With PQDT Open, you can read the full text of open access dissertations and theses free of charge.
About PQDT Open
Search
COMING SOON! PQDT Open is getting a new home!
ProQuest Open Access Dissertations & Theses will remain freely available as part of a new and enhanced search experience at www.proquest.com.
Questions? Please refer to this FAQ.
We present a randomized algorithm for the approximate nearest neighbor problem in d-dimensional Euclidean space. Given N points {xj} in [special characters omitted], the algorithm attempts to find k nearest neighbors for each of xj, where k is a user-specified integer parameter. The algorithm is iterative, and its CPU time requirements are proportional to T · N · (d · (log d) + k · (d + log k) · (log N)) + N · k 2 · (d + log k), with T the number of iterations performed. The memory requirements of the procedure are of the order N · (d + k).
A byproduct of the scheme is a data structure, permitting a rapid search for the k nearest neighbors among {xj} for an arbitrary point x ∈ [special characters omitted]. The cost of each such query is proportional to T · (d · (log d) + log(N/k) · k · (d + log k)), and the memory requirements for the requisite data structure are of the order N · (d + k) + T · (d + N).
The algorithm utilizes random rotations and a basic divide-and-conquer scheme, followed by a local graph search. We analyze the scheme's behavior for certain types of distributions of {xj}, and illustrate its performance via several numerical examples.
Advisor: | Rokhlin, Vladimir |
Commitee: | |
School: | Yale University |
School Location: | United States -- Connecticut |
Source: | DAI-B 72/10, Dissertation Abstracts International |
Source Type: | DISSERTATION |
Subjects: | Applied Mathematics, Computer science |
Keywords: | Approximate nearest neighbors, Euclidean space, Fast random rotations, Randomized algorithm, User-specified integer parameters |
Publication Number: | 3467911 |
ISBN: | 978-1-124-80611-2 |