Theoretical aspects of the SOM algorithm

The SOM algorithm is very astonishing. On the one hand, it is very simple t o write down and to simulate, its practical properties are clear and easy t o observe. However, on the other hand, its theoretical properties still rem ain without proof in the general case, despite the tremendous efforts of se veral authors. In this paper, we briefly review the previous results and pr ovide some conjectures for future work. (C) 1998 Elsevier Science B.V. All rights reserved.