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106 nips-2007-Invariant Common Spatial Patterns: Alleviating Nonstationarities in Brain-Computer Interfacing

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Author: Benjamin Blankertz, Motoaki Kawanabe, Ryota Tomioka, Friederike Hohlefeld, Klaus-Robert Müller, Vadim V. Nikulin

Abstract: Brain-Computer Interfaces can suffer from a large variance of the subject conditions within and across sessions. For example vigilance ﬂuctuations in the individual, variable task involvement, workload etc. alter the characteristics of EEG signals and thus challenge a stable BCI operation. In the present work we aim to deﬁne features based on a variant of the common spatial patterns (CSP) algorithm that are constructed invariant with respect to such nonstationarities. We enforce invariance properties by adding terms to the denominator of a Rayleigh coefﬁcient representation of CSP such as disturbance covariance matrices from ﬂuctuations in visual processing. In this manner physiological prior knowledge can be used to shape the classiﬁcation engine for BCI. As a proof of concept we present a BCI classiﬁer that is robust to changes in the level of parietal α -activity. In other words, the EEG decoding still works when there are lapses in vigilance.

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 de Abstract Brain-Computer Interfaces can suffer from a large variance of the subject conditions within and across sessions. [sent-7, score-0.078]

2 alter the characteristics of EEG signals and thus challenge a stable BCI operation. [sent-9, score-0.076]

3 In the present work we aim to deﬁne features based on a variant of the common spatial patterns (CSP) algorithm that are constructed invariant with respect to such nonstationarities. [sent-10, score-0.242]

4 We enforce invariance properties by adding terms to the denominator of a Rayleigh coefﬁcient representation of CSP such as disturbance covariance matrices from ﬂuctuations in visual processing. [sent-11, score-0.212]

5 As a proof of concept we present a BCI classiﬁer that is robust to changes in the level of parietal α -activity. [sent-13, score-0.077]

6 1 Introduction Brain-Computer Interfaces (BCIs) translate the intent of a subject measured from brain signals directly into control commands, e. [sent-15, score-0.306]

7 The classical approach to brain-computer interfacing is operant conditioning ([2, 7]) where a ﬁxed translation algorithm is used to generate a feedback signal from the electroencephalogram (EEG). [sent-18, score-0.179]

8 Users are not equipped with a mental strategy they should use, rather they are instructed to watch a feedback signal and using the feedback to ﬁnd out ways to voluntarily control it. [sent-19, score-0.297]

9 Recently machine learning techniques were applied to the BCI ﬁeld and allowed to decode the subject’s brain signals, placing the learning task on the machine side, i. [sent-22, score-0.122]

10 a general translation algorithm is trained to infer the speciﬁc characteristics of the user’s brain signals [8, 9, 10, 11, 12, 13, 14]. [sent-24, score-0.198]

11 This is done by a statistical analysis of a calibration measurement in which the subject performs well-deﬁned mental acts like imagined movements. [sent-25, score-0.28]

12 Here, in principle no adaption of the user is required, but it is to be expected that users will adapt their behaviour during feedback operation. [sent-26, score-0.118]

13 One of them is to make the system invariant to non task-related ﬂuctuations of the measured signals during feedback. [sent-30, score-0.173]

14 These ﬂuctuations may be caused by changes in the subject’s brain processes, e. [sent-31, score-0.122]

15 The calibration measurement that is used for training in machine learning techniques is recorded during 10-30 min, i. [sent-35, score-0.164]

16 The present contribution focusses on invariant feature extraction for BCI. [sent-38, score-0.097]

17 In particular we aim to enhance the invariance properties of the common spatial patterns (CSP, [15]) algorithm. [sent-39, score-0.217]

18 CSP is the solution of a generalized eigenvalue problem and has as such a strong link to the maximization of a Rayleigh coefﬁcient, similar to Fisher’s discriminant analysis. [sent-40, score-0.143]

19 [16] in the context of kernel Fisher’s discriminant analysis contains the key idea that we will follow: noise and distracting signal aspects with respect to which we want to make our feature extractor invariant is added to the denominator of a Rayleigh coefﬁcient. [sent-42, score-0.176]

20 We demonstrate how our invariant CSP (iCSP) technique can be used to make a BCI system invariant to changes in the power of the parietal α -rhythm (see Section 2) reﬂecting, e. [sent-44, score-0.303]

21 We would like to stress that adaptation and invariant classiﬁcation are no mutually exclusive alternatives but rather complementary approaches when striving for the same goal: a BCI system that is invariant to undesired distortions and nonstationarities. [sent-50, score-0.194]

22 Macroscopic brain activity during resting wakefulness contains distinct ‘idle’ rhythms located over various brain areas, e. [sent-52, score-0.39]

23 the parietal α -rhythm (7-13 Hz) can be measured over the visual cortex [17] and the µ -rhythm can be measured over the pericentral sensorimotor cortices in the scalp EEG, usually with a frequency of about 8–14 Hz ([18]). [sent-54, score-0.239]

24 The strength of the parietal α -rhythm reﬂects visual processing load as well as attention and fatigue resp. [sent-55, score-0.116]

25 The moment-to-moment amplitude ﬂuctuations of these local rhythms reﬂect variable functional states of the underlying neuronal cortical networks and can be used for brain-computer interfacing. [sent-57, score-0.069]

26 Speciﬁcally, the pericentral µ - and β rythms are diminished, or even almost completely blocked, by movements of the somatotopically corresponding body part, independent of their active, passive or reﬂexive origin. [sent-58, score-0.089]

27 This attenuation of brain rhythms is termed event-related desynchronization (ERD) and the dual effect of enhanced brain rhythms is called event-related synchronization (ERS) (see [19]). [sent-60, score-0.412]

28 Since a focal ERD can be observed over the motor and/or sensory cortex even when a subject is only imagining a movement or sensation in the speciﬁc limb, this feature can be used for BCI control: The discrimination of the imagination of movements of left hand vs. [sent-61, score-0.274]

29 To this end, spatial ﬁltering is an indispensable technique; that is to take a linear combination of signals recorded over EEG channels and extract only the component that we are interested in. [sent-65, score-0.203]

30 In particular the CSP algorithm that optimizes spatial ﬁlters with respect to discriminability is a good candidate for feature extraction. [sent-66, score-0.094]

31 05 Figure 1: Topographies of r2 –values (multiplied by the sign of the difference) quantifying the difference in log band-power in the alpha band (8–12 Hz) between different recording sessions: Left: Difference between imag_move and imag_lett. [sent-70, score-0.25]

32 Due to lower visual processing demands, alpha power in occipital areas is stronger in imag_lett. [sent-71, score-0.378]

33 The latter has decreased alpha power in centro-parietal areas. [sent-73, score-0.249]

34 The ultimate challenge will be on-line feedback with strong ﬂuctuations of task demands etc, a project envisioned for the near future. [sent-86, score-0.109]

35 Brain activity was recorded from the scalp with multi-channel ampliﬁers using 55 EEG channels. [sent-88, score-0.165]

36 5–6 seconds one of 3 different visual stimuli indicated for 3 seconds which mental task the subject should accomplish during that period. [sent-90, score-0.188]

37 The investigated mental tasks were imagined movements of the left hand, the right hand, and the right foot. [sent-91, score-0.126]

38 Since the movement of the object was independent from the indicated targets, target-uncorrelated eye movements are induced. [sent-93, score-0.055]

39 Due to the different demands in visual processing, the background brain activity can be expected to differ substancially in those two types of recordings. [sent-94, score-0.27]

40 A sham_feedback paradigm was designed in order to charaterize invariance properties needed for stable real-world BCI applications. [sent-98, score-0.072]

41 In this measurement the subjects received a fake feedback sequence which was preprogrammed. [sent-99, score-0.167]

42 The aim of this recording was to collect data during a large variety of mental states and actions that are not correlated with the BCI control states (motor imagery of hands and feet). [sent-100, score-0.175]

43 Subjects were told that they could control the feedback in some way that they should ﬁnd out, e. [sent-101, score-0.107]

44 They were instructed not to perform movements of hands, arms, legs and feet. [sent-104, score-0.055]

45 The type of feedback was a standard 1D cursor control. [sent-105, score-0.118]

46 The preprogrammed ‘feedback’ signal was constructed such that it was random in the beginning and then alternating periods of increasingly more hits and periods with chance level performance. [sent-109, score-0.042]

47 A decreased alpha power in centro-parietal areas during sham_feedback can be observed. [sent-114, score-0.249]

48 Note that this recording includes much more variations of background mental activity than the difference between imag_move and imag_lett. [sent-115, score-0.181]

49 The CSP technique ([15]) allows to determine spatial ﬁlters that maximize the variance of signals of one condition and at the same time minimize the variance of signals of another condition. [sent-117, score-0.246]

50 Since variance of band-pass ﬁltered signals is equal to bandpower, CSP ﬁlters are well suited to discriminate mental states that are characterized by ERD/ERS effects ([20]). [sent-118, score-0.147]

51 As such it has been well used in BCI systems ([8, 14]) where CSP ﬁlters are calculated individually for each subject on the data of a calibration measurement. [sent-119, score-0.158]

52 Technically the Common Spatial Pattern (CSP) [21] algorithm gives spatial ﬁlters based on a discriminative criterion. [sent-120, score-0.094]

53 Let X1 and X2 be the (time × channel) data matrices of the band-pass ﬁltered 3 EEG signals (concatenated trials) under the two conditions (e. [sent-121, score-0.108]

54 , right-hand or left-hand imagination, respectively2) and Σ1 and Σ2 be the corresponding estimates of the covariance matrices Σi = Xi Xi . [sent-123, score-0.067]

55 We deﬁne the two matrices Sd and Sc as follows: Sd = Σ(1) − Σ(2) : discriminative activity matrix, Sc = Σ : common activity matrix. [sent-124, score-0.186]

56 (1) +Σ (2) The CSP spatial ﬁlter v ∈ RC (C is the number of channels) can be obtained by extremizing the Rayleigh coefﬁcient: {max, min}v∈RC v Sd v . [sent-125, score-0.094]

57 v Sc v (1) This can be done by solving a generalized eigenvalue problem. [sent-126, score-0.106]

58 (2) The eigenvalue λ is bounded between −1 and 1; a large positive eigenvalue corresponds to a projection of the signal given by v that has large power in the ﬁrst condition but small in the second condition; the converse is true for a large negative eigenvalue. [sent-128, score-0.218]

59 On the other hand, the projection of the activity that is common to two classes v Sc v should be minimized because it doesn’t contribute to the discriminability. [sent-132, score-0.077]

60 The norm is deﬁned by the common activity matrix Sc . [sent-137, score-0.077]

61 Moreover we denote by V the matrix we obtain by putting the C generalized eigenvectors into columns, namely V = {v j }C ∈ j=1 RC×C and call patterns the row vectors of the inverse A = V −1 . [sent-144, score-0.085]

62 Note that a ﬁlter v j ∈ RC has its corresponding pattern a j ∈ RC ; a ﬁlter v j extracts only the activity spanned by a j and cancels out all other activities spanned by ai (i = j); therefore a pattern a j tells what the ﬁlter v j is extracting out (see Fig. [sent-145, score-0.077]

63 The selection of patterns is typically based on eigenvalues. [sent-149, score-0.051]

64 But when a large amount of calibration data is not available it is advisable to use a more reﬁned technique to select the patterns or to manually choose them by visual inspection. [sent-150, score-0.17]

65 The CSP spatial ﬁlters extracted as above are optimized for the calibration measurement. [sent-158, score-0.174]

66 However, in online operation of the BCI system different non task-related modulations of brain signals may occur which are not suppressed by the CSP ﬁlters. [sent-159, score-0.249]

67 The reason may be that these modulations have not been recorded in the calibration measurement or that they have been so infrequent that they are not consistently reﬂected in the statistics (e. [sent-160, score-0.215]

68 The proposed iCSP method minimizes the inﬂuence of modulations that can be characterized in advance by a covariance matrix. [sent-163, score-0.086]

69 In this manner we can code neurophysiological prior knowledge 2 We use the term covariance for zero-delay second order statistics between channels and not for the statistical variability. [sent-164, score-0.069]

70 In the following motivation we assume that Ξ is the covariance matrix of a signal matrix Y . [sent-167, score-0.077]

71 Using (1) (1) the notions from above, the objective is then to calculate spatial ﬁlters v j such that var(X1 v j ) is (1) (1) (2) maximized and var(X2 v j ) and var(Y v j ) are minimized. [sent-168, score-0.094]

72 Dually spatial ﬁlters v j are determined (2) (2) (2) that maximize var(X2 v j ) and minimize var(X1 v j ) and var(Y v j ). [sent-169, score-0.094]

73 Note that the idea of iCSP is in the spirit of the invariance constraints in (kernel) Fisher’s Discriminant proposed in [16]. [sent-179, score-0.072]

74 As mentioned, iCSP is aiming at robust spatial ﬁltering against disturbances whose covariance Ξ can be anticipated from prior knowledge. [sent-181, score-0.163]

75 Lemma 1 (Inﬂuence of generalized eigenvalue problems) Let λk and wk be k-th eigenvalue and eigenvector of the generalized eigvenvalue problem Aw = λ Bw, (5) respectively. [sent-187, score-0.431]

76 Suppose that the matrices A and B are perturbed with small matrices ε ∆ and ε P where ε 1. [sent-188, score-0.064]

77 The generalized eigenvalue problem eqns (3) and (4) can be rephrased as Σ1 v = d{(1 − ξ )(Σ1 + Σ2 ) + ξ Ξ}v, Σ2 u = c{(1 − ξ )(Σ1 + Σ2 ) + ξ Ξ}u. [sent-190, score-0.106]

78 0 α=2 filter pattern Figure 2: Comparison of CSP and iCSP on test data with artiﬁcially increased occipital alpha. [sent-219, score-0.09]

79 The upper plots show the classiﬁer output on the test data with different degrees of alpha added (factors α = 0, 0. [sent-220, score-0.217]

80 The lower panel shows the ﬁlter/pattern coefﬁcients topographically mapped on the scalp from original CSP (left) and iCSP (right). [sent-222, score-0.055]

81 Here the invariance property was deﬁned with respect to the increase in the alpha activity in the visual cortex (occipital location) using an eyes open/eyes closed recording. [sent-223, score-0.487]

82 M1k := Σ−1/2 (Σ−1/2 Σ1 Σ−1/2 − dk I)+ Σ−1/2 , M2k := Σ−1/2 (Σ−1/2 Σ2 Σ−1/2 − dk I)+ Σ−1/2 , and Σ := 1 (1 − ξ )(Σ1 + Σ2 ) + ξ Ξ. [sent-225, score-0.11]

83 χ2k ) of the k-th eigenvalue vanishes and also the k-th eigenvector does coincide with the one for the original problem up to ε order, because the ﬁrst term of ψ 1k (resp. [sent-229, score-0.072]

84 ψ 2k ) becomes zero (we note that dk and ck also depend on ξ ). [sent-230, score-0.055]

85 5) on motor imagery data with the invariance characterized by data from a measurement during ‘eyes open’ (approx. [sent-234, score-0.209]

86 While the performance of the original CSP is more and more deteriorated with increased alpha mixed in, the proposed iCSP method maintains a stable performance independent of the amount of increased alpha activity. [sent-241, score-0.434]

87 The spatial ﬁlters that were extracted by CSP analysis vs. [sent-242, score-0.094]

88 While the pattern of the original CSP has positive weights at the right occipital side which might be susceptible to α modulations, the corresponding iCSP has not. [sent-249, score-0.09]

89 A more detailed inspection shows that both ﬁlters have a focus over the right (sensori-) motor cortex, but only the invariant ﬁlter has a spot of opposite sign right posterior to it. [sent-250, score-0.142]

90 For the same values of ξ the iCSP ﬁlters + LDA classiﬁer trained on imag_move were applied to calcu6 35 35 Subject cv test train 30 20 15 cv zv zk zq 20 15 10 5 5 0 0. [sent-254, score-0.08]

91 The case for subject zk shows that the selection of ξ may be a delicate issue. [sent-283, score-0.12]

92 For evaluation we used the imag_move session (see Section 2) as training set and the imag_lett session as test set. [sent-288, score-0.11]

93 Obviously BCI users are subject to variations in attention and motivation. [sent-294, score-0.078]

94 By substituting the expansions of λk and wk to Eq. [sent-307, score-0.219]

95 (11), (A − λk B)ψ k = −(∆ − λk P)wk + χk Bwk = −(A − λk B)Mk (∆ − λk P)wk , 7 (11) holds, where we used the constraints w j Bwk = δ jk and (A − λk B)Mk = ∑ Bw j w j = I − Bwk wk . [sent-314, score-0.219]

96 By a multiplication with wk B, the constant c turns out to be c = −wk Pwk /2, where we used the fact wk BMk = 0 and wk Bψ k = −wk Pwk /2 derived from the normalization wk (B + ε P)wk = 1. [sent-317, score-0.876]

97 Stokes, “Learning to control brain activity: A review of the production and control of EEG components for driving brain-computer interface (BCI) systems”, Brain Cogn. [sent-358, score-0.233]

98 Pfurtscheller, “Real-time EEG analysis with subject-speciﬁc spatial patterns for a Brain Computer Interface (BCI)”, IEEE Trans. [sent-381, score-0.145]

99 Sajda, “Linear spatial integration for single trial detection in encephalography”, NeuroImage, 7(1): 223–230, 2002. [sent-408, score-0.094]

100 Andrews, “Normal differentiation of occipital and precentral regions in man”, Arch. [sent-494, score-0.09]

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