Concerning the differentiability of the energy function in vector quantization algorithms - IMT Mines Alès Accéder directement au contenu
Article Dans Une Revue Neural Networks Année : 2007

Concerning the differentiability of the energy function in vector quantization algorithms

Résumé

The adaptation rule of Vector Quantization algorithms, and consequently the convergence of the generated sequence, depends on the existence and properties of a function called the energy function, defined on a topological manifold. Our aim is to investigate the conditions of existence of such a function for a class of algorithms including the well-known ‘K-means’ and ‘Self-Organizing Map’ algorithms. The results presented here extend several previous studies and show that the energy function is not always a potential but at least the uniform limit of a series of potential functions which we call a pseudo-potential. It also shows that a large number of existing vector quantization algorithms developed by the Artificial Neural Networks community fall into this class. The framework we define opens the way to studying the convergence of all the corresponding adaptation rules at once, and a theorem gives promising insights in that direction.

Dates et versions

hal-04663117 , version 1 (26-07-2024)

Identifiants

Citer

Dominique Lepetz, Max Némoz-Gaillard, Michaël Aupetit. Concerning the differentiability of the energy function in vector quantization algorithms. Neural Networks, 2007, 20 (5), pp.621-630. ⟨10.1016/j.neunet.2006.11.006⟩. ⟨hal-04663117⟩

Collections

CEA EM-ALES DAM
0 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More