Sampled Sinusoidal Stimulation Profile and Multichannel Fuzzy Logic Classification for Monitor-based Phase-coded SSVEP Brain-Computer Interfacing

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1 Sampled Sinusoidal Stimulation Profile and Multichannel Fuzzy Logic Classification for Monitor-based Phase-coded SSVEP Brain-Computer Interfacing Nikolay V. Manyakov, Nikolay Chumerin, Arne Robben, Adrien Combaz, Marijn van Vliet, and Marc M. Van Hulle Laboratorium voor Neuro- en Psychofysiologie, KU Leuven, Campus Gasthuisberg, O&N, Herestraat 49, 3 Leuven, Belgium {NikolayV.Manyakov, Nikolay.Chumerin, Arne.Robben, Adrien.Combaz, Marijn.vanVliet, Marc.VanHulle}@med.kuleuven.be Abstract. We introduce new stimulation and decoding methods for electroencephalogram (EEG)-based brain-computer interfaces (BCI) that have targets flickering at the same frequency but with different phases. The phase information is estimated from the EEG data, and used for target command decoding. All visual stimulation is done on a conventional (6 Hz) LCD screen. Instead of the on/off visual stimulation that is commonly used in phase-coded BCI, we use a sampled sinusoidal intensity profile. We show that this enables us not only to encode more commands, under the same conditions, but also to obtain EEG responses with more stable phases. To fully exploit the circular nature of the data, we introduce a filter feature selection procedure based on circular statistics and develop a fuzzy logic classifier designed to cope with circular information from multiple channels jointly. Keywords: Brain-computer interface, steady-state visual evoked potential, EEG, phase, visual stimulation, fuzzy logic classifier Submitted to: J. Neural Eng. Equally contributing authors.

2 . Introduction A brain-computer interface (BCI) reads and decodes brain activity to enable a subject to interact with the external world without any muscular- or peripheral nerve activity. In this study, brain activity is read noninvasively, using electroencephalography (EEG). The considered BCI is based on the steady-state visual evoked potential (SSVEP). This type of BCI employs the psychophysiological properties of EEG brain responses recorded from the occipital area during periodic visual stimulation (e.g., flickering stimuli). If the latter is at a sufficiently high rate (higher than 6 Hz), then the individual transient visual responses, which are time- and phase locked to the stimulus onset, overlap and form a steady state signal that resonates at the stimulation frequency and its integer multipliers []. This means that, when the subject is looking at stimulus flickering at the frequency f, the evoked increase in amplitudes at frequencies f, f, 3f,... can be detected in the Fourier transform of the EEG signal recorded from the subject s occipital pole. By using several frequencies, one can encode several corresponding targets and in this way achieve a frequency-coded SSVEP-based BCI. It has been shown that the overall performance of the frequency-coded SSVEP BCI can be increased by also considering phase information in addition to amplitude information in the decoding process [, 3]. However, when using a computer screen in combination with the standard on/off visual stimulation (see Fig. a) some restrictions are imposed on the number of stimulation frequencies that can be adopted: they should all be related to the refresh rate of the computer screen [4], preferably restricted to a specific subject-dependent frequency band [5]. In addition, the harmonics of some stimulation frequencies could interfere with one another, leading to a deterioration of the decoding performance [4]. To overcome these restrictions it was proposed [5, 6, 7, 8] to encode the targets not by the frequency, but rather by the phase of the SSVEP: the N targets are simultaneously flickering at the same frequency f, but with different time delays t m = (m )/(fn), corresponding to phase delays ϕ m = π(m )/N, one for each target command m (m =,..., N). But still, when using a computer screen as a stimulation device, the number of phase-coded targets is also limited in the case of the on/off stimulation: the target stimuli are either maximally bright ( on ) or completely dark ( off ) depending on the video frame rate. For example, to produce a 5 Hz stimulus on a screen with 6 Hz refresh rate, there are only four video frames per stimulation period, which leads to only four possible phase-shifts that can be rendered (as, for example, in Fig. b). In order to deal with this, one can rely on the fact that video frames on computer screens are updated progressively, usually from top to bottom. This means that relatively small stimuli at different vertical positions physically appear on the screen at different moments in time, thus, causing different phase lags. This effect can be used to increase the number of phase-coded stimuli [9]. Albeit useful, this approach still relies on frequencies that are integer dividers of the screen refresh rate. In addition, it poses some restrictions on the stimulus layout: e.g., it is not possible to achieve an arbitrary phase shift between pairs

3 3 f = 3 Hz f = Hz f 3 = 5 Hz (a) On / off frequency-coded stimulation. f = 5 Hz, ϕ = f = 5 Hz, ϕ = π f = 5 Hz, ϕ 3 = π f = 5 Hz, ϕ 4 = 3π (b) On / off (5 % duty cycle) phase-coded stimulation. Figure : Examples of the frame-based on/off stimulation patterns. The white-shaded squares represent on frames, the dark-shaded ones off frames. A 6 Hz screen refresh rate is assumed. of horizontally arranged stimuli. In this study we propose another way to overcome the current limitations of phase-coded SSVEP. In phase-coded SSVEP BCI, the classifier has to operate on phase information, extracted from EEG data, which is circular by nature. The output classes are associated with phases, and therefore are circularly interrelated as well. However, the majority of the conventional classifiers used for phase-coded BCIs assume noncircular data, which, in turn, implies some (unfolding) conversion of the input/output circular data. Usually this conversion is done in a straight-forward way not preserving the topological structure of the data and, therefore, in fact inappropriately. This calls for a new BCI decoding algorithm specifically designed/tuned for circular data. Due to the complex nature of the problem, phase-coded SSVEP BCI systems have been proposed that consider only the phase extracted from a single channel (either Oz referenced to the mastoid [6, ], or by using a bipolar lead [5, 8]). To incorporate phase information from several channels, spatial filtering can be used [,, 3, 4, 5]: it constructs weighted mixtures of recording channels, leading to new channels from which the phases can be further extracted. The phase can then be processed either by the mentioned single channel decoding approach [], or by applying standard multichannel decoding strategies such as single layer neural networks [], support vector machines [3] or probabilistic neural networks [4]. While such classification procedures lead to adequate results, the proposed decoding strategies either do not meet the multichannel requirement as in the case of [] (the authors admitted that the whole methodology is not fully based on multiple channels ), or do not cope with the discussed circular nature of the problem as in [, 3, 4]. In this paper we present a fully multichannel approach based on a fuzzy logic classifier that deals with circular information from several channels either without the use of spatial filtering or atop of it. As it is customary when adopting a multichannel solution, first a feature selection is performed to select the optimal (in terms of decoding accuracy) channels and to reduce

4 the dimensionality of the data. In this study we propose a filter-based feature selection technique based on circular statistics and specifically designed for our fuzzy classifier. 4. Methods.. EEG Data Acquisition and processing The EEG data were recorded using an 8-channel EEG system [6] developed by Holst Centre. Each EEG channel is sampled at 4 Hz with bits per sample. We used active Ag/AgCl electrodes (ActiCap, Brain Products) located primarily on the occipital pole, namely at positions PO7, PO3, POz, PO4, PO8, O, Oz, O according to the international system. The reference and ground electrodes were placed on the right and left mastoids respectively (mainly to compare our results with [6], where the recordings were done with a single Oz electrode referenced to the right mastoid). Additionally to the EEG channels mentioned above, for further analysis we also considered these electrodes re-referenced with respect to a common average reference (CAR) and all possible bipolar combinations, thus 44 channels s i (t) in total. For each stimulation stage the phases ϕ i were estimated as: ( ϕ i = arg s i (t) cos(πnft) + j ) s i (t) sin(πnft), t t where f is the stimulation frequency, n indicates the considered (sub)harmonic and j =. Only the fundamental stimulation frequency was used in this study, thus n =, leading to 44-dimensional feature space of phases ϕ i s (i =,..., K, K = 44). For our assessment we considered N t = 5 cases, in which the segments s i (t) of length T =,..., 5 seconds were taken from the beginning of each stimulation stage... Visual stimulation The stimulation frequency in our experiments is f = 5 Hz, which is known to elicit the largest SSVEP amplitude [7]. For visual stimulation, we used a laptop LCD screen with a reported refresh rate of about 6 Hz. More precisely, the estimated refresh rate was on average 59.9 Hz, which led to an on/off stimulation very close to, but not exactly at 5 Hz. To encode more than N = 4 targets (which is the limit for on/off stimulation at the corresponding stimulation frequency) and to be closer to 5 Hz, we propose to vary the desired stimulus intensity continuously between and using a sinusoidal periodic profile with frequency f = 5 Hz, specified as α f (t) = ( + sin(πft + ϕ)). For each video frame, the intensity of each target is estimated by sampling the desired intensity profile at the time t when the stimulus appears on the screen (see Fig. ). In this way, the stimulation relies on time t, rather than on the frame counter.

5 5.5 ϕ =.5 ϕ = π/3 desired requested rendered.5 ϕ 3 = 4π/ Time (s) Figure : Schematic representation of the intensity profiles in the sampled sinusoidal stimulation case. The profiles of three target stimuli are shown. All stimuli flicker at 5 Hz, but with different phase shifts ϕ i, i =,..., 3. The considered time interval is ms. The green dashed curves represent the desired sinusoidal stimulation profiles. The requested sampled sinusoidal stimulus intensities are shown as red dot-dashed curves. The stimulus intensities rendered by the screen are (schematically) depicted as blue curves. The vertical gray dotted lines indicate the time moments of the video frame flips. Note that the rendered intensities do not perfectly adhere to a rectangular shape due to a nonzero pixel response time of the screen..3. Luminance profiles of the stimuli In order to find out the real shape of the stimulus luminance profiles and confirm our prediction (depicted in Fig. as the rendered profile), we recorded the actual luminance of the stimuli with a photodiode. The photodiode measurements are expressed in volts, while we were interested in luminance measured in cd m, thus we had to find a way to convert the photodiode s output into luminance. To build this mapping we collected a series of luminance measurements (using a Minolta Chroma Meter CS-) along with the readouts from the photodiode. By scanning the requested intensity from to we collected about measurements of the stimulus luminance and the corresponding photodiode output. The collected data were then fitted with a polynome. Fig. 3 shows the stimulus luminance profiles recorded with the photodiode for both the on/off and the sampled sinusoidal stimulations. All luminance-related recordings were done using the same setup as in our experiments (see Section.4)..4. Experimental procedure Seven (N s = 7) male subjects (aged 3 35 with average 8.3 years) participated in the experiments. The subjects were sitting about 6 cm from the laptop s LCD screen on which the stimuli of size 6 cm 6 cm were shown. The following two experiments were performed:

6 6 Luminance (cd/m ) Time (s) sinusoidal on / off Figure 3: The stimulus luminance profiles recorded by a photodiode at khz sampling rate. The output of the photodiode was converted into luminance using a nonlinear mapping derived from the photodiode calibration data (see text). Both profiles were recorded in the experimental conditions described in Section. from the stimuli flickering at 5 Hz. Each profile corresponds to one out of two considered stimulation styles. The vertical gray dotted lines indicate the timing of the video frame flips.. A stimulus flickering at f = 5 Hz with zero phase shift ( ϕ = ) was presented in the center of the screen for five seconds with a fixation point (a small marker on the screen indicating the location which subject should attend to) in the center of the stimulus, followed by one second of no stimulation. This was repeated 3 times with the standard on/off (5 % duty cycle) and the proposed sampled sinusoidal stimulation. The recorded data were used to investigate the phase stability.. A set of N = 6 stimuli (5 % more than the number of targets available with the standard on/off stimulation) flickering at f = 5 Hz with phase shifts ϕ m = π(m )/3 (m =,..., 6) were simultaneously presented using the proposed sampled sinusoidal stimulation. The 6 cm 6 cm stimuli were arranged in two rows and three columns, separated 7.5 cm horizontally and 7.75 cm vertically. The fixation point indicated the stimulus, which subject has to attend to. All stimuli were flickering for five seconds followed by one second without stimulation, allowing the subject to shift his focus to the new position of the fixation point. Each stimulus was requested to be attended by the subject times. In total, we acquired 6 = five-second-long EEG data intervals per subject..5. Feature selection To reduce the amount of information for the subsequent classification we propose a filterbased (thus not relying on any classifier) feature selection procedure on training data, which among all class-feature pairs P = {(m, i) : m =,..., N, i =,..., K} selects only a subset S P of statistically most relevant (for the desired class separation) pairs. Since the input features (the phase values ϕ i estimated from the channels s i, i =,..., K) are circular, we suggest to employ circular statistics [8], and assume that the input features ϕ i from the m-th class are sampled from a von Mises distribution p m i (ϕ µ m i, κ m i ) = exp(κ m i cos(ϕ µ m i ))/(πi (κ m i )), where I is the modified zero-order Bessel function, κ m i is the concentration parameter (a reciprocal measure of dispersion)

7 and µ m i is the circular mean parameter (the distribution is clustered around µ m i ). For each feature i separately and for all possible pairs of classes {m, m } (m, m =,..., N, m < m ) we perform a paired Watson-Williams test (a circular analogue of the one-factor ANOVA) assuming underlying von Mises distributions. For each pair of classes {m, m } we take n features I = {i,..., i n } with minimal p-values (in the case of equality, we take the ones with the minimal circular standard deviation), leading to the inclusion of class-feature pairs (m, i ), (m, i ),..., (m, i n ), (m, i n ) into S. This procedure could be seen as an implementation of a one vs. one classification strategy. In addition to this, we assign to each feature i the maximum p-value obtained among all pairs of classes {m, m }, indicating the worst separability among all possible pairs of classes. Then, by choosing the n best features I = {ĩ,..., ĩ n } (with minimal assigned values), we extend the selection S with all the class-feature pairs related to the indices from I : (, ĩ ),..., (N, ĩ ),..., (, ĩ n ),..., (N, ĩ n ). Thus, here, for each feature ĩ I, all N classes are selected. Hence, such a procedure allows to select those whole channels for which any class has the best separability with respect to all other classes (which can be seen as a one vs. all strategy). This extension of the set S might be seen as redundant, but it will enable us to perform a comparison with the single channel-based classifiers described in the literature..6. Classification During the training stage (see Algorithm ) the system learns to distinguish between N phase shifted stimuli/classes using the previously selected set S of class-feature pairs. To each class-feature pair (m, i) S we assign a characteristic membership function µ A m i ( ) indicating the level of affiliation of feature i to class m. It is defined as a normalized to [; ] von Mises distribution: 7 µ A m i (ϕ) = pm i (ϕ µ m i, κ m i ) p m i (µm i µm i, κm i ) = exp(κm i (cos(ϕ µ m i ) )). The classifier is based on a fuzzy system [9] with a K-dimensional input (here, for the sake of simplicity, all K features are considered keep in mind that some of the features could be eliminated by the feature selection procedure) and a two-dimensional output. The fuzzy system (FUZZY ) consists of N (one for each class m =,..., N) fuzzy IF-THEN rules R m of the form: R m : IF (ϕ is A m AND AND ϕ K is A m K) THEN (y is B m AND y is B m ), where the fuzzy sets A m i and Bl m are characterized by the membership functions µ A m i and µ B m l respectively. Since the resulting classes are distributed circularly, we divide the unit circle into N equal segments [π(m )/N; πm/n) (m =,..., N), centered

8 8 at ϕ m = π(m.5)/n, and use as output membership functions µ B m are singletons at cos ϕ m and sin ϕ m respectively. and µ B m, which Algorithm Construct circular fuzzy classifier FUZZY Input: set S of selected class-feature pairs, training set consisting of N c samples Φ = {(ϕ s,..., ϕ s K )} and corresponding class labels L = {L s : L s {,..., N}}, s =,..., N c. Output: fuzzy classifier FUZZY represented by a set of functions {µ A m i (ϕ), µ B m l (y)}, where (m, i) S and l =,...,. for m = to N do for all (m, i) S do Φ m i {ϕ s i : L s = m} µ m i circular mean of set Φ m i κ m i circular concentration of set Φ m i µ A m i (ϕ) exp(κ m i (cos(ϕ µ m i ) )) end for ϕ m π(m.5)/n µ B m (y) cos ϕm (y) µ B m (y) sin ϕm (y) end for The classification (see Algorithm ) is based on the Mamdani-type of reasoning, where antecedents and consequences of each rule are connected by the min T -norm, leading to a universal approximator []. Fuzzifications of the actual (denoted with a bar) input values ϕ i are done based on the singleton fuzzifier. Thus, each rule R m leads to the result: µ Bm l (y l ) = min {i:(m,i) S} {µ A m i ( ϕ i), µ B m l (y l )}, l =,...,. As a consequence, the resulting (output) fuzzy sets (taken among all rules m =,..., N) will be: µ Bl (y l ) = max{µ B l (y l ),..., µ BN l (y l )}, l =,...,. The defuzzification is based on the center of gravity method and produces crisp values ȳ and ȳ, which are then used to estimate the target class index m that satisfies the inequality π( m )/N arg(ȳ + jȳ ) < π m/n. {, if x = a, By a singleton at a we mean the function a (x) =, if x a

9 9 Algorithm Classify using FUZZY Input: sample ϕ = ( ϕ,..., ϕ K ), classifier FUZZY. Output: resulting class index m {,..., N}. for l = to do for m = to N do µ Bm l (y l ) min {i:(m,i) S} {µ A m i ( ϕ i ), µ B m l (y l )} end for µ Bl (y l ) max{µ B l (y l ),..., µ BN l (y l )} ȳ l center of gravity of function µ Bl (y l ) end for m m : π(m )/N arg(ȳ + jȳ ) < πm/n 3. Results 3.. Phase stability and class separability While the sampled sinusoidal stimulation may allow us to encode more targets, it also could be that this stimulation increases the scatter of the phases within each class (characterized by the circular variance) in comparison to on/off mode. To verify this, the data from the first experiment were used. Phases were estimated and subjected to an F -test with the null hypothesis that two independent samples resulted from on/off and sampled sinusoidal stimulations come from distributions with the same variance. Such a test was performed separately for each subject, and for different stimulation intervals T, and all features i (in total N s N t K tests). Here, we should note that a smaller variance potentially leads to more separable classes and, therefore, to the encoding of more targets simultaneously. The phase stability analysis revealed that only in 7.7 % of tests, the on/off stimulation produced a significantly (p < 5) smaller variance, than the sampled 4π/3 π π/3 5π/3 π/3 π/3 π 4π/3 π/3 5π/3 4π/3 π 5π/3 π/3 π/3 (a) Oz (b) POz Oz (c) Oz w.r.t. CAR Figure 4: Distributions of phases estimated from channels. Each class is drawn on a circle of different radius.

10 sinusoidal case. The sampled sinusoidal stimulation appeared to be significantly better (i.e., the variance is smaller) in 4.3 % of all tests. For the remaining cases there were no significant differences. If we consider only the best n channels (N s N t n tests), the above mentioned percentage for the sampled sinusoidal stimulation case even increases. For example, for n = 5 the sampled sinusoidal stimulation is significantly better in 7.4 % whereas the on/off stimulation in only.8 % of all tests. In addition to the previous group of tests, we estimated the circular variances for both stimulation designs for every subject, every feature i and every stimulation interval T. Looking separately at each channel and each stimulation interval, a repeated measures ANOVA was performed to assess the differences between stimulation methods (K N t tests). In 9.6 % of the tests the sampled sinusoidal stimulation was better (p < 5), while in the other tests there were no significant differences between the stimulation methods. Thus, we can conclude that the sampled sinusoidal stimulation at 5 Hz on an LCD screen is not worse than the on/off method: the deviation from the circular mean in the case of sampled sinusoidal stimulation is not higher than for the on/off one. These results are probably due to the fact that the sinusoidal intensity modulation does not rely on the screen refresh rate to the same extend as the on/off stimulus (note that in our case it was even not exactly 6 Hz), as explained in Section.. We also explored the feasibility of encoding more than four simultaneous targets at 5 Hz on a 6 Hz monitor by using the proposed sampled sinusoidal stimulation. For this, we used all recorded data from the second experiment. As one can see from Fig. 4, depending on the observed channel, the classes can be well separated, confirming the hypothesis that more than four targets can be encoded. The results for the Oz electrode referenced to the right mastoid, as used in [6] (see Fig. 4a), and for the bipolar combination Oz POz, as exploited in [5] (see Fig. 4b), show less separation between classes than Oz referenced w.r.t. CAR (see Fig. 4c). However, the class separability as well as the optimal channel vary from one subject to another. This supports the necessity of the proposed feature selection procedure prior to classification. 3.. Classification performance In order to analyze the performance of the proposed classifier we acquired fivesecond-long EEG data intervals for each subject, which corresponds to trials per target class. A comparable amount of data as used in similar studies [5,, 5], where correspondingly 5, and trials per class were used. We have employed leaveone-out cross-validation to compare the performance of the considered classifiers. This method is commonly used in BCI research not only to estimate performance of a BCI system [5, ], but also to compare different approaches [5]. Figure 5 shows the leave-one-out cross-validation classification results (using data from the second experiment) based on the proposed fuzzy classifier for different EEG segment lengths T used for phase derivation and classification. We compare the results to other methods proposed in the literature, applied to our data. The feature selection

11 Accuracy (%) Data segment length (s) 4 5 Lee et al. Jia et al. Lee et al. (opt) Jia et al. (opt) proposed Figure 5: Discrimination accuracy (averaged over all subjects) versus EEG segment length T p used for decoding. The results for the different methods are shown in different colors: dark-blue is used for the method from [6] (channel Oz referenced to mastoid); light-blue depicts the results of method from [5] (bipolar POz Oz); green shows the results of method from [6] with optimal channel, orange represents the results of method from [5] with optimal lead; and the results of the proposed fuzzy method are presented in brown. The numbers above the horizontal braces (at the top of the chart) are corresponding repeated-measures ANOVA p-values for the differences between the proposed method and the optimal channel versions [6] and [5]. parameters (n, n ) were obtained through a grid-search (n, n =,..., 3) on the training data (leaving the test data for the sole purpose of measuring the classifiers performance). The statistical significance of the difference in accuracy between the different methods were assessed using repeated-measures ANOVA tests. When comparing the results obtained by applying the methods proposed in [5, 6] to our data (with the data measured from the Oz channel referenced to the right mastoid and from the Oz POz bipolar combination, respectively) we observe a superior performance of the proposed method (p < ). By applying the single-channel methods from [5, 6] to the optimal channel (obtained via an exhaustive search through all channels s i, using a wrapper approach applied on the training data), we also observe the superiority of our multichannel fuzzy classifier. This shows a better generalization performance of the proposed fuzzy method, in particular since the multichannel information increases the decoding accuracy compared to the single-channel case. To verify this assertion, we also repeated the classification with the same fuzzy classifier for all pairs (n, n ) used in the grid search. We found that the best accuracy was reached uniquely by a single-channel mode (n =, n = ) in only 6 % of the cases. In 7 % of the cases this was achieved solely by a multichannel mode (other combinations of (n, n )) and in the remaining 4 % the

12 Lee et al. Jia et al. Lee et al. (opt) Predicted class Predicted class Predicted class Actual class Actual class Actual class Jia et al. (opt) Proposed method Predicted class Predicted class Actual class Actual class Figure 6: Confusion matrices (average among all subjects) for all five classifiers considered and for T = second of EEG data used for classification. Shown are the distributions of the actual classes among the detected ones (in percent). Hence, the sum within each column is equal to %. best accuracy could be reached by both modes of the classifier. This means that in 7 94 % of the cases, the gain in accuracy was due to the multichannel mode. In Fig. 6, we present the averaged across subjects results for all five classifiers considered. With increasing T (the length of the EEG segment used for classification) all classifiers reveal a saturating accuracy. The comparison of the classifiers become more informative when they are evaluated on more difficult conditions, i.e., when T is small as in our case. That is why we present our results for the shortest considered length of the EEG segment used for classification: T = second. As it can be seen from Fig. 6, the proposed classifier has a superior performance for all classes compared to other classifiers within the same experiment and for the same subjects. Our classification results suggest one more time that the proposed stimulation method allows to encode more targets than by using the standard on/off stimulation, in which case the amount of targets is restricted by the screen refresh rate.

13 3 4. Discussion In this paper we proposed a sampled sinusoidal stimulation profile that allows one to overcome some of the limitations of the conventional on/off stimulation mode on a regular computer screen. The proposed stimulation design allows for any phase shift ϕ in the stimulation profile. This can be used not only to increase the number of target stimuli, but also to compensate for the stimulus appearance lags caused by the progressive rendering of the screen. But the question about how many additional targets can be involved in this scenario is still to be investigated. As it is shown for the best channel in Fig. 4c, the class mean phases are not equidistantly distributed on the unit circle. This was also noticed in [5, ] for an on/off stimulus on a computer screen. In [] the author hypothesized that this could be due to the layout of the target stimuli: as an attended target is surrounded by several other flickering targets, it is likely that this influences the phase of the subject s EEG. In our experiments, we tried to separate the stimuli on the screen as much as possible, but the distance between the stimuli was, probably, not large enough to avoid any influence from neighboring stimuli. This influence can be seen in the results presented in Fig. 6 for the three best classifiers, where the first and the fifth classes have better detection accuracies. This is, probably, not due to the stimulation (which is identical for each class, since we have 5 Hz for each target, but with different initial phase shifts), but could be explained by the stimulus layout on the screen. Classes one and five correspond to the stimuli shown at the top-left and top-right corners of the screen. Following the above mentioned hypothesis, one can assume that the targets in the corners of the screen are detected with a higher accuracy, as they have less neighbors. This assumption would need to be explored by specific experiments with stimuli placed at different locations on the screen. Based on the outcome, one could experimentally verify whether the targets layout on the screen, and the stimulation mode, or neither of them, influence the decoding accuracy. As it can be seen from Fig. 4, different channel combinations and referencing strategies influence the separability of the classes. Thus, the proper selection of the channels should always be considered, as indicated in [5]. Compared to [5], where only a single channel was considered, we report on a multichannel approach supplied with an automatic feature selection procedure, both of which can be observed as a step forward in the phase-coded SSVEP BCI domain, as only some channel combinations provide a good separability. This calls for a search of the proper spatial filtering approach, aimed at the construction of an optimal weighted sum of all channels to achieve the best separability. As a step in this direction, the approaches of [,, 3, 4, 5] can be considered. Since our study is not focused on spatial filtering (preprocessing), but rather on multichannel classification, we considered some commonly used channel combinations: original EEG channels, bipolar channel combinations and channels referenced to CAR. But the proposed system performance could be further improved by adapting the spatial filter to the given data.

14 In [5] the authors analyzed how the decoding is affected by the involvement of the harmonics and found that the latter improves the decoding quality. In our paper we restricted ourselves to the fundamental frequency only (n = ), but, as we have already mentioned, the proposed decoding algorithm is able to incorporate features from the harmonics among other signal features. We expect this will lead to even better results. We constructed a fuzzy classifier of which the membership function parameters were statistically derived from the training data. One could possibly further increase the accuracy of the detector by applying a more flexible architecture of neuro-fuzzy system [9]. Another improvement can be expected from an optimization of the stimulation profile. The real screen luminance profile does not have an exact rectangular shape, but rather a smooth curve, highly depending on the screen type []. When stimulating with intensity values from the [; ] range (rather than from binary ones) and accounting for the screen-specific pixel intensity dynamics, one could construct an intensity profile in a such way that it would closely follow the desired one Conclusion We advocated the use of a sinusoidal stimulation mode for phase-coded SSVEP BCIs. We showed that it yields stable phase estimates and that it enables one to encode more targets with respect to the traditional on/off stimulation mode despite of the limitations of the screen. We introduced a filter-based feature selection procedure relying on circular statistics to select the relevant features according to their impact on the stimuli/class separability. We also proposed a multichannel classifier based on fuzzy logic with which we were able to incorporate information in decoding stage from several channels, which distinguishes our approach from the single-channel phase-coded methods previously proposed for BCI. Acknowledgment NVM is supported by the research grant GOA /9, NC is supported by the Tetra project Spellbinder, AR and AC are supported by IWT doctoral grants, MvV is supported by IUAP P6/9, MMVH is supported by PFV//8, CREA/7/7, G.588.9, IUAP P6/9, GOA /9 and the Tetra project Spellbinder. References [] C. Herrmann, Human EEG responses to Hz flicker: resonance phenomena in visual cortex and their potential correlation to cognitive phenomena, Experimental Brain Research, vol. 37, no. 3, pp ,. [] J. Wilson and R. Palaniappan, Augmenting a SSVEP BCI through single cycle analysis and phase weighting, in Neural Engineering, 9. NER 9. 4th International IEEE/EMBS Conference on. IEEE, may 9, pp

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