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24 nips-2006-Aggregating Classification Accuracy across Time: Application to Single Trial EEG

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Author: Steven Lemm, Christin Schäfer, Gabriel Curio

Abstract: We present a method for binary on-line classiﬁcation of triggered but temporally blurred events that are embedded in noisy time series in the context of on-line discrimination between left and right imaginary hand-movement. In particular the goal of the binary classiﬁcation problem is to obtain the decision, as fast and as reliably as possible from the recorded EEG single trials. To provide a probabilistic decision at every time-point t the presented method gathers information from two distinct sequences of features across time. In order to incorporate decisions from prior time-points we suggest an appropriate weighting scheme, that emphasizes time instances, providing a higher discriminatory power between the instantaneous class distributions of each feature, where the discriminatory power is quantiﬁed in terms of the Bayes error of misclassiﬁcation. The eﬀectiveness of this procedure is veriﬁed by its successful application in the 3rd BCI competition. Disclosure of the data after the competition revealed this approach to be superior with single trial error rates as low as 10.7, 11.5 and 16.7% for the three diﬀerent subjects under study. 1

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 To provide a probabilistic decision at every time-point t the presented method gathers information from two distinct sequences of features across time. [sent-6, score-0.08]

2 Disclosure of the data after the competition revealed this approach to be superior with single trial error rates as low as 10. [sent-9, score-0.324]

3 1 Introduction The ultimate goal of brain-computer interfacing (BCI) is to translate human intentions into a control signal for a device, such as a computer application, a wheelchair or a neuroprosthesis (e. [sent-13, score-0.032]

4 Most pursued approaches utilize the accompanying EEG-rhythm perturbation in order to distinguish between single trials (STs) of left and right hand imaginary movements e. [sent-16, score-0.181]

5 Up to now there are just a few published approaches utilizing additional features, such as slow cortical potential, e. [sent-19, score-0.109]

6 [3, 4, 9] This paper describes the algorithm that has been successfully applied in the 2005 international data analysis competition on BCI-tasks [2] (data set IIIb) for the on-line discrimina∗ steven. [sent-21, score-0.22]

7 de tion between imagined left and right hand movement. [sent-24, score-0.082]

8 The objective of the competition was to detect the respective motor intention as early and as reliably as possible. [sent-25, score-0.403]

9 Consequently, the competing algorithms have to solve the on-line discrimination task as based on information on the event onset. [sent-26, score-0.087]

10 Thus it is not within the scope of the competition to solve the problem of detecting the event onset itself. [sent-27, score-0.22]

11 We approach this problem by applying an algorithm that combines the diﬀerent characteristics of two features: the modulations of the ongoing rhythmic activity and the slow cortical Movement Related Potential (MRP). [sent-28, score-0.205]

12 Both features are diﬀerently pronounced over time and exhibit a large trial to trial variability and can therefore be considered as temporally blurred. [sent-29, score-0.284]

13 Consequently, the proposed method combines at one hand the MRP with the oscillatory feature and on the other hand gather information across time as introduced in [8,16]. [sent-30, score-0.156]

14 More precisely, at each time point we estimate probabilistic models on the labeled training data - one for each class and feature - yielding a sequence of weak instantaneous classiﬁers, i. [sent-31, score-0.091]

15 The classiﬁcation of an unlabeled ST is then derived by weighted combination of these weak probabilistic classiﬁers using linear combination according to their instantaneous discriminatory power. [sent-34, score-0.177]

16 The paper is organized as follows: section II describes the feature and its extraction, In section III introduces the probabilistic model as well as the combinatorial framework to gather information from the diﬀerent features across time. [sent-35, score-0.125]

17 In section III the results on the competition data are given, followed by a brief conclusion. [sent-36, score-0.22]

18 1 Feature Neurophysiology The human perirolandic sensorimotor cortices show rhythmic macroscopic EEG oscillations (µ-rhythm) [6], with spectral peak energies around 10 Hz (localized predominantly over the postcentral somatosensory cortex) and 20 Hz (over the precentral motor cortex). [sent-38, score-0.405]

19 , by motor activity, both actual and imagined [7, 13, 18], as well as by somatosensory stimulation [12]. [sent-41, score-0.272]

20 Standard trial averages of µ-rhythm power show a sequence of attenuation, termed event-related desynchronization (ERD) [13], followed by a rebound (event-related synchronization: ERS) which often overshoots the pre-event baseline level [15]. [sent-42, score-0.214]

21 In case of sensorimotor cortical processes accompanying ﬁnger movements Babiloni et al. [sent-43, score-0.209]

22 [1] demonstrated that movement related potentials (MRPs) and ERD indeed show up with diﬀerent spatio-temporal activation patterns across primary (sensori-)motor cortex (M1), supplementary motor area (SMA) and the posterior parietal cortex (PP). [sent-44, score-0.323]

23 Thus, in order to extract the rhythmic information we map the EEG to the time-frequency domain by means of Morlet wavelets [19], whereas the slow cortical MRP are extracted by the application of a low pass ﬁlter, in form of a simple moving average ﬁlter. [sent-47, score-0.215]

24 , x[T ]] denote the EEG signal of one single trial (ST) of length T , recorded from the two bipolar channels C3 and C4, i. [sent-52, score-0.151]

25 The label information about the corresponding motor intention of a ST is denoted by Y ∈ {L, R}. [sent-55, score-0.183]

26 This observational horizon becomes important with respect to the causality of the feature extraction process, especially in order to ensure the causality of ﬁlter operations we have to restrict the algorithm to a certain observational horizon. [sent-62, score-0.231]

27 Considering ERD as a feature for ST classiﬁcations we model the hand-speciﬁc time course of absolute µ-rhythm amplitudes over both sensorimotor cortices. [sent-65, score-0.135]

28 Therefore we utilize the time-frequency representations of the ST at two diﬀerent frequency bands (α, β), obtained by convolution of the EEG signal with complex Morlet wavelets [19]. [sent-66, score-0.045]

29 Using the notation Ψα , and Ψβ for a wavelet centered at the individual spectral peak in the alpha (8-12Hz) and the beta (16-24Hz) frequency domain, the ERD feature of a ST, observed until time s is calculated as: ERD|s = with erd|s [1], . [sent-67, score-0.086]

30 =  |(C3|s ∗ Ψβ )[t]|  |(C4|s ∗ Ψβ )[t]|  erd|s [t] (1) In a similar manner we deﬁne the ST feature for the MRP by convolution with a moving average ﬁlter of length 11, abbreviated as MA(11). [sent-71, score-0.053]

31 X (k), Y (k) maps to a STs in feature space, namely (MRP(k) , ERD(k) ). [sent-78, score-0.053]

32 3 Probabilistic Classiﬁcation Model Before we start with the model description, we brieﬂy introduce two concepts from Bayesian decision theory. [sent-79, score-0.045]

33 p(x|µL , ΣL ) + p(x|µR , ΣR ) (3) Furthermore the discriminative power between these two distributions can be estimated using the Bayes error of misclassiﬁcation [5]. [sent-82, score-0.114]

34 However, by using the Chernoﬀ bound [5] we can derive an upper bound and ﬁnally approximate the discriminative power w between the two distributions by 2w ∼ 1 − min = 0≤γ≤1 p(x|µL , ΣL )γ p(x|µR , ΣR )1−γ dx. [sent-84, score-0.114]

35 Therefore we ﬁrst model the class-conditional distribution of each feature at each time instance as multivariate Gaussian distribution. [sent-87, score-0.053]

36 Hence at each time instance we estimate the class means and the class covariance matrices in the feature space, based on the mapped training STs, i. [sent-88, score-0.053]

37 (6) For convenience we summarize the estimated model parameters for the ERD feature as Θ[t] := (µL [t], ΣL [t], µR [t], ΣR [t]), whereas Ξ[t] := (ηL [t], ΓL [t]), ηR [t], ΓR [t]) denote the class means and the covariance matrices obtained in the similar manner from mrp(k) [t]. [sent-92, score-0.053]

38 Given an arbitrary observation x from the appropriate domain, applying Bayes formula as introduced in (3), yields a posterior distribution for each feature: p y erd, Θ[t] , erd ∈ R4 (7) 2 p y mrp, Ξ[t] , mrp ∈ R . [sent-93, score-0.913]

39 (8) Additionally, according to (4) we get approximations of the discriminative power w[t] and v[t] of the ERP resp. [sent-94, score-0.114]

40 In order to ﬁnally derive the classiﬁcation of an unlabeled single trial at a certain time s ≤ T , we incorporate knowledge from all preceding samples t ≤ s, i. [sent-96, score-0.172]

41 t≤s w[t] + v[t] (9) As described in [16] this yields an evidence accumulation over time about the decision process. [sent-104, score-0.045]

42 Due to the submission requirements of the competition the ﬁnal decision at time s is C[s] = 1 − 2 · c(L, s), (10) where a positive or negative sign refers to right or left movement, while the magnitude indicates the conﬁdence in the decision on a scale between 0 and 1. [sent-107, score-0.351]

43 1 Application Competition data The EEG from two bipolar channels (C3, C4) was provided with bandﬁlter settings of 0. [sent-109, score-0.047]

44 Except for the ﬁrst data set, each contains 540 labeled (for training) and 540 unlabeled trials (for competition) of imaginary hand movements, with an equal number of left and right hand trials (ﬁrst data set provides just 320 trials each). [sent-112, score-0.296]

45 Each trial has a duration of 7 s: after a 3 s preparation period a visual cue is presented for one second, indicating the demanded motor intention. [sent-113, score-0.25]

46 This is followed by another 3 s for performing the imagination task (for details see [2]). [sent-114, score-0.035]

47 The particular competition data was provided by the Dept. [sent-115, score-0.22]

48 The speciﬁc competition task is to provide an on-line discrimination between left and right movements for the unlabeled STs for each subject based on the information obtained from the labeled trials. [sent-123, score-0.441]

49 More precisely, at every time instance in the interval from 3 to 7 seconds a strictly causal decision about the intended motor action and its conﬁdence must be supplied. [sent-124, score-0.25]

50 After competition deadline, based on the disclosure of the labels Y (k) for the previously unlabeled STs the output C (k) [t] of the methods were evaluated using the time course of the mutual information (MI) [17], i. [sent-125, score-0.359]

51 t − 3s (13) Note, that the feature extraction relies on a few hyperparameters, i. [sent-131, score-0.091]

52 The resulting posterior distributions were then combined according to (9) in order to obtain the ﬁnal classiﬁcation of the unlabeled STs. [sent-138, score-0.068]

53 After disclosure of the label information our method turned out to succeed with a MI steepness (cf. [sent-139, score-0.317]

54 2 summarizes the results in terms of the achieved minimum binary classiﬁcation error, the maximum MI, and the maximum steepness of MI for each subject and each competitor in the competition. [sent-145, score-0.253]

55 0489 Table 1: Overall ranked results of the competing algorithms (ﬁrst row corresponds to the proposed method) on the competition test data. [sent-219, score-0.252]

56 For three diﬀerent subjects (O3, S4 and X11) the table states diﬀerent performance measures of classiﬁcation accuracy (min. [sent-220, score-0.039]

57 Error rate, max MI, steepness of MI), where the steepness of the MI was used as the objective in the competition. [sent-221, score-0.41]

58 The resulting time courses for the MI and the steepness of the MI are presented in the left panel of Fig. [sent-225, score-0.279]

59 5 seconds after cue presentation) the classiﬁcation is rather by chance, after 3. [sent-229, score-0.059]

60 5 seconds a steep ascent in the classiﬁcation accuracy can be observed, reﬂected by the raising MI. [sent-230, score-0.094]

61 The maximum steepness for these two subjects is obtained quite early, between 3. [sent-231, score-0.244]

62 In opposite, for subject one the maximum is achieved at 4. [sent-234, score-0.048]

63 However, a low value is also found for the submission of all other competitors. [sent-236, score-0.041]

64 64 Bit per trial at 7 seconds, which might indicate a delayed performance of subject one. [sent-238, score-0.152]

65 For subject two one can clearly observe a switch in the regime between the ERP and the MRP feature at 5 seconds, as indicated by a crossing of the two weighting functions. [sent-242, score-0.101]

66 From this we conclude that the steep increase in MI for this subject between 3 and 5 seconds is mainly due to the MRP feature, whereas the further improvement in the MI relies primarily on the ERD feature. [sent-243, score-0.142]

67 Subject one provides nearly no discriminative MRP and the classiﬁcation is almost exclusively based on the ERD feature. [sent-244, score-0.053]

68 For subject three the constant low weights at all time instances, reveal the weak discriminative power of the estimated class-conditional distributions. [sent-245, score-0.162]

69 1 the advantage of the integration process across time can clearly be observed, as the MI is continuously increasing and the steepness of the MI is surprisingly high even for this subject. [sent-247, score-0.205]

70 Figure 1: Left panel: time courses of the mutual information (light, dashed) and the competition criterion - steepness of mutual information (thin solid) cf. [sent-248, score-0.46]

71 (13)- for the classiﬁcation of the unlabeled STs is presented. [sent-249, score-0.068]

72 Right panel: the time course of the weights reﬂecting the discriminative power (cf. [sent-250, score-0.114]

73 (4)) at every time instance for the two diﬀerent features (ERD dark, solid; MRP - light dashed). [sent-251, score-0.035]

74 In each panel the subjects O3, S4, X11 are arranged top down. [sent-252, score-0.078]

75 Basically this evaluation reveals that the proposed algorithm outperforms all competing approaches. [sent-254, score-0.032]

76 Moreover, any arbitrary number of features can be combined in the proposed way of temporal weighting, by utilizing the estimated discriminative power over time. [sent-256, score-0.149]

77 More precisely due to the distinct covariance matrices of the Gaussian distributions the individual decision boundaries are of quadratic form. [sent-263, score-0.045]

78 In particular to solve the competition task we combined classiﬁers based on the temporal evolution of diﬀerent neuro-physiological features, i. [sent-264, score-0.22]

79 The resulting on-line classiﬁcation model ﬁnally turned out to succeed for the single trial on-line classiﬁcation of imagined hand movement in the BCI competition 2005. [sent-267, score-0.497]

80 Human movement-related potentials vs desynchronization of EEG alpha rhythm: A high-resolution EEG study. [sent-282, score-0.113]

81 The BCI competition III: Validating alternative apo proachs to actual BCI problems. [sent-287, score-0.22]

82 Human cortical oscillations: a neuromagnetic view through the skull. [sent-317, score-0.118]

83 Electrocorticograms in man: Eﬀect of voluntary movement upon the electrical activity of the precentral gyrus. [sent-322, score-0.124]

84 Probabilistic modeling of sensoria motor µ rhythms for classiﬁcation of imaginary hand movements. [sent-327, score-0.282]

85 Combining gamma-band power with slow cortical potentials to improve single-trial classiﬁcation of electroencephalographic signals. [sent-338, score-0.201]

86 Enhancement of left-right sensorimotor o EEG diﬀerences during feedback-regulated motor imagery. [sent-356, score-0.228]

87 Dynamics of mu-rhythm suppression caused by median nerve stimulation: a magnetoencephalographic study in human subjects. [sent-368, score-0.032]

88 Evaluation of event-related desynchronization preceding and following voluntary self-paced movement. [sent-375, score-0.086]

89 EEG-based discrimination between imagination of right and left hand movement. [sent-385, score-0.123]

90 Modulation of human a cortical rolandic rhythms during natural sensorimotor tasks. [sent-396, score-0.228]

91 Binary on-line classiﬁcation based a on temporally integrated information. [sent-399, score-0.041]

92 Involvement of a primary motor cortex in motor imagery: a neuromagnetic study. [sent-416, score-0.381]

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