Convergence and Ordering of Kohonen's Batch mAP
Abstract
The convergence and ordering of Kohonen's batch-mode self-organizing map with Heskes and Kappen's (1993) winner selection are proved. Selim and Ismail's (1984) objective function for k-means clustering is generalized in the convergence proof of the self-organizing map. It is shown that when the neighborhood relation is doubly decreasing, order in the map is preserved. An unordered map becomes ordered when a degenerate state of ordering is entered, where the number of distinct winners is one or two. One strategy to enter this state is to run the algorithm with a broad neighborhood relation.
Cite
Text
Cheng. "Convergence and Ordering of Kohonen's Batch mAP." Neural Computation, 1997. doi:10.1162/NECO.1997.9.8.1667Markdown
[Cheng. "Convergence and Ordering of Kohonen's Batch mAP." Neural Computation, 1997.](https://mlanthology.org/neco/1997/cheng1997neco-convergence/) doi:10.1162/NECO.1997.9.8.1667BibTeX
@article{cheng1997neco-convergence,
title = {{Convergence and Ordering of Kohonen's Batch mAP}},
author = {Cheng, Yizong},
journal = {Neural Computation},
year = {1997},
pages = {1667-1676},
doi = {10.1162/NECO.1997.9.8.1667},
volume = {9},
url = {https://mlanthology.org/neco/1997/cheng1997neco-convergence/}
}