What is the Nearest Neighbor in High Dimensional Spaces?

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What is the Nearest Neighbor in High Dimensional Spaces? (2000)

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by Alexander Hinneburg , Charu Aggarwal , Daniel A. Keim

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134 - 11 self

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@INPROCEEDINGS{Hinneburg00whatis,
    author = {Alexander Hinneburg and Charu Aggarwal and Daniel A. Keim},
    title = {What is the Nearest Neighbor in High Dimensional Spaces?},
    booktitle = {},
    year = {2000},
    pages = {506--515},
    publisher = {Morgan Kaufmann}
}

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Abstract

Nearest neighbor search in high dimensional spaces is an interesting and important problem which is relevant for a wide variety of novel database applications. As recent results show, however, the problem is a very difficult one, not only with regards to the performance issue but also to the quality issue. In this paper, we discuss the quality issue and identify a new generalized notion of nearest neighbor search as the relevant problem in high dimensional space. In contrast to previous approaches, our new notion of nearest neighbor search does not treat all dimensions equally but uses a quality criterion to select relevant dimensions (projections) with respect to the given query. As an example for a useful quality criterion, we rate how well the data is clustered around the query point within the selected projection. We then propose an efficient and effective algorithm to solve the generalized nearest neighbor problem. Our experiments based on a number of real and synthetic data sets show that our new approach provides new insights into the nature of nearest neighbor search on high dimensional data.

Keyphrases

high dimensional space neighbor search quality issue high dimensional data new approach neighbor problem effective algorithm useful quality criterion important problem relevant problem new insight relevant dimension synthetic data set performance issue new notion recent result wide variety previous approach new generalized notion novel database application quality criterion query point

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