Pages G., Vorono' tesselation, Space quantization algorithms and numerical integraiion, Proc. ESANN'93, M.Vedeysen Ed., Editions D Facto, Bruxelles, 221-228, 1993. Home/Search Document Not in Database Summary Related Articles Check |
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Kohonen Maps Versus Vector Quantization for Data Analysis - de Bodt, Verleysen, Cottrell (1997) (Correct)
....points Xt, X2, Xv converges (in law) to the initial probability P. The rate of convergence can also be characterised. Of course, when speaking about vector quantization, the n centroids Y2, Yn cannot be considered as independent drawings according to f(x) and this result cannot be used. In [14], the Kohonen algorithm terminated with 0 neighbour at the end of learning is studied. According to the comment at the end of section 3, the convergence of this algorithm is thus equivalent to the convergence of a classical VQ technique as the competitive learning . The result in [14] shows that ....
....be used. In [14] the Kohonen algorithm terminated with 0 neighbour at the end of learning is studied. According to the comment at the end of section 3, the convergence of this algorithm is thus equivalent to the convergence of a classical VQ technique as the competitive learning . The result in [14] shows that the centroids after VQ are a good discrete skeleton for reconstructing the initial density f(x) provided that each centroid is weighted by the probability (estimated by the frequency) of its Voronoi region. In other terms, ifyt, y2, y are the centroids after learning, and Ct, ....
[Article contains additional citation context not shown here]
Pages G., Vorono' tesselation, Space quantization algorithms and numerical integraiion, Proc. ESANN'93, M.Vedeysen Ed., Editions D Facto, Bruxelles, 221-228, 1993.
Kohonen Maps Versus Vector Quantization for Data Analysis - de Bodt, Verleysen, Cottrell (1997) (Correct)
....2 , X N converges (in law) to the initial probability P. The rate of convergence can also be characterised. Of course, when speaking about vector quantization, the n centroids y 1 , y 2 , y n cannot be considered as independent drawings according to f(x) and this result cannot be used. In [14], the Kohonen algorithm terminated with 0 neighbour at the end of learning is studied. According to the comment at the end of section 3, the convergence of this algorithm is thus equivalent to the convergence of a classical VQ technique as the competitive learning . The result in [14] shows that ....
....be used. In [14] the Kohonen algorithm terminated with 0 neighbour at the end of learning is studied. According to the comment at the end of section 3, the convergence of this algorithm is thus equivalent to the convergence of a classical VQ technique as the competitive learning . The result in [14] shows that the centroids after VQ are a good discrete skeleton for reconstructing the initial density f(x) provided that each centroid is weighted by the probability (estimated by the frequency) of its Voronoi region. In other terms, if y 1 , y 2 , y n are the centroids after learning, and C ....
[Article contains additional citation context not shown here]
Pags G., Vorono tesselation, Space quantization algorithms and numerical integration, Proc. ESANN'93, M.Verleysen Ed., Editions D Facto, Bruxelles, 221-228, 1993.
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