CEM, EM, and DAEM Algorithms for Learning Self-Organizing Maps

Abstract

In this paper, we propose a generative model for self-organizing maps (SOM). Based on this model, we derive three EM-type algorithms for learning SOM, namely, the SOCEM, SOEM, and SODAEM algorithms. SOCEM is derived by using the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">classification</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">EM</i> (CEM) algorithm to learn the classification likelihood; SOEM is derived by using the EM algorithm to learn the mixture likelihood; and SODAEM is a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">deterministic</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">annealing</i> variant of SOCEM and SOEM. From our experiments on the organizing property of SOM, we observe that SOEM is less sensitive to the initialization of the parameters when using a small-fixed neighborhood than SOCEM, while SODAEM can overcome the initialization problem of SOCEM and SOEM through an annealing process.