Near neighbor search in nonmetric space
Résumé
We consider the computational problem of the Near Neighbor Search (NNS) in nonmetric spaces. Nonmetric spaces are the generalization of the metric spaces because they do not require the triangular inequality assumption. Nonmetric spaces are important because many similarity measures (between images, proteins, etc) do not verify the triangular inequality. We show the nonmetric situation calls for different evaluation criterions of NNS algorithms. As a first attempt, to our knowledge, to perform general nonmetric NNS, we introduce such evaluation criterions. The insights provided by those criterions lead us to introduce a new category of search structures, called "densitrees", that extend the classical metric tree algorithm for the nonmetric NNS. Against well established datasets, our preliminary empirical results lead us to a counter-intuitive conclusion: "the triangular inequality has only a secondary contribution on the efficiency metric". Additionally, the densitrees, although very naively implemented, performs reasonably well both in metric and nonmetric situations.
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