# A convergence criterion for self-organizing maps

#### Abstract

Currently, only computationally complex, probabilistic models for convergence exist for self-organizing maps (SOMs). The complexity of these algorithms seems to take away from the simple intuitive nature of SOMs in addition to making them computationally unwieldy. The hypothesis proposed is that the original SOM algorithm is heuristic in nature and will almost always converge on a set of code vectors (or neurons) which reflect the underlying distribution from which the original sample (or training) vectors were drawn. This study shows that this hypothesis is valid for the basic SOM algorithm by imposing a convergence criterion on the basic SOM algorithm. The convergence criterion (or convergence measure) imposed treats the SOM as a conventional two sample test (i.e. one sample being the training data and one sample being the code vectors). If the hypothesis holds, then imposing a population based convergence criterion on SOMs will increase their accuracy and utility by allowing an end user of the maps to differentiate between “good” maps (which converged well) and “bad” maps (which did not converge well), hence allowing only the best maps to be selected for use. The convergence criterion could also be used as an indicator for the appropriate number of training iterations necessary for a given set of training data. For instance, if a convergence check were to show that a given SOM has not yet converged, then the number of training iterations could be increased in the next SOM construction. Alternatively, the learning rate could be increased in order to increase the SOM's ability to capture the variance of the training vectors. ^ In addition to testing this hypothesis via the calculation of the proposed convergence measure (using the two sample, population based, approach), another existing method of testing SOMs for reliability and organization (i.e. convergence or “goodness”) is calculated and compared to the results of the convergence measure proposed in this study. What has been observed is that the SOM does indeed converge and that the convergence measure proposed in this thesis is more conservative than the existing, and much more computationally intensive, algorithm to which it is compared. Hence, when the convergence criterion proposed herein is satisfied, the reliability and organization criterion are implied. In addition to being more conservative, it also correlates better with lower quantization errors.^

#### Subject Area

Artificial Intelligence|Computer Science

#### Recommended Citation

Benjamin H Ott,
"A convergence criterion for self-organizing maps"
(2012).
*Dissertations and Master's Theses (Campus Access).*
Paper AAI1508312.

http://digitalcommons.uri.edu/dissertations/AAI1508312