mm-GNAT: Index Structure for Arbitrary Lp Norm

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For fast ε-similarity search, various index structures have been proposed. Yi, et al. proposed a concept multi-modality support and suggested inequalities by which ε-similarity search by L1, L2 and L∞ norm can be realized. We proposed an extended inequality which allows us to realize ε-similarity search by arbitrary Lp norm using an index based on Lq norm. In these investigations a search radius of a norm is converted into that of other norm. In this paper, we propose an index structure which allows search by arbitrary Lp norm, called mm-GNAT (multi-modality support GNAT), with the extention of ranges of GNAT, instead of extending the search radius. The index structure is based on GNAT (Geometric Near-neighbor Access Tree). We show that ε-similarity search by arbitrary Lp norm is realized on mm-GNAT. In addition, we performed search experiments on mm-GNAT with artificial data and music data. The results show that the search by arbitrary Lp norm is realized and the index structure has better search performance than Yi's method except for search by L2 norm.
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