Improved Manifold Learning with competitive Hebbian rule

Manifold Learning methods aim to find meaningful low-dimensional structures hidden in their high-dimensional observations. Recently, they are faced with critical problems of how to reduce computational and space complexity in big data applications, how to determine neighborhood size adaptive to different data sets and how to deal with new observations in an out-of-sample mode. This paper presents a new method called TLOE (Topology Learning and Out-of-sample Embedding) to deal with the above three problems. TLOE uses the competitive Hebbian rule to construct the topology preserving network on a given manifold. It is capable of: 1) automatical selection of the right number and position of landmarks, 2) adaptive determination of neighborhood sizes for landmarks and 3) online embedding of new observations. Experiments on both synthetic and real-world data sets show its promising results.