Kohonen's algorithm for the numerical parametrisation of manifolds
T. Kohonen has described an algorithm for fitting a k-dimensional grid of points to a set of points taken from a k-manifold in R n , for k⩽ n. The algorithm is inspired by a neural model and bears some of the marks of its ancestry. In this paper we show that if the process converges, it converges to...
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| Veröffentlicht in: | Pattern recognition letters 1990, Vol.11 (5), p.313-319 |
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| container_title | Pattern recognition letters |
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| creator | Alder, Michael Togneri, Roberto Lai, Edmund Attikiouzel, Yianni |
| description | T. Kohonen has described an algorithm for fitting a
k-dimensional grid of points to a set of points taken from a
k-manifold in
R
n
, for
k⩽
n. The algorithm is inspired by a neural model and bears some of the marks of its ancestry. In this paper we show that if the process converges, it converges to a locally 1-1 mapping of the grid onto the manifold. Hitherto this result has only been proved for the case where
k=1. |
| doi_str_mv | 10.1016/0167-8655(90)90040-9 |
| format | Article |
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k-dimensional grid of points to a set of points taken from a
k-manifold in
R
n
, for
k⩽
n. The algorithm is inspired by a neural model and bears some of the marks of its ancestry. In this paper we show that if the process converges, it converges to a locally 1-1 mapping of the grid onto the manifold. Hitherto this result has only been proved for the case where
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k-dimensional grid of points to a set of points taken from a
k-manifold in
R
n
, for
k⩽
n. The algorithm is inspired by a neural model and bears some of the marks of its ancestry. In this paper we show that if the process converges, it converges to a locally 1-1 mapping of the grid onto the manifold. Hitherto this result has only been proved for the case where
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k-dimensional grid of points to a set of points taken from a
k-manifold in
R
n
, for
k⩽
n. The algorithm is inspired by a neural model and bears some of the marks of its ancestry. In this paper we show that if the process converges, it converges to a locally 1-1 mapping of the grid onto the manifold. Hitherto this result has only been proved for the case where
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| fulltext | fulltext |
| identifier | ISSN: 0167-8655 |
| ispartof | Pattern recognition letters, 1990, Vol.11 (5), p.313-319 |
| issn | 0167-8655 1872-7344 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_25699010 |
| source | ScienceDirect Journals (5 years ago - present) |
| subjects | Exact sciences and technology Mathematical methods in physics Numerical approximation and analysis Physics |
| title | Kohonen's algorithm for the numerical parametrisation of manifolds |
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