Optical EngineeringExtended dot product representations of graphs with application to radar image segmentation
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Graph-based dimensionality reduction methods are popular in pattern recognition and machine learning. In contrast to the manifold learning approaches, the dot product representation of graphs (DPRG) seeks a solution to dimensionality reduction by assigning vectors to each node of a graph such that the dot product of every pair of nodes approximates the similarity between them. The DPRG has many potential applications, for the reason that there is no prior assumption of the data distribution. It has been found, however, that the DPRG tends to reduce the distances of the graph nodes represented in a low-dimensional space, which in turn degrades the performance of data clustering. Motivated by this observation, we propose an extended DPRG (EDPRG) model by simply employing negative similarity values. The theoretical analysis and experiments on synthetic data show that the modification is effective in increasing between-class distances. We demonstrate the effectiveness of the EDPRG model by experiments on synthetic aperture radar (SAR) image segmentation. The proposed image segmentation method has two steps. The first one presegments the image by the mean shift algorithm. The second merges the resulting regions by means of the EDPRG model.