A New Family Of Near-metrics For Universal Similarity

Abstract

We propose a family of near-metrics based on local graph diffusion to capture similarity for a wide class of data sets. These quasi-metametrics, as their names suggest, dispense with one or two standard axioms of metric spaces, specifically distinguishability and symmetry, so that similarity between data points of arbitrary type and form could be measured broadly and effectively. The proposed near-metric family includes the forward k-step diffusion and its reverse, typically on the graph consisting of data objects and their features. By construction, this family of near-metrics is particularly appropriate for categorical data, continuous data, and vector representations of images and text extracted via deep learning approaches. We conduct extensive experiments to evaluate the performance of this family of similarity measures and compare and contrast with traditional measures of similarity used for each specific application and with the ground truth when available. We show that for stru

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• arxiv keywang2017a

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