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.