JOURNAL OF NEURAL ENGINEERING 2004 Dec;1(4):212-7. Epub 2004 Nov 17.

1. A new approach in the BCI research based on fractal dimension as feature and Adaboost as classifier JOURNAL OF NEURAL ENGINEERING 2004 Dec;1(4):212-7. Epub 2004 Nov 17. Reza Boostani and Mohammad Hassan Moradi 2005/10/13 M09356002 劉明機

2. Scheme • BCI的研究內容？ • 實驗如何設計？ • 所用的特徵值與分類器為何？ • 不同的特徵值與不同的分類器互相組合比較的結果如何？

3. Abstract • 如何提高心智活動的分類正確率仍然是BCI領域的熱門研究之一。 • 本論文使用基於碎形維度fractal dimension當特徵值，Adaboost當分類器的新方法來增加分類的正確率，並對五各受試者進行測試。 • 本論文同時使用band power, Hjorth parameters當特徵值與LDA當分類器做比較。

4. Introduction • brain computer interface (BCI) • 無法自由行動的併發症(locked-in-syndrome) • 嚴重脊髓受傷(severe spinal cord injury) • move his limbs by functional electrical stimulation controlled with thoughts • non-invasive EEG as input • optimize pre-processing, feature extraction and feature classification methods.

5. Introduction • the Graz-BCI team have employed different features such as band power , adaptive autoregressive coefficients and some classifiers including LDA, FIRMLP , LVQ and HMM to improve the classification rate between different motor imagery tasks.They have also used DSLVQand G.A. for feature selection • Deriche and Al-Ani selected the best feature combination among the variance,AR coefficients, wavelet coefficients, and fractal dimension by a modified mutual information method and classified them by aMLP classifier • Cincotti et al compared the performance of three classifiers (ANN, Mahalonobis distance and HMM) to classify the band power feature for six subjects

6. Introduction • The aim of this paper is to improve the classification rate of a cuebased BCI by a new approach based on fractal dimension and Adaboost classifier • As a comparison, band power and Hjorth parameters along with LDA are assessed on the same data set (five subjects).

7. Subjects and data acquisition • Five healthy subjects (L1, o3, k3, f8 and o8) • sat in a relaxing chair with armrests about 1.5 m in front of the computer screen • Three bipolar EEG channels were recorded from 6 Ag/AgCl electrodes placed 2.5 cm anterior and 2.5 cm posterior to the standardized positions C3, Cz and C4 (international 10–20 system). • filtered 0.5-70Hz • sample rate 128 Hz

8. Subjects and data acquisition • Each trial lasted 8 s and started with the presentation of a blank screen • A short acoustical warning tone was presented at second 2 and a fixation cross appeared in the middle of the screen • From second 3 to second 7 an arrow(cue), representing the mental task to perform, was prompted • An arrow pointing either to the left or to the right indicated the imagination of a left hand or right hand movement • The order of appearance of the arrows was randomized • at second 7 the screen content was erased • The trial finished with the presentation of a randomly selected inter-trial period (up to 2 s) beginning at second 8

9. Training paradigm Subjects and data acquisition • Three sessions were recorded for each subject on three different days. • Each session consisted of three runs with 40 trials each.

10. Feature extraction and classification • Feature extraction • The goal of feature extraction is to find a suitable representative of the data that simplify the subsequent classification or detection of brain patterns • Band power -> frequency bands; • Hjorth parameters ->morphological characteristics • fractal dimension -> entropy

11. Feature extraction and classification • Band power (BP) • The EEG contains different specific frequency components,for example, alpha and beta bands which are particularly important to classify the different brain states, especially for discriminating motor imagery tasks. • 10–12 Hz,16–24 Hz • 1s time window • 250 ms overlap

12. Feature extraction and classification • Hjorth parameters • describe the signal characteristics in terms of • activity (variance (VAR) of signal) • mobility (a measure of mean frequency) • complexity (a measure of the deviation from sine shape) • 500 ms time window • without overlapping • an exponential window has been applied to the features for smoothing

13. Feature extraction and classification • Hjorth parameters y : the signal y' : the derivative of the signal N : the number of samples in the window μ : the mean of the signal in the window

14. Feature extraction and classification • Fractal dimension (FD) • Fractal dimension can be interpreted simply as the degree of meandering (or roughness or irregularity) of a signal. • methods for calculating fractal dimension • Katz, Higuchi and Peterson • Katz method is more robust,implemented in this research • 1s time window • 250 ms overlap

15. Feature extraction and classification • Fractal dimension (FD) • 自我重覆性或自我相似性（self-similarity） • 無論將其形狀放大或縮小至何種程度，它仍然會表現出與原來相似之形狀 • 物體整體外觀與組成部分之形狀所具有的相似性，稱之為碎形。一般而言可分為完全自相似碎形與統計自相似碎形，前者如三角 Koch 曲線，它具有一層層縮小而相似的特性，事實上在自然界找不到像這類完全自我相似的例子，其只能作為數學模型。但後者卻普遍地存在於自然界中，就統計意義上而言，其整體與組成部分是相似的，故稱為統計自相似碎形，如河川、山脈、島嶼及海岸線等 。 • 具有非整數的維度，稱為「碎維維度」( fractal dimension ) • 碎維維度的數值越大，其彎曲度越大，故碎維維度是量測一個幾何結構粗糙程度或複雜程度的指標。

16. Feature extraction and classification • Fractal dimension (FD) • Katz fractal dimension L : the total length of the curve d : the diameter estimated as the distance between the first point of the sequence and the point of the sequence that provides the farthest distance

17. Feature extraction and classification • Linear discriminant analysis (LDA) • Fisher's linear discriminant is maximizing the between-group variance to the within-group variance ratio,which in this case is measured by the ratio of the determinants of the preceding two matrices.

18. Feature extraction and classification • Adaboost • The principle of theAdaboost is that a committee machine can adaptively adjust to the errors of its components, the so-called weak learners. • The classification rate of each weak learner should exceed 50%. • a neural network with one hidden layer is selected as the weak learner.

19. Feature extraction and classification • Adaboost • 委員會機器(Committee Machine)在類神經網路領域中的應用，主要是用來結合數個單一類神經網路，透過某些投票方式，以及整合的方法，可以將數個單一類神經網路結合，建立一委員會機器；如同社會上各種會議結構，都有一定的議程和投票方式，整合各方委員的意見來決策某些事項。

20. Feature extraction and classification • Adaboost A committee of neural networks generated using Adaboost

21. Feature extraction and classification • Adaboost

23. Feature extraction and classification • Adaboost • First, the first neural network trains with the equal error weight for all the samples D1(i):the error weight for the samples in the first iteration N:the number of input samples.

24. Feature extraction and classification • Adaboost • For the next iteration, the error weight of the samples is changed regarding their error in the previous iteration by the following relation:

25. Feature extraction and classification • Adaboost Fn-1(x): the output of the (n-1)th weak learner εn-1 :the error of the weak learner in the (n-1)th step di :the label of the ith input sample βn-1 :measures the importance of the hypothesis of Fn-1(x) and it ecreases with error.

26. Feature extraction and classification • Adaboost • the misclassified samples in each stage are given a high value of Dn(i) (error weight) for the next stage. • This iterative procedure repeats till the time that n reaches T (the maximum considered value for the number of weak learners).

27. Feature extraction and classification • Adaboost • After the training phase, total output of the Adaboost is calculated as follows:

28. Feature extraction and classification • Adaboost • For this classifier, all the feature values must be normalized in the interval [-1, 1].

29. Evaluation of classification performance • The training set is evaluated ten times, by tenfold cross validation • The best classifiers from the evaluation phase have been selected and applied to the test data • 360 trials have been recorded for each subject • for each subject • 240 trials for cross validation • 120 trials for the testing phase • then artefact trials were removed

30. Evaluation of classification performance • 交互效度檢定(cross-validation)。基本原理是再抽取另一樣本對該模式進行擬合度檢定。 • In bioinformatics, if you have a set of 100 data can be used as a training set to tune your program. You may use 99 of them to train your program and predict the last one. To show this is not a chance, you need to pick another 99 to train your program and predict the last one again. If you do the same thing again and again, each data set will be predicted based on the program trained by the rest 99 data set. The whole process is called "cross validation".

31. Results • No combination of the features has been considered in this paper • BP with LDA yielded the best performance for four subjects (L1, o3, o8, f8) • k3 for which Hjorth parameters along with both classifiers showed a significant result.

32. Results L1 o1 o8 cross validation data

33. Results k3 f8 cross validation data

34. Results • In the test phase, • FD and Adaboost showed the best result (16.5% error) for subject L1 • o8 and k3 with LDA and BP. • FD along with LDA has shown good results in cases k3 and L1. • But for the three other subjects (o3, o8 and f8) the test results confirm the cross validation phase.

35. Results L1 o1 o8 test data

36. Results k3 f8 Test data

37. Results • To have significant results, the F test and the T test were performed on the test results • Test and training data were randomly chosen from the pure data for 20 times • All results were significant, which means that the P value was lower than 0.05 for all evaluated results. • the test curves for FD and BP along with two classifiers (LDA and Adaboost) for the whole paradigm are depicted in figures 3–12 for our subjects • Hjorth results are eliminated from the graphs, because these results are not the best in any case

38. BP , L1 BP , o8 BP , o3 FD , o3 FD , L1 Results

39. FD , o8 BP , f8 BP , K3 FD , k3 FD , f8 Results

40. Discussion • Cross validation results in four cases indicate that the best combination for classifying the imagery tasks is BP with LDA.But in the test phase, results did not completely confirm the cross validation results. • FD and Adaboost showed a significant result for subject L1,k3 and o8. • FD with LDA in the cases k3 and L1. • FD with both classifiers can be an acceptable alternative with the combination of BP and LDA.

41. Discussion • In many articles BP and LDA are presented as a gold-standard technique for BCI applications,This paper showed that the selection of a feature and a classifier is extremely dependent on the case. • In the above-mentioned articles results were shown for a maximum of two or three cases and no appropriate comparison was made.

42. Discussion • There is a trade-off between the minimal error rate and its latency, • latency of minimal error rate after 2.5 s of the cue stimulus is acceptable. • 9.5% error for case o3 (happening in 6.25 s) cannot be acceptable,because, in the real application, a subject might lose concentration if he does not see the feedback on the screen. • The evaluation was also performed for different window lengths in the 250 ms interval, FD shows supremacy to BP and Hjorth parameters. • As the time window increases, the classification rate improves but it causes a delay in reporting the changes in the EEG.

43. Discussion • Of the two classifiers • LDA shows a very reliable and robust behaviour. • Adaboost is more time consuming for the training • a chaotic behaviour in the case L1, therefore, FD can present it much better than two other features, and the non-linear classifier (Adaboost) could find a more flexible margin through the classes.

44. Discussion • the biological properties of every human are unique,therefore, gold-standard combination does not make sense for all the cases. • for each individual, we have to find the best combination of feature and classifier or on some occasions,a combination of the features by evolutionary algorithms or a tree combination of classifiers which can lead to the best result.

45. END Thank you