Detecting spread spectrum pseudo random noise tags in EEG/MEG using a structure-based decomposition

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1 Detecting spread spectrum pseudo random noise tags in EEG/MEG using a structure-based decomposition P Desain 1, J Farquhar 1,2, J Blankespoor 1, S Gielen 2 1 Music Mind Machine Nijmegen Inst for Cognition and Information Radbound University, Nijmegen The Netherlands desain@nicirunl 2 Biophysics Dept Radbound University Medical School Radbound University, Nijmegen The Netherlands Abstract A method is presented to tag (watermark) stimuli with carefully chosen binary pseudo random noise codes, and to decompose the EEG response into short waveforms for each rising or falling transition in the stimulus This decomposition can be used for EEG classification by computing the class which has maximum correlation between the measured and predicted EEG response Classification performance when a single class is present is excellent (85%), and very robust when a small pass band or short time interval is used A unique feature of this method is that, while it is easy to generate tags for any number of classes, training the classifier is needed only for responses to one stimulus class, and few trials (up to about a minute of data) suffice for training 1 Introduction The neural responses of stimuli with a repetitive character have been well studied in EEG and MEG These Steady State Evoked Potentials (SSEP) are thought to reflect the frequency- and phase-locked responses of neural circuits to periodic stimulation [1] This has been shown in the tactile, visual, and auditory domains [2, 3, 4] As certain features of these stimuli, such as power and phase at the stimulation frequency, are modulated by (selective) attention, SSEPs have been used as the basis of BCIs [5] Furthermore, the phase difference between stimulus and response can be used as a probe for cognitive processing time and order (modulo the stimulation period) However, interesting frequencies in the various domains ( Hz) are in the same range as spontaneous oscillations that occur in the brain (alpha, theta, gamma) which may complicate analysis One approach to attenuating the relatively narrow band noise from other cognitive process would be to use a spectrally spread stimulus One could think of chirps, frequency hopping, pseudo random noise and other signals that have a broadband spectral character This will only work if the underlying hypothesis of an attuning process claimed to explain SSEP does not hold: oscillators cannot attune to non-periodic or fast changing signals Thus a test with this signal is valuable both for scientific reasons to explore the dynamics of interacting neuronal populations and for the pragmatic aim to increase the robustness of BCI systems Broadband signals have already been used for single cell behavior[6] In [7] this approach is elaborated for amplitude modulated auditory stimuli and EEG responses In this paper we focus on the classification process and a way to structurally decompose the noise codes and demonstrate how they form a powerful new method for probing cognitive processing 1

2 Amplitude Spectrum Amplitude Amplitude Frequency (Hz) Frequency (Hz) Figure 1: a) Average spectrum of a set of 31 golden codes of 31 bits long, presented at a bit rate of 31 Hz b) Average spectrum of long sequence of a repeating golden code 2 Pseudo random codes Pseudo random noise is an optimal deterministic periodic signal with statistical properties close to that of Gaussian White Noise For applications in signal detection the random bit codes need certain properties To be able to detect the time-lag of a code in a response, the auto-correlation of a code should be close to zero for all time lags different from zero To distinguish different codes easily, the cross-correlation between codes should be minimal at all time lags There is a family of codes, golden common codes [8], which have this property and is used heavily in broadband communication systems (WIFI, cell phones) The spectrum of these codes is shown in Figure 1 3 Decomposition of the signal One nice property of purely periodic stimuli, such as the more commonly used frequency tags, is that they can be detected by simply looking for an increase in signal power at the stimulation frequency in the neural response This is possible because the total response after the current stimulus is simply the sum of the appropriately delayed responses to all previous stimuli As the delays between stimuli are set the terms in this sum are constant hence giving a fixed total response Thus purely periodic stimuli generate a periodic response with the same frequency This is true even if the responses to individual stimuli have a much longer duration than the inter-stimulus interval, ie the stimulus responses overlap Unfortunately for non-period stimuli, such as Pseudo-Random noise tags, this is no-longer true because the delays between stimuli are no-longer fixed When inter-stimulus interval is much longer than the stimulus response, then this is not a problem as one can directly learn an estimate of individual stimulus responses This is the approach taken in Event Related Potential BCI systems such as visual P300 spellers However, as stimulus response durations can be quite long, eg in P300 systems significant response lasts up to 700ms after stimulation [10], this non-overlapping requirement places quite a strong limit on the stimulation rates and hence system bit-rates What we would like is to estimate a single isolated stimulus s individual impulse-response from an over-lapping set of training responses We can the used the impulse-response to re-construct the estimated total response to a known overlapping stimulus sequence, and use the correlation between the recorded and estimated responses as the basis of a classification system This paper presents such an approach where we decompose the response to a stimulus sequence as a sum of overlapping impulse-responses to the stimulus events contained in the sequence We learn the individual impulse responses using a least-squares technique The effectiveness of the technique is demonstrated with classification results on EEG data derived from pseudo-random-noise tagging experiments The input stimulus is a binary modulation sequence As we believe the brain responses mainly 2

3 stimulus v ^ v ^ v ^ v ^ prediction eeg Figure 2: The decomposition of a mean EEG into its structural components and the fit to the data to changes in input, we treat the transitions in this bit sequence as the stimulus events Further, we postulate that the brain responds differently to rising (0-1) and falling (1-0) transitions Finally, assume that each transition contributes a time-limited impulse-response waveform which combine linearly to give the total stimulus response Figure 2 illustrates this model The same decomposition model was used for timing signals in [9] In algebraic terms this model can be written as: L x(t) = I r (t)r(t τ) + I f (t)f(t τ) (1) τ=1 where, x(t) is the total response at time t, L is the duration of the response, r(),f() are the temporal responses of the brain to a rising (resp falling) edge in the stimulus, and I r (t), I f (t) are indicator functions which have the value 1 if there is a rising/falling edge at time, t, and 0 otherwise This model can more compactly be expressed in matrix notation using a structure matrix M to encode the indicator functions I r, I f, as, x = I r (i : i + L) I f (i : i + L) [ ] r = Mp (2) f where, x is the column vector of modeled response for each time, the rows of M signify sample times with each row being the previous row shifted 1 element to the right, and p is the concatenation of the two types of response function Equation 2 is linear in the temporal responses, r and p, so these parameters can be found using a least-squares regression with the average measured response 4 Experiments We collected the 128 channel EEG responses for 140 trials of listening to a saw-tooth carrier wave of 420Hz, AM modulated by one of two cosine filtered pseudo random noise modulators presented at 168 bits/second For details of the experimental procedure see [7] Two noise-tags were used, 3

4 up edge component (for best electrode C31 ) 015 fit to class A trials fit to class B trials mean and windowed 01 down edge component (for best electrode C31 ) 015 fit to class A trials fit to class B trials mean and windowed time time Figure 3: Edge components derived from the regression fit, for two classes and the averaged and windowed waveform used for classification called code A and B, in a sequential purely perceptual mode The classification problem was to identify which stimulus the subject was exposed to at each point in time All classification results are estimated using 3 seconds of EEG data with 10-fold cross validation, with 20 testing trials, from a dataset containing 280 trials (140 per class) To classify EEG signals we use a simple correlation approach, where the predicted class is that which has maximal correlation with its class prototype We present results for 2 types of class-dependent prototypes The first is simply the mean EEG response for this class This is used as a base-line for comparison The second is the decomposition approach presented above, where the decomposition was conducted independently for each channel 1 This yielded very good fits: predictions explained up to 33% of the variance for the best electrode In Figure 3 the impulse-response functions are shown for the two classes It can be seen how the responses are similar in the central region but differ towards the edges We believe these differences are due to overfitting, and use a simple cosine window (parameters) and the mean of the two waveforms to suppress these differences Note, using an appropriately regularized parameter estimate may be a better approach to deal with this overfitting issue We intend to pursue this approach in future work 41 Results To estimate classification performances a subset of the channels were used, where the subset was found using two different strategies The first used a stepwise forward selection procedure to incrementally add the single best electrode until training set performance was maximized The second approach used first used Independent components analysis to determine create a set of virtual electrodes from which the forward selection procedure was again used In terms of classification performance using the mean EEG response obtained 79% correct, using all 128 channels Using the decomposition with electrode selection on the raw EEG channels gave a significantly better 85% correct, whereas using ICA derived virtual channels gave 94% (using on average 9 ICA components) In Figure 4(a) it is shown which channels were used in the 1 Note these different approaches have different advantages and disadvantages The decomposition approach treats all rising and falling edges as the same and so cannot represent any non-linearity or history dependence of the response However, because it uses an order of magnitude fewer parameters, the decomposition may extract underlying regularities better and be less prone to over-fitting 4

5 Channel usage across folds 1 ICA topology component Figure 4: a) Channels used in the various folds of the cross-validation, b)topology of the most often selected ICA component 100 Classification rate vs frequency band width 100 Classification rate vs training set size % correct 75 % correct [34,48] [28,57] [24,67] [20,80] [17,95] [14,113] frequency band size of training set Figure 5: (a)classification rate for octave-wide pass-band signals (b) classification rate vs training set size decomposition classification The topology of the most often selected ICA component is shown in Figure 4(b) This shows a clear dipole nature over the auditory cortex, as would be expected for an auditory stimulus To demonstrate the robustness of the decomposition approach (and the pseudo-random noise tags) Figure 5 shows the classification performance as a function of the pass-band of a spectral filter and as a function of the training set size This clearly shows that classification performance gracefully degrades as more of the signal it attenuated away (ie the pass band narrows) Further, only a very small amount of training data, 25 trials which is 75s of data, are required to obtain 75% of the full-training set performance Finally, to demonstrate that impulse-responses learned on one stimulus sequence can be used with another, we trained the decomposition using only data from one code and tested it on the other Classification rates only dropped by only a few percent (from 94 to 91%) This proved the validity of the approach and limits the amount of time needed for collecting training data in multi-class setups considerably This is not possible in the mean EEG method which uses complete induced or evoked responses directly 5 Conclusion We have demonstrated how pseudo random noise sequences with certain characteristics can be exploited as a stimulus tagging method Furthermore, the EEG response can be predicted from a decomposition based on the structure of rising and falling edges in the tag For auditory amplitude modulation this decomposition technique proved very successful: classification rates are high and 5

6 can be reached with very little data, and even from data obtained from a different tagging sequence Furthermore, the detection is robust with shorter durations or small pass bands causing a slow and graceful degradation of the classification rate These properties show that noise tagging represents a very promising approach for the development of a BCI It is usable in the tactile and visual domain as well For P300 spellers the possibility to handle overlapping responses at fast flashing rates seems promising to optimize these types of BCI s [10] One possible improvement that we are investigating is the construction of bit codes which preserve their low auto and cross correlation properties when short sub-sequences are used Noise tagging is also potentially very useful for tracing and decomposing cognitive processing through a set of sequential modules, each with their own location and time delay Further the systematic comparison of this new method to the use fixed frequency tags, would allow us to gain insight in how far and where in the brain oscillatory attunement present, if at all We intend to investigate this issue further in future work This investigation could further be enhanced by decomposing the individual electrode responses as weighted and time delayed versions of an individual edge response Acknowledgments We gratefully acknowledge the support of the BrainGain Smart Mix Programme of the Netherlands Ministry of Economic Affairs and the Netherlands Ministry of Education, Culture and Science References [1] DRegan Steady-state evoked potentials J Opt Soc America, 67: , 1977 [2] TW Picton, MS John, A Dimitrijevic, and D Purcell Human auditory steady-state responses Int J Audiol, 42: , 2003 [3] P Fries, JH Reynolds, AE Rorie, and R Desimone Modulation of oscillatory neuronal synchronization by selective visual attention Science, 291:1560 3, Feb 2001 [4] M Bauer, R Oostenveld, M Peeters, and P Fries Tactile spatial attention enhances gammaband activity in somatosensory cortex and reduces low-frequency activity in parieto-occipital areas Journal of Neuroscience, 26(2): , 2006 [5] P Desain, AMG Hupse, MGJ Kallenberg, BJ de Kruif, and RS Schaefer Braincomputer interfacing using frequency tagged stimuli In Proceedings of the 3rd International Brain-Computer Interface Workshop & Training Course, 2006 [6] AR Möller Use of pseudorandom noise in studies of frequency selectivity: The periphery of the auditory system Biol Cybernetics, 47:95 102, 1983 [7] J Farquhar, J Blankespoor J, R Vechk, and P Desain Noise tagging for bci In Porceedings of the 4th International Brain-Computer Interface Workshop and Training Course, 2008 [8] R Gold Optimal binary sequences for spread spectrum multiplexing IEEE Transactions on Information Theory, 13(4): , 1967 [9] WL Windsor, P Desain, A Penel, and M Borkent A structurally guided method for the decomposition of expresssion in music performance Journal of the Acoustic Society of America, 119(2): , 2006 [10] J Hill, J Farquhar, S Martens, F Bießmann, and B Schölkopf Balancing psychophysiological and information-theoretic effects in the design of a visual brain-computer interface speller Technical report, Max Planck Inistute for Biological Cybernetics,