A SOM-Based Method for Manifold Learning and Visualization

Abstract

To avoid getting stuck in local minima and obtain better visualization results for data sets lying on low-dimensional nonlinear manifolds embedded in a high-dimensional space, a new SOM-based method, i.e. TOSOM (Training Orderly-SOM), was presented in this paper. By training the data set orderly according to its neighborhood structure, starting from a small neighborhood in which the data points lie on or close to a locally linear patch, the map can be guided onto the manifold surface and the global visualization results can be achieved step by step. Experimental results show that TO-SOM can discover the intrinsic manifold structure of the data set more faithfully than SOM. As a new manifold learning method, TO-SOM is less sensitive to the neighborhood size than other manifold learning methods such as ISOMAP and LLE, which can also be verified by experimental results.