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Fast exact $$k$$ nearest neighbors search using an orthogonal search tree. (English) Zbl 1192.68587
Summary: The problem of $$k$$ nearest neighbors $$(kNN)$$ is to find the nearest $$k$$ neighbors for a query point from a given data set. In this paper, a novel fast $$kNN$$ search method using an orthogonal search tree is proposed. The proposed method creates an orthogonal search tree for a data set using an orthonormal basis evaluated from the data set. To find the $$kNN$$ for a query point from the data set, projection values of the query point onto orthogonal vectors in the orthonormal basis and a node elimination inequality are applied for pruning unlikely nodes. For a node, which cannot be deleted, a point elimination inequality is further used to reject impossible data points. Experimental results show that the proposed method has good performance on finding $$kNN$$ for query points and always requires less computation time than available $$kNN$$ search algorithms, especially for a data set with a big number of data points or a large standard deviation.

##### MSC:
 68T10 Pattern recognition, speech recognition
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##### References:
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