Neural Network Modeling of Spectral Embedding

Most of spectral embedding algorithms such as Isomap, LLE and Laplacian Eigenmap only give map on training samples. One main problem of these methods is to find the embedding of new samples, which is known as the outof-sample problem of spectral embedding. In this paper, we propose a neural network based method to solve this problem. Neural network is used to train and perform both the forward map from high dimensional image space to low dimensional embedding space, and the backward map in the reverse direction. Additionally, combining the forward and backward network, this method is able to build auto-association model to retrieve high dimensional data, and cross association model to learn high dimensional correspondences. Experiments are conducted on real images for forward and backward map, auto-association and cross association.