Foreword |
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xiii | |
Preface |
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xv | |
Acknowledgments |
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xxiii | |
Acronyms |
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xxv | |
Introduction |
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1 | (7) |
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8 | (64) |
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8 | (11) |
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8 | (6) |
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14 | (2) |
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16 | (2) |
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18 | (1) |
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18 | (1) |
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Correlation Detection in Single Neurons |
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19 | (6) |
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Correlation in Ensembles of Neurons: Synchrony and Population Coding |
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25 | (6) |
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Correlation is the Basis of Novelty Detection and Learning |
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31 | (7) |
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Correlation in Sensory Systems: Coding, Perception, and Development |
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38 | (9) |
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Correlation in Memory Systems |
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47 | (5) |
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Correlation in Sensorimotor Learning |
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52 | (5) |
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Correlation, Feature Binding, and Attention |
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57 | (2) |
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Correlation and Cortical Map Changes after Peripheral Lesions and Brain Stimulation |
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59 | (8) |
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67 | (5) |
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Correlation in Signal Processing |
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72 | (57) |
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Correlation and Spectrum Analysis |
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73 | (18) |
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73 | (6) |
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79 | (2) |
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Locally Stationary Process |
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81 | (2) |
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83 | (1) |
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Hilbert Spectrum Analysis |
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83 | (2) |
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Higher Order Correlation-Based Bispectra Analysis |
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85 | (2) |
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Higher Order Functions of Time, Frequency, Lag, and Doppler |
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87 | (2) |
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Spectrum Analysis of Random Point Process |
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89 | (2) |
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91 | (4) |
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95 | (4) |
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Recursive Least-Squares Filter |
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99 | (1) |
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100 | (2) |
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Higher Order Correlation-Based Filtering |
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102 | (2) |
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104 | (4) |
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104 | (2) |
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Correlation Filter for Spatial Target Detection |
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106 | (2) |
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Correlation Method for Time-Delay Estimation |
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108 | (2) |
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Correlation-Based Statistical Analysis |
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110 | (12) |
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Principal-Component Analysis |
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110 | (2) |
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112 | (1) |
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Canonical Correlation Analysis |
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113 | (5) |
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Fisher Linear Discriminant Analysis |
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118 | (1) |
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Common Spatial Pattern Analysis |
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119 | (3) |
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122 | (7) |
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Appendix 2A: Eigenanalysis of Autocorrelation Function of Nonstationary Process |
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122 | (1) |
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Appendix 2B: Estimation of Intensity and Correlation Functions of Stationary Random Point Process |
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123 | (2) |
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Appendix 2C: Derivation of Learning Rules with Quasi-Newton Method |
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125 | (4) |
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correlation-based neural learning and machine learning |
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129 | (89) |
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Correlation as a Mathematical Basis for Learning |
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130 | (28) |
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Hebbian and Anti-Hebbian Rules (Revisited) |
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130 | (1) |
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131 | (1) |
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Grossberg's Gated Steepest Descent |
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132 | (1) |
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Competitive Learning Rule |
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133 | (2) |
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135 | (1) |
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136 | (4) |
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Generalizations of PCA Learning |
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140 | (4) |
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144 | (1) |
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Wake---Sleep Learning Rule for Factor Analysis |
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145 | (1) |
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146 | (1) |
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Perceptron Rule and Error-Correcting Learning Rule |
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147 | (2) |
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Differential Hebbian Rule and Temporal Hebbian Learning |
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149 | (3) |
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Temporal Difference and Reinforcement Learning |
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152 | (4) |
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General Correlative Learning and Potential Function |
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156 | (2) |
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Information-Theoretic Learning |
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158 | (24) |
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Mutual Information versus Correlation |
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159 | (1) |
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159 | (1) |
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Hebbian Learning and Maximum Entropy |
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160 | (3) |
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163 | (1) |
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Local Decorrelative Learning |
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164 | (3) |
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167 | (2) |
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Independent-Component Analysis |
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169 | (5) |
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174 | (2) |
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Energy-Efficient Hebbian Learning |
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176 | (2) |
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178 | (4) |
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Correlation-Based Computational Neural Models |
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182 | (36) |
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Correlation Matrix Memory |
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182 | (2) |
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184 | (3) |
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Brain-State-in-a-Box Model |
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187 | (1) |
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187 | (3) |
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190 | (1) |
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Neuronal Synchrony and Binding |
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191 | (2) |
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193 | (1) |
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Modeling Auditory Functions |
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193 | (5) |
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Correlations in the Olfactory System |
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198 | (1) |
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Correlations in the Visual System |
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199 | (1) |
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200 | (5) |
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205 | (2) |
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207 | (1) |
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Appendix 3A: Mathematical Analysis of Hebbian Learning |
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208 | (1) |
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Appendix 3B: Necessity and Convergence of Anti-Hebbian Learning |
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209 | (1) |
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Appendix 3C: Link between Hebbian Rule and Gradient Descent |
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210 | (1) |
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Appendix 3D: Reconstruction Error in Linear and Quadratic PCA |
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211 | (7) |
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Correlation-Based Kernel Learning |
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218 | (31) |
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218 | (3) |
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Kernel PCA and Kernelized GHA |
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221 | (4) |
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Kernel CCA and Kernel ICA |
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225 | (5) |
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230 | (2) |
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Kernel Discriminant Analysis |
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232 | (3) |
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235 | (3) |
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Kernel-Based Correlation Analysis: Generalized Correlation Function and Correntropy |
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238 | (4) |
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242 | (1) |
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243 | (6) |
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Correlative Learning in a Complex-Valued Domain |
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249 | (34) |
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250 | (7) |
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Complex-Valued Extensions of Correlation-Based Learning |
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257 | (20) |
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Complex-Valued Associative Memory |
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257 | (1) |
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Complex-Valued Boltzmann Machine |
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258 | (1) |
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259 | (3) |
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Complex-Valued PCA Learning |
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262 | (7) |
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Complex-Valued ICA Learning |
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269 | (4) |
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Constant-Modulus Algorithm |
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273 | (4) |
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Kernel Methods for Complex-Valued Data |
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277 | (3) |
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Reproducing Kernels in the Complex Domain |
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277 | (2) |
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Complex-Valued Kernel PCA |
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279 | (1) |
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280 | (3) |
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Alopex: A Correlation-Based Learning Paradigm |
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283 | (24) |
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283 | (1) |
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284 | (2) |
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286 | (4) |
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Unnikrishnan and Venugopal's Alopex |
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286 | (1) |
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287 | (1) |
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Improved Version of Alopex-B |
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288 | (1) |
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289 | (1) |
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Other Types of Correlation Mechanisms |
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290 | (1) |
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290 | (5) |
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Monte Carlo Sampling-Based Alopex |
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295 | (12) |
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Sequential Monte Carlo Estimation |
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295 | (3) |
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298 | (4) |
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302 | (1) |
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Appendix 6A: Asymptotic Analysis of Alopex Process |
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303 | (1) |
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Appendix 6B: Asymptotic Convergence Analysis of 2t-Alopex |
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304 | (3) |
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307 | (49) |
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Hebbian Competition as Basis for Cortical Map Reorganization? |
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308 | (12) |
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Learning Neurocompensator: Model-Based Hearing Compensation Strategy |
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320 | (13) |
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320 | (1) |
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Model-Based Hearing Compensation Strategy |
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320 | (6) |
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326 | (4) |
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330 | (3) |
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333 | (1) |
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Online Training of Artificial Neural Networks |
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333 | (7) |
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333 | (1) |
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334 | (1) |
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Online Option Price Prediction |
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334 | (2) |
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Online System Identification |
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336 | (3) |
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339 | (1) |
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Kalman Filtering in Computational Neural Modeling |
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340 | (16) |
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340 | (2) |
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Overview of Kalman Filter in Modeling Brain Functions |
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342 | (4) |
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Kalman Filter for Learning Shape and Motion from Image Sequences |
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346 | (8) |
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General Remarks and Implications |
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354 | (2) |
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356 | (7) |
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Summary: Why Correlation? |
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356 | (3) |
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Hebbian Plasticity and the Correlative Brain |
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357 | (1) |
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Correlation-Based Signal Processing |
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358 | (1) |
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Correlation-Based Machine Learning |
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358 | (1) |
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359 | (4) |
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Generalizing the Correlation Measure |
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359 | (1) |
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Deciphering the Correlative Brain |
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360 | (3) |
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Appendix A Autocorrelation and Cross-Correlation Functions |
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363 | (5) |
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A.1 Autocorrelation Function |
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363 | (1) |
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A.2 Cross-Correlation Function |
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364 | (3) |
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A.3 Derivative Stochastic Processes |
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367 | (1) |
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Appendix B Stochastic Approximation |
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368 | (3) |
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Appendix C Primer on Linear Algebra |
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371 | (7) |
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372 | (3) |
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C.2 Generalized Eigenvalue Problem |
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375 | (1) |
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C.3 SVD and Cholesky Factorization |
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375 | (1) |
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C.4 Gram-Schmidt Orthogonalization |
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376 | (1) |
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C.5 Principal Correlation |
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377 | (1) |
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Appendix D Probability Density and Entropy Estimators |
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378 | (6) |
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D.1 Gram-Charlier Expansion |
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379 | (2) |
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381 | (1) |
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381 | (1) |
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382 | (2) |
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Appendix E Expectation-Maximization Algorithm |
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384 | (57) |
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E.1 Alternating Free-Energy Maximization |
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384 | (1) |
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E.2 Fitting Gaussian Mixture Model |
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385 | (56) |
Index |
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441 | |