## Energy Functions for Self-Organizing Maps (1999)

Citations: | 41 - 1 self |

### BibTeX

@MISC{Heskes99energyfunctions,

author = {Tom Heskes},

title = {Energy Functions for Self-Organizing Maps},

year = {1999}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper is about the last issue. After people started to realize that there is no energy function for the Kohonen learning rule (in the continuous case), many attempts have been made to change the algorithm such that an energy can be defined, without drastically changing its properties. Here we will review a simple suggestion, which has been proposed 2 and generalized in several different contexts. The advantage over some other attempts is its simplicity: we only need to redefine the determination of the winning ("best matching") unit. The energy function and corresponding learning algorithm are introduced in Section 2. We give two proofs that there is indeed a proper energy function. The first one, in Section 3, is based on explicit computation of derivatives. The second one, in Section 4 follows from a limiting case of a more general (free) energy function derived in a probabilistic setting. The energy formalism allows for a direct interpretation of disordered configurations in terms of local minima, two examples of which are treated in Section 5.