A bayesian approach for adaptive BCI classification

A Bayesian Approach for Adaptive BCI Classi?cation

M.Kawanabe1,M.Krauledat1,2,B.Blankertz1

1Fraunhofer FIRST(IDA),Berlin,Germany

2Technical University Berlin,Berlin,Germany

E-mail:nabe@?rst.fhg.de

SUMMARY:In this article,we present an adap-tive classi?er for BCI based on a mixture of Gaus-sian(moG)model of the features and a dynamical Bayesian model of the class means.We apply this approach to feedback data from the Berlin Brain-Computer Interface(BBCI).The proposed model can improve the classi?cation performance by compen-sating for substantial changes of EEG signals be-tween training and feedback sessions as well as for gradual nonstationarity in the feedback sessions. INTRODUCTION

EEG-based BCI systems are often subject to nonsta-tionarities that are caused by changes in the subject’s mental state during an experiment(e.g.due to fa-tigue,change of task involvement and demands for visual processing etc.).Recently Shenoy et al.[2] showed that a simple bias recalculation for the clas-si?er obtained from the training data can eliminate sources most detrimental effects of nonstationarities during feedback operation.In this paper,we pro-pose a Bayesian version of such adaptive classi?ers, where the class means are treated as random vari-ables and their posterior distributions are approxi-mated by a sequential manner as Kalman?lters.The proposed method was applied to BBCI data collected from three subjects.

MATERIALS AND METHODS

We investigate data from a study of three subjects us-ing the BBCI system similar to[1]but with very long feedback blocks without break.The experiments con-sisted of a calibration measurement and a feedback period.In the calibration measurement,visual stim-uli(L),(R)(for imagined left and right hand move-ment)and(F)(for imagined foot movement)were presented to the subjects.Based on the recorded sig-nals,subject-speci?c features for the further analysis were calculated.The most discriminative frequency band for two of the three classes was selected man-ually by experts,and common spatial patterns(CSP) were calculated.For the data sets we analyzed,6(al),

2(aw)and4(VPt)CSP channels were used,respec-

tively.The bandpower of the CSP-projected channels

was estimated using windows of3seconds length,

and?nally a linear classi?er was trained by linear dis-

criminant analysis(LDA).

In the feedback phase,bandpower estimations of CSP

channels were calculated in a similar manner as in the

calibration session for sliding windows of1second

length.The real-valued output by the LDA classi?er

was used to move a cursor horizontally on the screen.

The subjects were then using this cursor for the oper-

ation of a text input(speller)software.

We employ the following mixture of Gaussian(moG)

model for each class distribution

p(x|y=1):=(1?p p)φ(x|μp,Σp)+p pφ(x|m,V), p(x|y=?1):=(1?p n)φ(x|μn,Σn)+p nφ(x|m,V),

whereφ(x|μ,Σ)is the Gaussian density function

with meanμand covarianceΣ.The?rst terms repre-

sent typical samples,while the common second term

corresponds to outliers with large covariance V.Al-

though we concentrated on the binary classi?cation

problem,the moG model also enables us to recog-

nize outlying observations from typical samples.In

the training session,we estimate the model parame-

ters,i.e.,the mean(μp,μn,m)and the covariance

(Σp,Σn,V)of each Gaussian prototype,their outlier

ratios(p p,p n),and the class probability(π:=p(y=

1))by EM algorithm with an extra restriction to keep

the covariance V of the outlier large.

To cope with the difference of EEG signals be-

tween training and feedback and the gradual non-

stationarity in the feedback session we assume that

the centers of both classes are random variables and

subject to the dynamical model(t≥1)

μp(t)=μp(t?1)+εp(t),

μn(t)=μn(t?1)+εn(t),

whereεp(t)～N(0,?p),εn(t)～N(0,?n).The

initial means are also assumed to be Gaussians cen-

tered at the estimators from the training session,i.e.

μp(0)～N( μp,Γp)andμn(0)～N( μn,Γn),re-

spectively.The covariances?p,?n,Γp andΓn con-

trol the speed of adaptation and should be chosen ac-

cording to the magnitude of the initial covariances.

The center m(t)of the outlier class is?xed at the

1

average of the positive and negative classes.The required parameters are determined on the training data.

When the samples and the labels D t={xτ,yτ}tτ=1 up to t-th trial are observed,we infer the posterior dis-tribution p(μp(t),μn(t)|D t)by a sequential scheme as Kalman?lter.However in contrast to the case in Kalman?lters,the posterior is not Gaussian in our moG model.Hence,we approximate it by a single Gaussian distribution with the same mean and covari-ance.We construct a classi?er based on the posterior distribution in order to predict the label of the(t+1)th trial from the inputs.In this study we adopted the classi?er based on the posterior probability of the typ-ical positive minus that of the typical negative class, i.e.f t(x):=P(y=1,z=0|x,D t)?P(y=?1,z=0|x,D t),where the latent variable z equals 1if the sample is an outlier and0otherwise. RESULTS

In our Bayesian framework,the posterior distribu-tions of the class meansμp(t)andμn(t)are approx-imated by Gaussians.In order to visualize the non-stationarity of the data infered by the moG model,we plotted the time course of the posterior means in Fig-ure1,where the horizontal axis is the direction of the original classi?er.Time is indicated by gray scale (black to white).At the beginning,because less in-formation about the class meansμp(t)andμn(t)is available,the posterior means can move by a large amount,while the changes get smaller as more trials are performed.For the subject aw,although the mean of the positive class again comes closer to the esti-mator from the training data after feedback learning, that of the negative class seems to stay away from the original estimator.This is the reason why classi?er modi?cation in the feedback session can improve the performance.

In Table1,we compare the classi?cation error in the feedback sessions of our approach(ADB)with the er-ror of the original classi?er(ORIG).ADB was much better for subject aw,equal for VPt and worse for al. Table1:Comparison of classi?cation errors (window-wise,the feedback error in the BCI task was lower)

al

22.59.0 VPt

英语作文关于共享单车的篇精编

(一) 假定你是红星中学初三学生李华。你的美国朋友Jim在给你的邮件中提到他对中国新近出现的一种共享单车“mobike”很感兴趣，并请你做个简要介绍。请你给Jim回信，内容包括： 1. 这种单车的使用方法(如：APP查看车辆、扫码开锁等); 2. 这种单车的优势; 3. 你对这种单车的看法。 注意：1. 词数不少于80; 2. 开头和结尾已给出，不计入总词数。 提示词：智能手机smartphone, 二维码the QR code 参考范文 Dear Jim, I’m writing to tell you more about the new form of sharing bike mobike mentioned in your latest letter. It’s very convenient to use if you have a smartphone. What you do is find a nearest mobikethrough the APP, scan the QR code on the bike, and enjoy your trip. Compared to other forms of sharing bike, the greatest advantage of mobike is that you can easily find one and never worry about where to park it. It is becoming a new trend as a means of transportation, which relieves the traffic pressure and does good to the environment as well. Hope to ride a mobike with you in China. Yours, Li Hua (二) 最近很多大城市都投放了共享单车(shared bikes)，比如摩拜单车(Mobike)、Ofo共享单车等。由于它们方便停放，骑车也能起到锻炼身体的作用，作为代步工具很受大家欢迎。但是，各地也出现了很多毁车现象，比如刮掉车上的二维码(QR code)、上私锁等。 你对这种现象怎么看?你对共享单车公司有什么建议吗?写一篇符合逻辑的英语短文，80词左右。 参考词汇：bike-sharing companies 共享单车公司，Mobike 和Ofo 是两家共享单车公司，convenience 方便，register登记 参考范文 The shared bikes like Mobike and Ofo bring great convenience to people. You needn’t lock them by simply using your smart phone. They can take you where the subway and bus don’t go. And they can be left anywhere in public for the next user. However, bad things happen. Some people damage the QR code on the bike, or use their own lock, which causes trouble to other users. In my opinion, it’s difficult to turn these people’s ideas in a short time. Therefore, bike-sharing companies like Mobike and Ofo need to do something. For example, those who damage the bike should pay for their actions. Also, because people use their real name toregister as a user, it’s a good way to connect to one’s personal credit. In the end, what I want to say is to take good care of public services. (三) 共享单车(bicycle sharing)已成为时下最热的话题之一，请你就这一话题写一篇短文。内容须包括三方面：1. 共享单车蓬勃发展，成为社会热潮;2. 共享单车带来便利，但也存在问题;3. 我对解决问题的建议。 参考范文 Bicycle Sharing With the development of technology, bicycle sharing comes into people's lives. It becomes more and more popular and much news reported it. At the same time, we should see that there are some problems caused by bicycle sharing. On one side, bicycle sharing makes it very convenient of people traveling. You can find a bicycle anywhere at any time when you want to go out for a cycling, and the price of one trip is very low. It can save time for people. On the other side, its management is not perfect. Even kids can open the lock and ride the bicycle, there is no doubt that such behavior is very dangerous.

图书馆空间设计研究

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介绍北京的英语作文(2) AsBeijinghasbeenconfirmedhomecityofOlympics2008,the spiritofgreenOlympics,scientificOlympicsandhumanizedOlymp icwillsurelybringmoreandmorechangestoBeijing,promotethed evelopmentofsportsandOlympicsinChinaaswellasintheworld,a ndstrengthenthefriendlycommunicationsbetweenChineseandf oreignpeople. 篇六：Beijing BeijingisthecapitalofPeoplesRepublicofChinaandthenation scentreforpolitics,economyandculture.Itenjoysalongandrichhis tory.Therearenumerousheritagesitesandwonderfulexamplesof ancientarchitecture,suchastheworld-famousGreatWall,theTem pleofHeavenandtheForbiddenCity. Besidessightseeingplaces,therearemanydeliciousfoodsuch asPekingducksandBeijingsnacks.Beijingisreallyagoodplacetotr avel. 篇七：Beijing AsthecaptainofChina，Beijinghasbeenthemostpopularcityofchina。SomoreandmorepeoplewanttovisitBeijing.

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