A Fast Algorithm to Find Best Matching Units in Self-Organizing Maps

Abstract

Self-Organizing Maps (SOM) are well-known unsupervised neural networks able to perform vector quantization while mapping an underlying regular neighbourhood structure onto the codebook. They are used in a wide range of applications. As with most properly trained neural networks models, increasing the number of neurons in a SOM leads to better results or new emerging properties. Therefore highly efficient algorithms for learning and evaluation are key to improve the performance of such models. In this paper, we propose a faster alternative to compute the Winner Takes All component of SOM that scales better with a large number of neurons. We present our algorithm to find the so-called best matching unit (BMU) in a SOM, and we theoretically analyze its computational complexity. Statistical results on various synthetic and real-world datasets confirm this analysis and show an even more significant improvement in computing time with a minimal degradation of performance. With our method, we explore a new approach for optimizing SOM that can be combined with other optimization methods commonly used in these models for an even faster computation in both learning and recall phases.