i I

Brain Computer Interface 2009 2

i 1 1 1.1.................................. 1 1.2............................... 2 1.3................................. 3 2 4 3 12 3.1 I..................................... 12 3.1.1.............................. 12 3.1.2........................ 12 3.1.3................................ 13 3.1.4.................................. 18 3.2 II..................................... 19 3.2.1.............................. 19 3.2.2...................... 20 3.2.3................................ 20 3.2.4.................................. 21 4 24 4.1................................ 24 4.2...................................... 24 25 A.1 Linear Discriminant Analysis........................ 25 A.2................................. 26 28

ii 31 32

iii 2.1 BCI................................ 5 2.2............................ 9 2.3............................... 10 2.4........................... 10 2.5................. 11 3.1 10-20...................... 14 3.2 8-13Hz........................... 14 3.3.......................... 16 3.4............................ 17 3.5 S1..................... 22 3.6 S2..................... 23 3.7 S3..................... 23

iv 2.1..................................... 6 3.1................ 15 3.2................................ 20 3.3................ 21

1 1 1.1 Brain-Computer Interface BCI 1 [1] BCI 2 Amyotrophic Lateral Sclerosis: ALS [3, 4] [5] BCI functional Magnetic Resonance Imaging fmri Near Infrared Spectroscopy NIRS Electrocorticography ECoG Electroencephalography EEG BCI EEG EEG-based BCI [6, 7] EEG-based BCI EEG Pfurtscheller Graz-BCI [8] 8-13Hz Linear Discriminant Analysis LDA [9] BCI LDA Support Vector Machine SVM [10] 1 Brain-Machine Interface BMI 2 16 7000 [2]

2 1 BCI 1 BCI 1 EEG [8, 11, 12] EEG Event-Related Desynchronization ERD 3 Single Trial [13] 1.2 BCI Forward Error Correction FEC Automatic Repeat request ARQ Hybrid ARQ HARQ HARQ Reliability-Based Hybrid ARQ RB-HARQ [14] BCI BCI Dornhege [15] 3 8-12Hz

1.3. 3 1.3 1 2 BCI 3 EEG BCI 4 BCI BCI BCI

4 2 2 EEG-based BCI EEG 2.1 BCI Quadratic Discriminant Analysis QDA Linear Discriminant Analysis LDA [10] k x k p f k (x) = f(x µ k, Σ k ) f k (x) x u k 1 2 3 FEC Forward Error Correction ARQ Automatic Repeat Request Hybrid ARQ HARQ HARQ Basic Type-I HARQ Type-I HARQ Type-II HARQ Type-I Type-II [16] HARQ Reliability-Based Hybrid ARQ RB-HARQ [14] RB-HARQ BCI 1 A.1 2 1 3 A.2

5 Intent Computer Neurons Distractions Sleepiness Classification Electrical Noise Feature Extraction Scalp EEG System Computer 2.1: BCI

6 2 2.1: H E L O 00 01 10 11 2.2 BCI HELLO {H E L O} 4 2.1 {0 1} 2.1 BCI Constant ARQ Reliability-Based ARQ RB-ARQ RB-HARQ FEC Millán [17] unknown Basic Type-I HARQ Basic RB-ARQ Constant ARQ Basic ARQ RB-ARQ t x ut T X u = {x u1, x u2,..., x ut } K x ut u k K f k (x) π k k

7 4 P (k X u ) = t ˆπ ˆf k k (x ut ) l K t ˆπ l ˆf l (x ut ) (2.1) ˆ λ 2.2 2.3 ˆk max P (k X u ) λ (2.2) k ˆk = arg max P (k X u ) (2.3) k Reliability-Based Automatic Repeat request RB-ARQ 1. k K f k (x) π k 1 X u = {x u1 } 2. 2.2 3 X u x ut 2 3. 2.3 2.2 x ut Constant ARQ Basic RB-ARQ T 2.3 X u = {x u1 x u1 R} K = {0, 1} k = 0 k = 1 2.4 2.3 2.4 λ Basic RB-ARQ T 1/T 5 2.3 x ut = ( 1 T t x ut x ut R) Constant ARQ 4 A.1 5 A.1

8 2 max k P (k x ut ) λ x ut c T c T = c 1 /T (2.4) RB-ARQ T Basic RB-ARQ Constant ARQ RB-ARQ Basic RB-ARQ Constant ARQ 2 K = {0, 1} µ 0 µ 1 σ 2 = σ 2 0 = σ 2 1 2.5 2.5 d = 0.2 d = 1 Constant ARQ Basic RB-ARQ RB-ARQ 2.5 RB-ARQ 1 1 d = µ 0 µ 1 σ d 2.6 (2.5) µ 0 µ 1 2 s 2 0 + s 2 1 (2.6) s 2 k k

9 情報源 送信機 通信路 受信機 受信者 メッセージ 送信信号 雑音源 受信信号 メッセージ 2.2:

10 2 Likelihood µ 0 µ L µ 1 x u1 2.3: µ L = (µ 0 + µ 1 )/2 1 0.9 max k P(k x u1 ) 0.8 0.7 0.6 0.5 µ 0 µ L µ 1 x u1 2.4: λ = 0.7

11 66 64 62 Accuracy [%] 60 58 56 54 52 1 2 3 4 5 6 7 8 9 10 11 Time [sec] Constant ARQ Basic RB-ARQ RB-ARQ (a) d = 0.2 100 95 90 Accuracy [%] 85 80 75 70 65 1 2 3 4 5 6 7 8 9 10 11 Time [sec] Constant ARQ Basic RB-ARQ RB-ARQ (b) d = 1 2.5:

12 3 3 RB-ARQ EEG 3.1 3.2 3.1 I 3.1.1 10-20 [18] 3.1 Pz A2 1000Hz Polymate AP216 10 10 1 12 1 A B 4 1 1 2 240 20 6 2 12 1 8-13Hz 3.1.2 22 11 2 8-13Hz

3.1. I 13 [19] 5% [20] 3.1 p p 2.3 10 3 (= 0.05/22) 3.1 3 3.2 A A B 8-13Hz 3.1.3 2 240 x k (n)(k {A, B}, n = 1, 2,..., 240) 2 n = 1, 2,..., 120 120 120 n = 121, 122,..., 240 A 1. T = 1 n = 121, k = A 2. X u x ut x k (n) 2.1 3. 2.2 2.3 T = 1 n = n+1 X u = ϕ T = T + 1 n = n + 1 n < 240 2 B k = B 10 Constant ARQ T Basic RB-ARQ RB-ARQ λ 2.5 3.3(a)(c)(e) 5 20 max k P (k x ut ) λ x ut 3.3(b)(d)(f) A C λ RB-ARQ 3.4 = 100 [%] (3.1)

14 3 Fp1 Fp2 F7 F3 Fz F4 F8 A1 A2 T3 C3 Cz C4 T4 T5 P3 Pz P4 T6 O1 O2 3.1: 10-20 35 30 Thought A Thought B Boundary 25 Frequency 20 15 10 5 0 5 10 15 20 Amplitude [uv] 3.2: 8-13Hz

3.1. I 15 3.1: A B 1 4.3E-01 2.9E-01 2 3.4E-01 1.5E-01 3 6.3E-02 2.5E-03 4 6.3E-13 7.4E-03 5 5.2E-03 2.6E-02 6 1.9E-01 1.4E-04 7 8.0E-02 3.0E-02 8 2.1E-03 5.0E-01 9 3.8E-02 3.5E-01 10 6.2E-03 7.6E-01 11 9.5E-01 6.5E-01

16 3 10 9 8 Constant ARQ Basic RB-ARQ RB-ARQ 14 13 12 Time [sec] 7 6 5 4 Amplitude [µv] 11 10 9 8 7 3 6 2 1 70 75 80 85 90 95 100 Accuracy [%] 5 MA5 Threshold MA20 Boundary 4 0 20 40 60 80 100 120 Data Number (a) Accuracy and Transmission Time (Subject A) (b) Moving Average and Threshold (Thought B at Subject A) 10 9 13 12 8 11 Time [sec] 7 6 5 4 Amplitude [µv] 10 9 8 7 6 3 Constant ARQ 2 Basic RB-ARQ RB-ARQ 1 65 70 75 80 85 90 95 100 Accuracy [%] 5 4 MA5 MA20 Threshold Boundary 3 0 20 40 60 80 100 120 Data Number (c) Accuracy and Transmission Time (Subject B) (d) Moving Average and Threshold (Thought B at Subject B) 10 9 8 14 12 Time [sec] 7 6 5 4 Amplitude [µv] 10 8 6 3 Constant ARQ 2 Basic RB-ARQ RB-ARQ 1 30 35 40 45 50 55 Accuracy [%] 4 MA5 Threshold MA20 Boundary 2 0 20 40 60 80 100 120 Data Number (e) Accuracy and Transmission Time (Subject C) (f) Moving Average and Threshold (Thought A at Subject C) 3.3:

3.1. I 17 10 9 Theoretical Value Experimental Value 8 7 Time [sec] 6 5 4 3 2 1 70 75 80 85 90 95 100 Accuracy [%] (a) Accuracy and Transmission Time (Subject A) 18 16 Theoretical Value Experimental Value 14 12 Time [sec] 10 8 6 4 2 0 30 40 50 60 70 80 90 100 Accuracy [%] (b) Accuracy and Transmission Time (Subject C) 3.4:

18 3 3.1.4 3.3(a) Basic RB-ARQ RB-ARQ Constant ARQ 3.1.2 A B A RB-ARQ T < 5 RB-ARQ T > 5 Basic RB-ARQ λ 3.3(c) RB-ARQ Basic RB-ARQ Constant ARQ 3.3(d) 20 B 10 20 Constant ARQ RB-ARQ 30 110 B Basic RB-ARQ RB-ARQ 40 50 B RB-ARQ EEG 2 [21, 22] 3.3(e) Constant ARQ Basic RB-ARQ RB-ARQ 50% 3.3(f) 90 Basic RB-ARQ RB-ARQ

3.2. II 19 λ λ A BCI C RB-ARQ 3.1 3.4(a) 2.4% 4.6% 3.4(b) 64.7% 44.2% 3.4(b) 2.5 d [23] 2 3.2 II BCI Competition BCI EEG Millán data set V [17] 1 RB-ARQ 3.2.1 3 5 10 4 3 K = {L, R, W } 15 4 C3 Cz C4 CP1 CP2 P3 Pz P4 3.1 8 512Hz 1 21 1 11 URL http://ida.first.fraunhofer.de/projects/bci/competition iii/

20 3 3.2: S1 S2 S3 C3 Cz C4 CP1 CP2 C3 Cz C4 CP1 C3 Cz C4 CP1 CP2 Pz 62.5msec 16Hz [24] 2Hz 8Hz 30Hz 96 1 3500 0.5sec 8 440 3.2.2 LDA QDA A 2 RB-ARQ A 3.2 LDA 4 1 A A A A 3.3 3 4 3.2.3 A RB-ARQ 0.5sec 1. T = 1 n = 1, k = L 2 20 5 21 1 11 URL http://ida.first.fhg.de/projects/bci/competition iii/results/martigny/irenesturm desc. txt

3.2. II 21 3.3: 5 Rank S1 S2 S3 AVG 1 79.60 70.31 56.0 68.65... 5 78.08 63.83 52.75 64.91 * 70.78 64.75 45.64 60.39 2. X u x ut x k (n) 3. T 8 2.1 4 T = T + 1 n = n + 1 2 4. 2.2 2.3 T = 1 n = n+1 X u = ϕ T = T + 1 n = n + 1 n < 240 2 T 8 0.5sec = 8 62.5msec 3 T %8 = 0 8 RB-ARQ 1 3 S1 3 3 4 3.5 3.7 16Hz T 8 2Hz T %8 = 0 λ {λ i λ i = exp( i/2) + 1, i = 0, 1,..., 49} 16Hz 2Hz 50 3.2.4 3.3 A A A A 1 3 3.5 3.7 λ

22 3 95 90 Accuracy [%] 85 80 75 2Hz 16Hz 70 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 Time [sec] 3.5: S1 16Hz 2Hz T = 8 16Hz T = 9 2Hz T 16 RB-ARQ I 1sec λ 49 1 3.5 3.7 100% I

3.2. II 23 90 85 Accuracy [%] 80 75 70 65 2Hz 16Hz 60 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 Time [sec] 3.6: S2 70 65 Accuracy [%] 60 55 50 2Hz 16Hz 45 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Time [sec] 3.7: S3

24 4 4 4.1 Brain-Computer Interface BCI ALS BCI RB-ARQ I II II 4.2 BCI 2 BCI

25 A.1 Linear Discriminant Analysis k K X k = {x k x k R p } x k A.1 p { 1 f k (x) = f(x µ k, Σ k ) = exp 1 } (2π) p/2 Σ k 1/2 2 (x µ k) Σ 1 k (x µ k) (A.1) k µ k Σ k π k ˆµ k = 1 X k ˆΣ k = 1 X k 1 ˆπ k = X k / X x k X k x k x k X k (x k ˆµ k )(x k ˆµ k ) (A.2) (A.3) (A.4) ˆ X = k K X k ˆΣ = ˆΣ k ˆΣ = 1 X K k K x k X k (x k ˆµ k )(x k ˆµ k ) x u k (A.5) P (k x u ) = ˆπ k ˆfk (x u ) l K ˆπ l ˆf l (x u ) (A.6) x u ˆk ˆk = arg max P (k x u ) k (A.7) Linear Discriminant Analysis LDA Quadratic Discriminant Analysis QDA

26 T x u1, x u2,..., x ut k t P (k x u1, x u2,..., x ut ) = ˆπ ˆf k k (x ut ) l K t ˆπ ˆf l l (x ut ) (A.8) T 1 k f k (x) = f(x µ k, Σ k /T ) x ut = 1 T P (k x u1, x u2,..., x ut ) = t x ut ˆπ k ˆ fk ( x ut ) l K ˆπ l ˆ fl ( x ut ) (A.9) A.2 A.1 LDA QDA K k K x k R p X k k µ k µ S w S b ˆµ k = 1 X k ˆµ = 1 X x k X k x k x k k K x k X k (A.10) (A.11) Ŝ w = (x k ˆµ k )(x k ˆµ k ) (A.12) k K x k X k Ŝ b = k K( ˆµ k ˆµ)( ˆµ k ˆµ) (A.13) ˆ X = k K X k A.14 w R p w Ŝ b w w Ŝ ww (A.14) Ŝ 1 w Ŝ= b P AP (A.15) A P A = (diag(d 1, d 2,..., d p ) d 1 d 2 d p ) P = (u 1 u 2 u p )

A.2. 27 A.14 d 1 u 1 w Tr(A) = p i d i (A.16) T 1 k ˆ S w = Ŝw T (A.17) Tr(Ā) = T Tr(A) (A.18)

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31 ( ) 1. BCI 2 D Vol.J92-D, No.1, pp.153-161, 2009. 1. BCI Reliability-Based ARQ ( ) 1. H.Takahashi, T.Yoshikawa and T.Furuhashi: A Study on Application of Reliability Based Automatic Repeat Request to Brain Computer Interfaces, In Proc. the 15th Int. Conf. on Neural Information Processing of the Asia-Pacific Neural Network Assembly, pp.366-367, 2008. ( ) 1. 23 pp. 557-560, 2007. 2. Brain Computer Interface 2, vol. 107, no. 263, pp. 63-67, 2007. 3. BCI Reliability-Based ARQ 4, pp. 5-1 5-4, 2008. 4. BCI 2008, p.20, 2008.

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