respect to the others. For this reason, we propose combining the considered correlations with using the Euclidean norm: The resulting combination would be used as a feature for classification in place of the largest canonical correlation only. The number can range from 1 to the minimum between and 2, with number of acquired channels and number of considered harmonics. In this work, we employed EEG channels (see Section 2.4 for details) and = 3 harmonics, so we explored the impact of taking all the possible numbers of considered correlations between 1 and 2.

##### 2.3. Variation 2: Preprocessing with Sinc-Windowing

Another possible variation with respect to literature may consist in adding a preprocessing step to the EEG segments before performing CCA. If we exclude the works in [22, 26], employing IIR filter banks, CCA is indeed typically applied without any prefiltering of the EEG signals. Nevertheless, we believe that a narrow-band prefiltering step around the employed stimulation frequencies and their harmonics might be useful to increase the signal-to-noise ratio, expectantly enhancing classification accuracy.

As a second variation, we evaluated the influence of such type of prefiltering with using a sinc-windowing implementation. The technique of sinc-windowing consists in the convolution of the analyzed signal with an adequately modulated sinc function. As it is known, the inverse Fourier transform of an ideal rectangular band-pass filter centered in and with bandwidth iswhere* f* is the frequency and is the inverse Fourier transform. Thus, the filtering around the stimulation frequencies and harmonics can be accomplished by means of a convolution with the following function:where is the bandwidth (in this work, Hz), is the number of harmonics, and are the stimulation frequencies.

##### 2.4. Data Acquisition

The EEG was recorded from 8 electrodes (PO7, PO8, PO3, PO4, O1, O2, POz, and Oz), positioned according to the international 10-20 system. The signals were acquired using a Brainbox EEG-1166 amplifier, with a 256 Hz sampling frequency and a 50 Hz Notch filter on.

SSVEP stimulation was provided through four blue LEDs, arranged around a PC monitor. Each LED flickered at a different stimulation frequency ( = 8 Hz, = 9 Hz, = 10 Hz, and = 11 Hz). The four stimulation frequencies were selected before the beginning of the study and were the same for all subjects. All stimulations were provided with a 50 percent duty-cycle. The behavior of the LEDs was controlled by a LabVIEW-Arduino interface.

##### 2.5. Experimental Paradigm

Ten healthy volunteers (aged 22 to 26, 4 males and 6 females) participated in the study. All of them had normal, or corrected to, normal vision. During the experiment, the participants sat on a comfortable chair, with their arms relaxed and their head still, approximately 60 cm distant from the PC monitor.

The experiment was organized into runs and the runs were organized into trials. Each participant underwent a total of 4 runs, each comprising 16 trials. Each trial consisted of three subsequent phases: a 1 s* preamble*, a 12 s* stimulation*, and a 2 s* break* period. During the* preamble*, a yellow square appeared on the screen indicating the target LED; then all LEDs started simultaneously flickering during* stimulation*, and the trial ended with a* break* period, where the LEDs shut off and the square disappeared. The order of the target LEDs was randomized and counterbalanced in each run, so that each LED was gazed for the same amount of time. To summarize, each experiment included a total of 4 runs × 16 trials × 12 seconds = 768 seconds of stimulation, that is, 192 seconds for each class.

##### 2.6. Performance Evaluation

For each subject, we evaluated the average classification accuracy at the end of each run. To highlight the impact of the two proposed variations (composition of the feature vector and sinc-windowing), all accuracies were recomputed using all the possible combinations of methods, that is, a number of considered correlations from one to = 6, with or without sinc-windowing. To evaluate the influence of considering different lengths of EEG signal for SSVEP recognition, all accuracies were recomputed with considering signal portions ranging from 0.5 s to 5 s, although the detailed results of statistical tests will be reported only in the case of a 1.5 s window length.

Another commonly used measure of BCI performance, encompassing the concepts of speed, accuracy, and number of choices, is the measure of information transfer rate (ITR), expressed in bit/min. For reasons of completeness, ITR was also provided, and it was computed according to [29] where is the number of choices, is the classification accuracy (expressed between 0 and 1), and is the epoch duration (in seconds).

For the sake of comparison with other CCA-based literature methods that might be related to ours, we finally recomputed classification accuracies with the method of Chen et al. in [26], employing IIR filter banks, while we omit the comparison with [22] as not reasonably adaptable to our setup.

##### 2.7. Statistical Analyses

At first, we compared each accuracy to chance level. The value of chance level was obtained by running the simulations as descripted in [30] in the case of a 4-class BCI and taking the upper bound of the confidence interval at *α* = 1% significance, as an analytical expression of chance level was not available for the multiclass case. As concerns statistical comparison between methods, we had to account for the fact that multiple data came from the same subject; that is, the samples could not be assumed to be completely independent. For this reason, instead of using paired-samples -test to compare each method against the others, we ran all evaluations as post hoc tests of a repeated-measures ANOVA. The ANOVA design included both the factors “method” (the within-subject factor) and “subject,” thus taking into consideration all dependencies among data. Post hoc tests were carried out using Bonferroni correction. The use of parametric statistical tests was justified by the normality of data distributions, as confirmed by the application of a preliminary Kolmogorov-Smirnov test.

#### 3. Results

The classification accuracies of each subject, run, and method are detailed in Table 1 and summarized in Figure 1. The last two rows of Table 1 indicate the average and peak increment of each method with respect to standard CCA (first column). All the obtained accuracies were significantly higher than chance, as the upper bound of the confidence interval for chance level (with a significance of %) in this particular setup was 30.27%. In Table 2, the results of the post hoc comparisons (Bonferroni-corrected) between each pair of methods are reported. In Figure 2, the accuracy curves of all the considered methods, evaluated with different windows lengths, are shown. In order to avoid redundancies, the detailed ITRs for each subject, run, and method are omitted, as they can be easily computed from the accuracy results in Table 1 and according to (7). Nevertheless, Table 3 reports the average and peak ITR of each combination of methods, together with the average and peak increment in ITR with respect to classical CCA, in the same manner as reported in the last rows of Table 1.