Improvement of PCA-Based Approximate Nearest Neighbor Search Using Distance Statistics
Toshiro Ogita*, Hidetomo Ichihashi**, Akira Notsu*,
and Katsuhiro Honda*
*Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, Sakai, Osaka 599-8531, Japan
**Department of Economics, Osaka University of Economics and Law, 6-10 Gakuonji, Yao, Osaka 581-8511, Japan
In many computer vision applications, nearest neighbor searching in high-dimensional spaces is often the most time consuming component and we have few algorithms for solving these high-dimensional nearest neighbor search problems that are faster than linear search. Approximately nearest neighbor search algorithms can play an important role in achieving significantly faster running times with relatively small errors. This paper considers the improvement of the PCA-tree nearest neighbor search algorithm  by employing nearest neighbor distance statistics. During the preprocessing phase of the PCA-tree nearest neighbor search algorithm, a data set is partitioned into clusters by successive use of Principal Component Analysis (PCA). The search performance is significantly improved if the data points are sorted by leaf node, and the threshold value is updated each time a smaller distance is found. The threshold is updated by the ε-approximate nearest neighbor approach together with the fixed-threshold approach. Performance can be further improved by the annulus bound approach. Moreover, nearest neighbor distance statistics is employed for further improving the efficiency of the search algorithm and the several experimental results are shown for demonstrating how its efficiency is improved.
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