Nonlinear Embedded Map Projection for Dimensionality Reduction

We describe a dimensionality reduction method used to perform similarity search that is tested on document image retrieval applications. The approach is based on data point projection into a low dimensional space obtained by merging together the layers of a Growing Hierarchical Self Organizing Map (GHSOM) trained to model the distribution of objects to be indexed. The low dimensional space is defined by embedding the GHSOM sub-maps in the space defined by a non-linear mapping of neurons belonging to the first level map. The latter mapping is computed with the Sammon projection algorithm. The dimensionality reduction is used in a similarity search framework whose aim is to efficiently retrieve similar objects on the basis of the distance among projected points corresponding to high dimensional feature vectors describing the indexed objects. We compare the proposed method with other dimensionality reduction techniques by evaluating the retrieval performance on three datasets.