Lie Group Machine Learning

Preface......Page 3
Contents......Page 6
Concepts of Lie group machine learning......Page 14
Algebraic model of Lie group machine learning [2, 3, 10]......Page 23
Geometric model of Lie group machine learning [2, 3, 8, 10, 12]......Page 26
Axiom hypothesis of Lie group machine learning [2, 3, 5]......Page 28
Geometric learning algorithm for dynkin graphs in Lie group machine learning [6–8]......Page 39
Linear classifier design of Lie group machine learning......Page 46
Bibliography......Page 50
Basic concepts of partial order and lattice in LML......Page 51
LML subspace orbit generating lattice learning algorithm......Page 68
)......Page 83
Summary......Page 91
Bibliography......Page 92
Problem presentation......Page 93
Design of the symplectic group classifier in Lie group machine learning......Page 100
Symplectic group classifier algorithm in Lie group machine learning......Page 117
Application example......Page 123
Bibliography......Page 131
Problem presentation......Page 134
Construction method of quantum group classifier in Lie group machine learning......Page 135
Application of quantum group learning algorithm in molecular docking......Page 143
Bibliography......Page 155
Problem presentation......Page 157
Fibre bundle model......Page 158
Fibre bundle learning algorithm......Page 163
Summary......Page 172
Bibliography......Page 173
Theory of Lie group machine learning covering algorithm......Page 174
Simply connected covering algorithm of the Lie group......Page 182
Multiply connected covering algorithm of Lie group machine learning......Page 190
Application of the covering algorithm in molecular docking......Page 198
Bibliography......Page 213
Introduction......Page 216
Lie group deep structure learning......Page 218
Lie group layered learning algorithm......Page 229
Lie group deep structure heuristic learning......Page 236
Summary......Page 240
Bibliography......Page 241
Introduction......Page 244
Semi-supervised learning model based on the Lie group......Page 253
Semi-supervised learning algorithm based on a linear Lie group......Page 258
Semi-supervised learning algorithm based on the parameter Lie group......Page 268
Summary......Page 278
Bibliography......Page 279
Matrix group learning algorithm......Page 283
Gaussian distribution on the Lie group......Page 292
Calculation of the Lie group inner mean value......Page 296
Lie-mean learning algorithm......Page 299
Nuclear learning algorithm of the Lie group......Page 306
Case application......Page 314
Summary......Page 322
Bibliography......Page 323
Data reduction based on tensor methods......Page 327
Data reduction model based on tensor fields......Page 331
The learning model and algorithm based on the tensor field......Page 340
Summary......Page 352
Bibliography......Page 353
Longitudinal space learning model based on frame bundle......Page 355
Longitudinal space connection learning model based on frame bundle......Page 358
Horizontal space connection learning model based on frame bundle......Page 360
Related applications......Page 361
Bibliography......Page 363
Concept and definition of spectral estimation......Page 364
Relevant theoretical basis......Page 366
Synchronous spectrum estimation learning algorithm......Page 372
The comparison principle of image feature manifolds......Page 378
Spectral estimation learning algorithm for topological invariance of image feature manifolds......Page 383
Summary......Page 387
Bibliography......Page 388
Basic concept......Page 390
KNN algorithm based on the Finsler metric......Page 391
Geometric learning algorithm based on the Finsler metric......Page 397
Bibliography......Page 405
Boundary learning algorithm......Page 407
Edge division method based on homological algebra......Page 410
Design and analysis of homology edge learning algorithm......Page 418
Bibliography......Page 419
Introduction......Page 421
Category representation of learning expressions......Page 431
Mapping mechanism for learning expressions......Page 439
Classifier design for learning expression mapping mechanism......Page 447
Example analysis......Page 457
Bibliography......Page 468
Introduction......Page 470
Core scientific problems......Page 474
Lie group cognitive theory framework......Page 476
Neuromorphic synergy learning theoretical framework......Page 480
Design of a neuromorphic synergy learning verification platform......Page 487
Bibliography......Page 488
Topological group......Page 490
Concept of diferential geometry......Page 493
Manifold learning algorithm......Page 495
Basic concept and nature of symplectic group......Page 499
Basic concepts of quantum groups......Page 504
Fibre bundle......Page 511
Index......Page 517