A New Robust Manifold Learning Algorithm Based on Self-Organizing Map

Abstract

While manifold learning algorithms, such as ISOMAP (isometric mapping) and LLE (locally linear embedding), can find the intrinsic low-dimensional nonlinear manifold embedded in the high-dimensional data space, they are sensitive to the neighborhood size and the noise. To overcome this problem, based on the robustness of SOM (self-organizing map), a new robust manifold learning algorithm, i.e. TO-SOM (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 can lie on or close to a locally linear patch, TO-SOM can guide the map onto the manifold surface, and thus can find the intrinsic manifold structure of the data set successfully. Finally, experimental results show that TO-SOM is more robust, that is, TO-SOM is less sensitive to the neighborhood size and the noise than ISOMAP and LLE.