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The group representation network: a general approach to invariant pattern classification

The group representation network: a general approach to invariant pattern classification
The group representation network: a general approach to invariant pattern classification
This chapter presents a highly general model for the group invariance problem. This model is called the “group representation network” (GRN). In principle, a GRN can be constructed for any linear transformation invariance problem, though to date, the supporting theory has only been developed for the case of a finite (or compact) invariance group. This universality makes the GRN particularly useful for problems for which there exist no established methods for producing invariant pattern classifiers—that is, those for which the invariance group is unusual. There are two principal ways of solving the invariant pattern classification problem: (1) to extract a set of features from the inputs that are invariant under the given group and (2) to process these features using some standard pattern classifier. Examples of this method include Fourier analysis or integral transform-based methods and the use of moment invariants. The second method is to build an adaptive invariant—that is, a function that is parameterized (and can thus be adapted to learn a desired mapping) and remains invariant under the prescribed transformations for all values of these parameters. The second method includes a number of neural network-type approaches, such as higher-order networks.
1076-5670
309-408
Wood, Jeffrey
ad113153-cf1f-4184-ad4d-27ede718ac22
Wood, Jeffrey
ad113153-cf1f-4184-ad4d-27ede718ac22

Wood, Jeffrey (1999) The group representation network: a general approach to invariant pattern classification. Advances in Imaging and Electron Physics, 107, 309-408. (doi:10.1016/S1076-5670(08)70189-7).

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Abstract

This chapter presents a highly general model for the group invariance problem. This model is called the “group representation network” (GRN). In principle, a GRN can be constructed for any linear transformation invariance problem, though to date, the supporting theory has only been developed for the case of a finite (or compact) invariance group. This universality makes the GRN particularly useful for problems for which there exist no established methods for producing invariant pattern classifiers—that is, those for which the invariance group is unusual. There are two principal ways of solving the invariant pattern classification problem: (1) to extract a set of features from the inputs that are invariant under the given group and (2) to process these features using some standard pattern classifier. Examples of this method include Fourier analysis or integral transform-based methods and the use of moment invariants. The second method is to build an adaptive invariant—that is, a function that is parameterized (and can thus be adapted to learn a desired mapping) and remains invariant under the prescribed transformations for all values of these parameters. The second method includes a number of neural network-type approaches, such as higher-order networks.

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Published date: 1999
Organisations: Electronics & Computer Science

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Local EPrints ID: 250468
URI: http://eprints.soton.ac.uk/id/eprint/250468
ISSN: 1076-5670
PURE UUID: 256e09b5-689b-487b-8dfc-2b2ae6f409fe

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Date deposited: 01 Jun 1999
Last modified: 16 Jul 2019 23:12

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Author: Jeffrey Wood

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