C++ Neural Networks and Fuzzy Logic
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C neural networks and fuzzy logic
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- Global minimum
- Heteroassociative
- Input layer
- LMS rule
- Long−term memory (LTM)
- Noise
- Outstar
- Short−term memory (STM)
- C++ Neural Networks and Fuzzy Logic by Valluru B. Rao MTBooks, IDG Books Worldwide, Inc. ISBN
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G Gain Sometimes a numerical factor to enhance the activation. Sometimes a connection for the same purpose.
A rule used in training of networks such as backpropagation training where hidden layer weights are modified with backpropagated error.
A point where the value of a function is no greater than the value at any other point in the domain of the function.
The number of places in which two binary vectors differ from each other. Hebbian learning A learning algorithm in which Hebb’s rule is used. The change in connection weight between two neurons is taken as a constant times the product of their outputs.
Making an association between two distinct patterns or objects. Hidden layer An array of neurons positioned in between the input and output layers. Hopfield network A single layer, fully connected, autoassociative neural network. I Inhibition The attempt by one neuron to diminish the chances of firing by another neuron. Input layer An array of neurons to which an external input or signal is presented. Instar C++ Neural Networks and Fuzzy Logic:Preface Glossary 425
A neuron that has no connections going from it to other neurons. L Lateral connection A connection between two neurons that belong to the same layer. Layer An array of neurons positioned similarly in a network for its operation. Learning The process of finding an appropriate set of connection weights to achieve the goal of the network operation.
Two subsets of a linear set having a linear barrier (hyperplane) between the two of them. LMS rule Least mean squared error rule, with the aim of minimizing the average of the squared error. Same as the Delta rule.
A point where the value of the function is no greater than the value at any other point in its neighborhood.
Encoded information that is retained for an extended period. Lyapunov function A function that is bounded below and represents the state of a system that decreases with every change in the state of the system.
A neural network in which the input layer has units that are Adalines. It is a multiple−Adaline. Mapping A correspondence between elements of two sets. N Neural network A collection of processing elements arranged in layers, and a collection of connection edges between pairs of neurons. Input is received at one layer, and output is produced at the same or at a different layer.
Noise Distortion of an input. Nonlinear optimization Finding the best solution for a problem that has a nonlinear function in its objective or in a constraint. O On center off surround Assignment of excitatory weights to connections to nearby neurons and inhibitory weights to connections to distant neurons.
Vectors whose dot product is 0. C++ Neural Networks and Fuzzy Logic:Preface Glossary
426 Outstar A neuron that has no incoming connections. P Perceptron A neural network for linear pattern matching. Plasticity Ability to be stimulated by new inputs and learn new mappings or modify existing ones. R Resonance The responsiveness of two neurons in different layers in categorizing an input. An equilibrium in two directions.
A condition of limitation on the frequency with which a neuron can fire. Self−organization A process of partitioning the output layer neurons to correspond to individual patterns or categories, also called unsupervised learning or clustering.
The storage of information that does not endure long after removal of the corresponding input. Simulated annealing An algorithm by which changes are made to decrease energy or temperature or cost. Stability Convergence of a network operation to a steady−state solution. Supervised learning A learning process in which the exemplar set consists of pairs of inputs and desired outputs. T Threshold value A value used to compare the activation of a neuron to determine if the neuron fires or not. Sometimes a bias value is added to the activation of a neuron to allow the threshold value to be zero in determining the neuron’s output. Training The process of helping in a neural network to learn either by providing input/output stimuli (supervised training) or by providing input stimuli (unsupervised training), and allowing weight change updates to occur. U Unsupervised learning Learning in the absence of external information on outputs, also called self−organization or clustering. C++ Neural Networks and Fuzzy Logic:Preface Glossary 427
V Vigilance parameter A parameter used in Adaptive Resonance Theory. It is used to selectively prevent the activation of a subsystem in the network.
A number associated with a neuron or with a connection between two neurons, which is used in aggregating the outputs to determine the activation of a neuron. Table of Contents Copyright © IDG Books Worldwide, Inc. C++ Neural Networks and Fuzzy Logic:Preface Glossary
428 C++ Neural Networks and Fuzzy Logic by Valluru B. Rao MTBooks, IDG Books Worldwide, Inc. ISBN: 1558515526 Pub Date: 06/01/95 Table of Contents Index A ABAM see Adaptive Bi−directional Associative Memory abstract class, 138 abstract data type, 22 accumulation−distribution, 402, 404, activation, 3, 18, 89 zero, 182 Adaline, 81, 82, 102, 103, 112 adaptation, 77, 120 Adaptive Bi−directional Associative Memory, 181, 212 Competitive, 212 Differential Competitive, 212 Hebbian, 212 adaptive filters, 120 adaptive linear element, 102 adaptive models, 120 adaptive parameters, 373 adaptive resonance, 118 Adaptive Resonance Theory I, 104, 107, 108, 115, 117, 243 algorithm for calculations, 246 equations for, 246 F1 layer calculations, 247 F2 layer calculations, 247 modifying connection weights, 248 Top−down inputs, 247 two−thirds rule, 244, 245 Adaptive Resonance Theory II, 248 Adaptive Resonance Theory III, 248 additive composition method, 506 advancing issues, 387 aggregation, 82, 87, 98 Ahmadian, 513 Aiken, 405 algorithm, 1 backpropagation, 7, 103, 271, 373, 375 constructive, 121 data clustering, 245 encoding, 94, 96 C++ Neural Networks and Fuzzy Logic:Preface Index 429
learning algorithm , 61, 79, 102, 118 adaptive steepest descent, 410 alpha, 273, 274, 330, 372, 373, 384 alphabet classifier system, 320 Amari, 104 analog, 73, 74, 322 signal, 8 AND operation , 64 Anderson, 105 annealing process, 430 schedule 113 simulated annealing, 113, 114 Anzai, 456, 472 application, 102, 374, 511 nature of , 74 approximation, 109 architecture, 7, 81, 120, 373 Artificial Intelligence , 6, 34 artificial neural network , 1 ART1 see Adaptive Resonance Theory I ART2 see Adaptive Resonance Theory II ART3 see Adaptive Resonance Theory III artneuron class, 249 ASCII, 305, 306, 307, 329 graphic characters, 306 assocpair class in BAM network, 186 association, 218 asynchronously , 1, 14 asynchronous update, 13, 62 attentional subsystem, 107, 243 Augusteijn, 512 autoassociation , 7, 8, 82,, 92, 102, 180 autoassociative network, 7, 64, 97, 375 average winner distance, 296 Azoff, 410
backpropagated errors, 144 Backpropagation, 10, 103, 104, 120, 123, 302, 325, 329, 374 algorithm, 7, 103, 271, 373, 375 beta, 330 calculating error, 396 calculations, 128, 130 changing beta while training, 337 choosing middle layer size, 372 convergence, 372 momentum term, 330 C++ Neural Networks and Fuzzy Logic:Preface Index 430
noise factor, 336 self−supervised, 375 simulator, 134, 173, 337, 375, 377, 396 training and testing, 396 training law, 333 variations of , 373 Baer, 516 BAM see Bi−directional Associative Memory bar chart, 403, 404 features, 513 Barron’s, 377, 378, 388 base class , 25, 28, 138 beta, 136, 337, 372, 373, 384 bias, 16, 77, 125, 128, 378 Bi−directional Associative Memory, 81, 92, 104, 115, 117, 179, 185, 215 connection weight matrix, 212 continuous, 211 inputs, 180 network, 104 outputs, 180 training, 181 Unipolar Binary, 212 bin, 325
binary , 8, 15, 51, 65, 73, 74, 104 input pattern, 51, 98 patterns 11, 97 string, 16, 62 binary to bipolar mapping, 62, 63 binding
dynamic binding , 24, 139 late binding , 24 static binding, 139 bipolar, 15, 17, 104 mapping, 97 string, 16, 62, 180 bit pattern, 13 Blending problem, 418 block averages, 393 bmneuron class, 186 Boltzmann distribution, 113 Boltzmann machine, 92, 112, 113, 118, 419, 512 Booch, 21 boolean logic, 50 bottom−up connection weight, 248 connections, 107, 244 Box−Jenkins methodology, 406 Brain−State−in−a−Box, 81, 82, 105 breadth, 387, 389 Buckles, 484 C++ Neural Networks and Fuzzy Logic:Preface Index 431
buy/sell signals, 409, 410 C cache, 137 Cader, 406 CAM see Content−Addressable−Memory Carpenter, 92, 107, 117, 243, 269, 517 car navigation, 374 cartesian product, 479 cascade−correlation, 512 Cash Register game, 3, 65 categorization of inputs, 261 category, 37 Cauchy distribution, 113 Cauchy machine, 112, 113, 419 cells
complex cells, 106 simple cells, 106 center of area method, 504 centroid, 507, 508 character recognition, 305 characters alphabetic, 305 ASCII, 306, 307 garbled, 322 graphic, 306, 307 handwritten, 320 Chawla, 514 Chiang, 513 cin, 25, 58, 71 clamping probabilities, 114 Clinton, Hillary, 405 C language, 21 class, 22 abstract class, 138 base class, 25, 28, 138, 139 derived class, 23, 25, 26, 144 friend class, 23 hierarchy, 27, 138, 139 input_layer class, 138 iostream class, 71 network class, 53, 66 output_layer class, 138 parent class, 26 classification, 322 C layer, 106 codebook vectors, 116 Cohen, 212 Collard, 405 C++ Neural Networks and Fuzzy Logic:Preface Index 432
column vector, 97 combinatorial problem, 422 comparison layer, 244 competition, 9, 94, 97 competitive learning, 243 compilers C++ compilers, 27 compilation error messages, 27 complement, 33, 185, 201, 202 complex cells, 106 composition max−min, 220 compressor, 375 Computer Science, 34 conditional fuzzy mean, 491 variance, 491 conjugate gradient methods, 373 conjunction operator, 505 connections, 2, 93, 102 bottom−up, 107 excitatory, 272 feedback , 82 inhibitory , 272 lateral, 93, 97, 107, 272, 276 recurrent, 82, 107, 179 top−down, 107 connection weight matrix, 220 connection weights, 89, 98 conscience factor, 302 constraints, 417 constructor, 23, 28, 55, 66 default constructor, 23 Consumer Price Index, 387 Content−Addressable−Memory, 5 continuous Bi−directional Associative Memory, 211 models, 98 convergence, 78, 79, 96, 118, 119, 132, 323, 372, 373, 375 cooperation, 9, 94 correlation matrix, 9, 63 correlation−product encoding, 220 cost function, 124, 373 Cottrell, 374 counterpropagation, 106 network, 92, 93, 302 cout, 25, 58 C++, 21
classes, 138 code, 36
comments, 58 C++ Neural Networks and Fuzzy Logic:Preface Index 433
compilers, 27 implementation, 185 crisp, 31, 73, 74 data sets, 475 rules, 48, 217 values, 50 cube, 84, 87, 89, 90 cum_deltas, 331 cycle, 78, 125 learning cycle, 103 cyclic information, 380
data biasing, 378 data hiding, 21, 22 data clustering, 109, 245 data completion, 102 data compression, 102, 302 Deboeck, 406 Davalo, 457 de la Maza, 410 Decision support systems, 75 declining issues, 387 decompressor, 375 decorrelation, 384 default
constructor, 23, 66 destructor, 23 defuzzification, 504, 506 degenerate tour, 424 degree of certainty, 31 membership, 32, 477 degrees of freedom, 383 delete, 24, 144 delta rule, 110−113 derived class, 23, 25, 26, 144 descendant, 139, 143 DeSieno, 302 destructor, 23, 24 digital signal processing boards, 325 dimensionality, 381, 382, 384 directed graph, 65 discount rate, 35 discretization of a character, 98 discrete models, 98 discriminator, 517 disjunction operator, 506 display_input_char function, 308 C++ Neural Networks and Fuzzy Logic:Preface Index 434
display_winner_weights function, 308 distance
Euclidean, 13 Hamming, 13 DJIA see Dow Jones Industrial Average DOF see degrees of freedom domains, 479, 484 dot product, 11, 12, 51, 64, 65 Dow Jones Industrial Average, 378, 386 dual confirmation trading system, 408 dynamic allocation of memory, 24 dynamic binding, 24, 139 dynamics adaptive, 74 nonadaptive, 74
EMA see exponential moving average encapsulate, 29 encapsulation, 21, 22 encode, 375 encoding, 7, 81, 220 algorithm, 94, 96 correlation−product, 220 phase, 94 thermometer, 380 time, 120 energy, 422 function, 119 level, 113, 422 surface, 177 Engineering, 34 epoch, 125 Ercal, 514 error signal, 103 error surface, 113 error tolerance, 136 Euclidean distance, 13, 280, 296 excitation, 94, 98, 276, 303 excitatory connections, 244, 272 exclusive or, 83 exemplar, 181−183, 201 class in BAM network, 186 pairs, 135, 177 patterns, 135, 177 exemplar pattern, 16, 64 exemplars, 64, 65, 74, 75, 115, 181 Expert systems, 48, 75, 217 exponential moving average, 399 C++ Neural Networks and Fuzzy Logic:Preface Index 435
extended (database) model, 486 extended−delta−bar−delta, 406 F factorial, 420 FAM see Fuzzy Associative Memories Fast Fourier Transform, 374 fault tolerance, 374 feature detector, 328 feature extraction, 7, 513 Federal Reserve, 388, 388 feedback, 4, 5, 93 connections, 123, 179 feed forward Backpropagation, 81, 92, 112, 115, 123, 384, network , 145, 406, 409, 511, architecture, 124, layout, 124, network, 10 operation, 185 type, 2
field, 82 filter, 322 financial forecasting, 377 fire, 3, 71, 87, 89 first derivative, 380 fiscal policy, 36 fit values, 32, 217 fit vector, 32, 217, 221 floating point calculations, 519 compilation for, 519 F1 layer, 245 calculations, 247 Fogel, 76, 77 forecasting, 102 model, 378 T−Bill yields, 405 T−Note yields, 405 forward, 93, 104 Fourier transform, 380 Frank, 515 Freeman, 246, 248 frequency component, 380 signature, 374 frequency spikes, 380 friend class, 23, 66, 68 F2 layer, 245 calculations, 247 C++ Neural Networks and Fuzzy Logic:Preface Index
436 Fukushima, 92, 106 function
constructor function, 28 energy function, 119 evaluation, 109 fuzzy step function, 101 hyperbolic tangent function, 100 linear function, 99, 102 logistic function, 86, 100 Lyapunov function, 118, 119 member function, 28, 308 objective, 417 overloading, 25, 139 ramp function, 99, 101, 102 reference function, 493 sigmoid
function, 99, 100, 126, 129, 133, 164, 177, 395 logistic function, 100 step function, 99, 101 threshold function, 52, 95, 99, 101 XOR function, 83−85, 87 fuzzifier, 35, 36, 47 program, 50 fuzziness, 48, 50 fuzzy adaptive system, 49 fuzzy ARTMAP, 517 fuzzy association, 217 Fuzzy Associative Memories, 49, 50, 81, 92, 104, 115, 117, 217, 218, 473 encoding, 219, 220 Fuzzy Cognitive Map, 48, 49 fuzzy conditional expectations, 490, 509 fuzzy control , 497, 509 system, 47, 48, 473 fuzzy controller, 47 fuzzy database, 473, 475, 509 fuzzy expected value, 490 fuzzy equivalence relation, 481 fuzzy events, 488, 509 conditional probability of, 491 probability of , 490 fuzzy inputs, 47, 73 fuzzy logic, 31, 34, 50, 473 controller, 473, 497, 509 fuzzy matrix, 217 fuzzy means, 488, 490, 509 fuzzy numbers, 493, 496 triangular, 496 fuzzy OR method, 505 fuzzy outputs, 47, 74 fuzzy quantification, 488 fuzzy queries, 483, 488 C++ Neural Networks and Fuzzy Logic:Preface Index 437
fuzzy relations, 479, 509 matrix representation, 479 fuzzy rule base, 502−504 fuzzy rules, 47, 50 fuzzy set, 32, 50, 218, 477, 488 complement, 218 height, 218 normal, 218 operations, 32, 217 fuzzy systems, 50, 217 fuzzy−valued, 34 fuzzy values, 477 fuzzy variances, 488, 490, 509 fzneuron class, 221 G Gader, 513 gain , 107 constant, 273 parameter, 429, 467 gain control, 243, 248 unit, 244 Gallant, 117 Ganesh, 514 Gaussian density function, 458, 459, 524 generalization, 121, 320, 382 ability, 121, 336 generalized delta rule, 112, 176 genetic algorithms, 75, 76, 385 global minimum, 113, 177 variable, 28 Glover, 471 gradient, 112, 113 grandmother cells, 117 gray scale, 305, 306, 322, 374 grid, 214, 305 Grossberg, 19, 92, 93, 107, 117, 243, 269 Grossberg layer, 9, 19, 82, 92, 106, 302 H Hamming distance, 13, 201, 202 handwriting analysis, 98 handwriting recognition, 102 handwritten characters, 92 heap, 144 Hebb, 110 Hebbian
C++ Neural Networks and Fuzzy Logic:Preface Index
438 conditioned learning, 302 learning, 105, 110 Hebb’s rule, 110, 111 Hecht−Nielsen, 93, 106, 302 Herrick Payoff Index, 401 heteroassociation, 7, 8, 82, 92, 102, 104, 180, 181 heteroassociative network, 7, 97 hidden layer, 2, 4, 75, 86, 89 hierarchical neural network, 407 hierarchies of classes, 27, 29 Hinton, 114 Hoff, 102, 112 holographic neural network, 408 Honig, 515 Hopfield, 422, 427, 429 memory, 73, 115, 117, 181 Hopfield network, 9, 11−14, 16, 19, 51, 79, 81, 82, 93, 111, 119, 120, 181, 472 Hotelling transform, 384 Housing Starts, 387 hybrid models, 75 hyperbolic tangent function, 429 hypercube, 218 unit, 218 hyperplane, 84 hypersphere, 273
image, 106, 302 compression, 374 processing, 98, 102 five−way transform, 516 recognition, 375 resolution, 322 implementation of functions, 67 ineuron class, 66 inference engine, 47 inheritance, 21, 25, 26, 138 multiple inheritance, 26 inhibition, 9, 94, 98 global, 428, 456 lateral, 272, 276 inhibitory connection, 272 initialization of bottom−up weights, 250 parameters, 246 top−down weights, 250 weights, 94 inline, 165 C++ Neural Networks and Fuzzy Logic:Preface Index
439 input, 98 binary input, 98 bipolar input, 98 layer, 2, 10 nature of , 73 number of , 74 patterns, 51, 65 signals, 65 space, 124 vector, 53, 71, 272, 112 input/output, 71 inqreset function, 251 instar, 93 interactions, 94 interconnections, 7 interest rate, 387 internal activation , 3 intersection, 32, 33 inverse mapping, 62, 182 Investor’s Business Daily, 388 iostream, 54, 71 istream, 58 iterative process, 78
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