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

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 classification EM (CEM) algorithm to learn the classification likelihood; SOEM is derived by using the EM algorithm to learn the mixture likelihood; and SODAEM is a deterministic annealing 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.