Modeling Nonlinear Manifolds with Mixtures of Localized Principal Subspaces under a Self-Organizing Framework

This paper presents a neural network which models nonlinear manifolds with mixtures of localized principal subspaces under an online self-organizing framework. Each neuron in our network approximately learns a principal subspace of the local data distribution. Compared to other similar networks, the local principal subspaces learned at neurons of our network have better local property due to a new cost function, which helps to avoid confusion of different local sub-models. It is proved that there is no local extremum for each local model. Experiments show that the new model is better adapted to nonlinear manifolds for various data distributions than other models in comparison. The online-learning property of this model makes it feasible for sequentially acquired data and large data sets. Potential applications of this model include deployment of directional sensor networks, mapping high-dimensional signal space to physical space in wireless sensor networks, or simply nonlinear dimension reduction for data mining in sensor networks.