Mathematics in Independent Component Analysis

More documents

Recommendations

Info

152 Chapter 9. Neurocomputing (in press), 2007 sources. Here, K = 12 for simplicity one-dimensional autocovariance matrices were used, both spatially and temporally. We masked the data using a fixed common threshold. In order to quantify algorithm performance, as before we determined the spatiotemporal source that had a time course with maximal autocorrelation with the stimulus protocol, and compared this autocorrelation. In figure 4(a), we show a boxplot of the autocorrelations together with the needed computational effort. The median autocorrelation was very high with 0.89. The separation was fast with a mean computation time of 0.25s on a 1.7GHz Intel Dual Core laptop running Matlab. In order to confirm this robustness of the algorithm, we analyzed the sample-size dependence of the method by running stSOBI on subsampled data sets. The bootstrapping was performed spatially with repetition, but reordering of the samples in order to maintain spatial dependencies. Figure 4(b-c) shows the algorithm performance when varying the subsampling percentage from 1 to 200 percent, where the statistics were done over 100 runs and over the 10 subjects. Even when using only 1 percent of the samples, we achieved a median autocorrelation of 0.66, which increased at a subsampling percentage of 10% to an already acceptable value of 0.85. This confirms the robustness and efficiency of the proposed method, which of course comes from the underlying robust optimization method of joint diagonalization. 7 Conclusion We have proposed a novel spatiotemporal BSS algorithm named stSOBI. It is based on the joint diagonalization of both spatial and temporal autocorrelations. Sharing the properties of all algebraic algorithms, stSOBI is easy to use, robust (with only a single parameter) and fast (in contrast to the online algorithm proposed by Stone). The employed dimension reduction allows for the spatiotemporal decomposition of high-dimensional data sets such as fMRI recordings. The presented results for such data sets show that stSOBI clearly outperforms spatial-only recovery and Stone’s spatiotemporal algorithm. Moreover, the proposed algorithm is not limited to second-order statistics, but can easily be extended to spatiotemporal ICA for example by jointly diagonalizing both spatial and temporal cumulant matrices. Acknowledgments The authors gratefully acknowledge partial financial support by the DFG (GRK 638) and the BMBF (project ‘ModKog’). They would like to thank D. Auer from the MPI of Psychiatry in Munich, Germany, for providing the 13
Chapter 9. Neurocomputing (in press), 2007 153 fMRI data, and A. Meyer- Bäse from the Department of Electrical and Computer Engineering, FSU, Tallahassee, USA for discussions concerning the fMRI analysis. The authors thank the anonymous reviewers for their helpful comments during preparation of this manuscript. References [1] A. Hyvärinen, J. Karhunen, E. Oja, Independent component analysis, John Wiley & Sons. [2] A. Cichocki, S. Amari, Adaptive blind signal and image processing, John Wiley & Sons, 2002. [3] L. Tong, R.-W. Liu, V. Soon, Y.-F. Huang, Indeterminacy and identifiability of blind identification, IEEE Transactions on Circuits and Systems 38 (1991) 499–509. [4] L. Molgedey, H. Schuster, Separation of a mixture of independent signals using time-delayed correlations, Physical Review Letters 72 (23) (1994) 3634–3637. [5] A. Belouchrani, K. A. Meraim, J.-F. Cardoso, E. Moulines, A blind source separation technique based on second order statistics, IEEE Transactions on Signal Processing 45 (2) (1997) 434–444. [6] A. Ziehe, K.-R. Mueller, TDSEP – an efficient algorithm for blind separation using time structure, in: L. Niklasson, M. Bodén, T. Ziemke (Eds.), Proc. of ICANN’98, Springer Verlag, Berlin, Skövde, Sweden, 1998, pp. 675–680. [7] H. Schöner, M. Stetter, I. Schießl, J. Mayhew, J. Lund, N. McLoughlin, K. Obermayer, Application of blind separation of sources to optical recording of brain activity, in: Proc. NIPS 1999, Vol. 12, MIT Press, 2000, pp. 949–955. [8] F. Theis, A. Meyer-Bäse, E. Lang, Second-order blind source separation based on multi-dimensional autocovariances, in: Proc. ICA 2004, Vol. 3195 of LNCS, Springer, Granada, Spain, 2004, pp. 726–733. [9] J. Stone, J. Porrill, N. Porter, I. Wilkinson, Spatiotemporal independent component analysis of event-related fmri data using skewed probability density functions, NeuroImage 15 (2) (2002) 407–421. [10] A. Bell, T. Sejnowski, An information-maximisation approach to blind separation and blind deconvolution, Neural Computation 7 (1995) 1129–1159. [11] J. Cardoso, A. Souloumiac, Blind beamforming for non gaussian signals, IEE Proceedings - F 140 (6) (1993) 362–370. [12] F. Theis, Y. Inouye, On the use of joint diagonalization in blind signal processing, in: Proc. ISCAS 2006, Kos, Greece, 2006. 14
Page 1 and 2:
Statistical machine learning of bio
Page 3:
to Jakob
Page 6 and 7:
vi Preface
Page 8 and 9:
viii CONTENTS 3 Signal Processing 8
Page 11 and 12:
Chapter 1 Statistical machine learn
Page 13 and 14:
1.1. Introduction 5 auditory cortex
Page 15 and 16:
1.2. Uniqueness issues in independe
Page 17 and 18:
1.2. Uniqueness issues in independe
Page 19 and 20:
S U M M A R Y T his �le contains
Page 21 and 22:
1.3. Dependent component analysis 1
Page 23 and 24:
Table 1.1: BSS algorithms based on
Page 25 and 26:
Page 27 and 28:
Page 29 and 30:
Page 31 and 32:
Page 33 and 34:
1.4. Sparseness 25 1.4 Sparseness O
Page 35 and 36:
1.4. Sparseness 27 Theorem 1.4.3 (S
Page 37 and 38:
1.4. Sparseness 29 R 3 R 3 A BSRA R
Page 39 and 40:
1.4. Sparseness 31 Sparse projectio
Page 41 and 42:
1.5. Machine learning for data prep
Page 43 and 44:
Page 45 and 46:
Page 47 and 48:
Page 49 and 50:
Page 51 and 52:
1.6. Applications to biomedical dat
Page 53 and 54:
Page 55 and 56:
Page 57 and 58:
Page 59 and 60:
1.7. Outlook 51 noise data signal i
Page 61:
Part II Papers 53
Page 64 and 65:
56 Chapter 2. Neural Computation 16
Page 66 and 67:
Page 68 and 69:
Page 70 and 71:
Page 72 and 73:
Page 74 and 75:
Page 76 and 77:
Page 78 and 79:
Page 80 and 81:
Page 82 and 83:
Page 84 and 85:
Page 86 and 87:
Page 88 and 89:
Page 90 and 91:
82 Chapter 3. Signal Processing 84(
Page 92 and 93:
Page 94 and 95:
Page 96 and 97:
Page 98 and 99:
90 Chapter 4. Neurocomputing 64:223
Page 100 and 101:
Page 102 and 103:
Page 104 and 105:
Page 106 and 107:
Page 108 and 109:
Page 110 and 111: 102 Chapter 4. Neurocomputing 64:22
Page 112 and 113: 104 Chapter 5. IEICE TF E87-A(9):23
Page 122 and 123: 114 Chapter 6. LNCS 3195:726-733, 2
Page 132 and 133: 124 Chapter 7. Proc. ISCAS 2005, pa
Page 138 and 139: 130 Chapter 8. Proc. NIPS 2006 Towa
Page 140 and 141: 132 Chapter 8. Proc. NIPS 2006 1.3
Page 142 and 143: 134 Chapter 8. Proc. NIPS 2006 stru
Page 144 and 145: 136 Chapter 8. Proc. NIPS 2006 5.5
Page 146 and 147: 138 Chapter 8. Proc. NIPS 2006
Page 148 and 149: 140 Chapter 9. Neurocomputing (in p
Page 164 and 165: 156 Chapter 10. IEEE TNN 16(4):992-
Page 170 and 171: 162 Chapter 11. EURASIP JASP, 2007
Page 184 and 185: 176 Chapter 12. LNCS 3195:718-725,
Page 194 and 195: 186 Chapter 13. Proc. EUSIPCO 2005
Page 200 and 201: 192 Chapter 14. Proc. ICASSP 2006 S
Page 202 and 203: 194 Chapter 14. Proc. ICASSP 2006 A
Page 204 and 205: 196 Chapter 14. Proc. ICASSP 2006
Page 206 and 207: 198 Chapter 15. Neurocomputing, 69:
Page 208 and 209: 200 Chapter 15. Neurocomputing, 69:
Page 210 and 211:
202 Chapter 15. Neurocomputing, 69:
Page 212 and 213:
Page 214 and 215:
Page 216 and 217:
Page 218 and 219:
Page 220 and 221:
Page 222 and 223:
Page 224 and 225:
Page 226 and 227:
Page 228 and 229:
Page 230 and 231:
Page 232 and 233:
Page 234 and 235:
Page 236 and 237:
Page 238 and 239:
230 Chapter 16. Proc. ICA 2006, pag
Page 240 and 241:
Page 242 and 243:
Page 244 and 245:
Page 246 and 247:
Page 248 and 249:
240 Chapter 17. IEEE SPL 13(2):96-9
Page 250 and 251:
Page 252 and 253:
Page 254 and 255:
246 Chapter 18. Proc. EUSIPCO 2006
Page 256 and 257:
Page 258 and 259:
Page 260 and 261:
252 Chapter 19. LNCS 3195:977-984,
Page 262 and 263:
254 Chapter 19. LNCS 3195:977-984,
Page 264 and 265:
256 Chapter 19. LNCS 3195:977-984,
Page 266 and 267:
258 Chapter 19. LNCS 3195:977-984,
Page 268 and 269:
260 Chapter 19. LNCS 3195:977-984,
Page 270 and 271:
262 Chapter 20. Signal Processing 8
Page 272 and 273:
Page 274 and 275:
Page 276 and 277:
Page 278 and 279:
Page 280 and 281:
Page 282 and 283:
Page 284 and 285:
Page 286 and 287:
Page 288 and 289:
Page 290 and 291:
Page 292 and 293:
Page 294 and 295:
Page 296 and 297:
Page 298 and 299:
Page 300 and 301:
292 Chapter 21. Proc. BIOMED 2005,
Page 302 and 303:
Page 304 and 305:
Page 306 and 307:
298 BIBLIOGRAPHY Barber, C., Dobkin
Page 308 and 309:
300 BIBLIOGRAPHY Georgiev, P. (2001
Page 310 and 311:
302 BIBLIOGRAPHY Keck, I., Theis, F
Page 312 and 313:
304 BIBLIOGRAPHY Schießl, I., Sch
Page 314 and 315:
306 BIBLIOGRAPHY Theis, F. and Inou
show all

Mathematics in Independent Component Analysis

Create successful ePaper yourself

Delete template?

Save as template?