Hidden space discriminant neighborhood embedding

Discriminant neighborhood embedding (DNE) algorithm is one of supervised linear dimensionality reduction methods. Its nonlinear version kernel discriminant neighborhood embedding (KDNE) is expected to behave well on classification tasks. However, since KDNE constructs an adjacent graph in the original space, the adjacency graph could not represent the adjacent information in the kernel mapping space. By introducing hidden space, this paper proposes a novel nonlinear method for DNE, called hidden space discriminant neighborhood embedding (HDNE). This algorithm first maps the data in the original space into a high dimensional hidden space by a set of nonlinear hidden functions, and then builds an adjacent graph incorporating neighborhood information of the dataset in the hidden space. Finally, DNE is used to find a transformation matrix which would map the data in the hidden space to a low-dimensional subspace. The proposed method is applied to ORL face and MNIST handwritten digit databases. Experimental results show that the proposed method is efficiency for classification tasks.