unh_cmac.ps

一个老外写的CMAC Neural Network源代码和说明

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(UNH_CMAC Version 2.1)1880 613 MS
(The University of New Hampshire Implementation of the)1117 731 MS
(Cerebellar Model Arithmetic Computer - CMAC)1339 849 MS
(August 31, 1994)2065 1085 MS
(\(last modified July, 1996\))1851 1203 MS
(W. Thomas Miller  and )1540 1439 MS
(Filson H. )2627 1439 MS
(Glanz)3078 1439 MS
(Robotics Laboratory)1958 1557 MS
(University of New Hampshire)1754 1675 MS
(Durham, New Hampshire 03824)1698 1793 MS
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(THE ALBUS CMAC)496 2054 MS
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(In this section we review the basic operating principles of the CMAC neural network as)646 2211 MS
(proposed by )496 2317 MS
(Albus  [2,4-7]. We then present a mathematical description of the conventional)1027 2317 MS
(CMAC in a form intended to facilitate software implementation. The notation used is somewhat)496 2423 MS
(different than in the original )496 2529 MS
(Albus papers, but the set of equations presented is numerically)1635 2529 MS
(equivalent to the original )496 2635 MS
(Albus algorithm.)1519 2635 MS
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(General Operation of the )496 2844 MS
(Albus CMAC)1603 2844 MS
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(The operation of the )646 3001 MS
(Albus CMAC [2,4-7,11] can most easily be described in terms of a)1498 3001 MS
(large set of overlapping, )496 3107 MS
(multi-dimensional receptive fields with finite boundaries. Any input)1506 3107 MS
(vector falls within the range of some of the local receptive fields \(the excited receptive fields\),)496 3213 MS
(and falls outside of the range of most of the receptive fields. The response of the CMAC neural)496 3319 MS
(network to a given input is the average of the responses of the receptive fields excited by that)496 3425 MS
(input, and is not affected by the other receptive fields. Similarly, neural network training for a)496 3531 MS
(given input vector affects the adjustable parameters of the excited receptive fields, but does not)496 3637 MS
(affect the parameters of the remaining majority of receptive fields.)496 3743 MS
(The organization of the receptive fields of a typical )646 3899 MS
(Albus CMAC neural network with a two-)2720 3899 MS
(dimensional input space is as follows. The total collection of receptive fields is divided into C)496 4005 MS
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(subsets, referred to in this document as \223layers\224 \(the layers represent parallel N-dimensional)496 4111 MS
(hyperspaces for a network with N inputs\). The receptive fields in each of the layers have)496 4217 MS
(rectangular boundaries and are organized so as to span the input space without overlap. Any)496 4323 MS
(input vector excites one receptive field from each layer, for a total of C exited receptive fields for)496 4429 MS
(any input. Each of the layers of receptive fields is identical in organization, but each layer is)496 4535 MS
(offset relative to the others in the input )496 4641 MS
(hyperspace. The width of the receptive fields produces)2086 4641 MS
(input generalization, while the offset of the adjacent layers of receptive fields produces input)496 4747 MS
(quantization. The ratio of the width of each receptive field \(input generalization\) to the offset)496 4853 MS
(between adjacent layers of receptive fields \(input )496 4959 MS
(quantization\) must be equal to C for all)2511 4959 MS
(dimensions of the input space. The integer parameter C is referred to as the )496 5065 MS
(generalization)3619 5065 MS
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(This organization of the receptive fields guarantees that only a fixed number, C, of receptive)646 5327 MS
(fields is excited by any input. However, the total number of receptive fields required to span the)496 5433 MS
(input space can still be large for many practical problems. On the other hand, it is unlikely that)496 5539 MS
(the entire input state space of a large system would be visited in solving a specific problem.)496 5645 MS
(Thus it is not necessary to store unique information for each receptive field. Following this logic,)496 5751 MS
(most implementations of the )496 5857 MS
(Albus CMAC include some form of pseudo-random hashing, so)1675 5857 MS
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(that only information about receptive fields that have been excited during previous training is)496 603 MS
(actually stored.)496 709 MS
(Each receptive field in the )646 865 MS
(Albus CMAC is assumed to be an on-off type of entity. If a)1725 865 MS
(receptive field is excited, its response is equal to the magnitude of a single adjustable weight)496 971 MS
(specific to that receptive field. If a receptive field is not excited, its response is zero. The CMAC)496 1077 MS
(output is thus the average of the adjustable weights of the excited receptive fields. If nearby)496 1183 MS
(points in the input space excite the same receptive fields, they produce the same output value.)496 1289 MS
(The output only changes when the input crosses one of the receptive field boundaries. The)496 1395 MS
(Albus CMAC neural network thus produces piece-wise constant outputs.)496 1501 MS
(The implementation of the )646 1657 MS
(Albus CMAC logically proceeds as follows:)1738 1657 MS
(1. Identify the C receptive fields excited by the input.)646 1813 MS
(2. Find the C adjustable weights for those receptive fields in a pool of stored weights.)646 1969 MS
(3. Compute the average of the C adjustable weights.)646 2125 MS
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(The )496 2334 MS
(Albus CMAC Computation)684 2334 MS
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(Consider a classic )646 2491 MS
(Albus CMAC neural network with a real valued input vector)1417 2491 MS
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(in an N-dimensional input space. Assume that the generalization parameter \(the number of)496 2830 MS
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