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Cover trees for nearest neighbor
Abstract
We present a tree data structure for fast nearest neighbor operations in general n-point metric spaces (where the data set consists of n points). The data structure requires O(n) space regardless of the metric's structure yet maintains all performance properties of a navigating net (Krauthgamer & Lee, 2004b). If the point set has a bounded expansion constant c, which is a measure of the intrinsic dimensionality, as defined in (Karger & Ruhl, 2002), the cover tree data structure can be constructed in O (c6n log n) time. Furthermore, nearest neighbor queries require time only logarithmic in n, in particular O (c12 log n) time. Our experimental results show speedups over the brute force search varying between one and several orders of magnitude on natural machine learning datasets.
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Cites
A Global Geometric Framework for Nonlinear Dimensionality Reduction
Tenenbaum, J. B., Silva, V. D., & Langford, J. C. (2000) · Science · doi:10.1126/science.290.5500.2319 · Cited by 13,585
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Cited by
Human3.6M: Large Scale Datasets and Predictive Methods for 3D Human Sensing in Natural Environments
Ionescu, C., Papava, D., Olaru, V., & Sminchisescu, C. (2014) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2013.248 · Cited by 3,653
DBSCAN Revisited, Revisited: Why and How You Should (Still) Use DBSCAN
Schubert, E., Sander, J., Ester, M., Kriegel, H. P., & Xu, X. (2017) · ACM Transactions on Database Systems · doi:10.1145/3068335 · Cited by 2,737
Kriegel, H., Kröger, P., Sander, J., & Zimek, A. (2011) · WIREs Data Mining and Knowledge Discovery · doi:10.1002/widm.30 · Cited by 900
Incremental nonlinear dimensionality reduction by manifold learning
Law, M. H. C., & Jain, A. K. (2006) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2006.56 · Cited by 284
Spectral Methods for Dimensionality Reduction
Saul, L. K., Weinberger, K. Q., Sha, F., Ham, J., & Lee, D. D. (2006) · Semi-Supervised Learning · doi:10.7551/mitpress/6173.003.0022 · Cited by 272
Metadata
- Authors
- Beygelzimer, A., Kakade, S., & Langford, J.
- Venue
- Proceedings of the 23rd international conference on Machine learning - ICML '06
- Publisher
- ACM Press
- Published
- 2006
- Pages
- 97-104
- OpenAlex
- W2133296809
- Cited by
- 813
- References
- 1
- FWCI
- 34.44
- Type
- conference paper
- Language
- en
- Open access
- closed
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- Beygelzimer, A., Kakade, S., & Langford, J. (2006). Cover trees for nearest neighbor. Proceedings of the 23rd international conference on Machine learning - ICML '06. https://doi.org/10.1145/1143844.1143857
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