Batch linear manifold topographic map with regional dimensionality estimation

This paper introduces an unsupervised batch algorithm for learning the underlying regional linear manifolds and estimating their dimensionalities using a data set in a topographic map. For this purpose, a unified free energy functional is designed and an expectation-maximization procedure is developed to minimize it. Regional dimensionality estimation controls the extent of the linear manifolds. This property makes the model appropriate for representing the datasets with varying regional intrinsic dimensions, compared to the resembling techniques without dimensionality learning capability. Experimental results show the good performance of the model on synthesized and realworld applications.