An O(n log n) algorithm for the all-nearest-neighbors problem
Discrete & Computational Geometry
Two algorithms for nearest-neighbor search in high dimensions
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Multidimensional divide-and-conquer
Communications of the ACM
Introduction to Algorithms
Efficient Search for Approximate Nearest Neighbor in High Dimensional Spaces
SIAM Journal on Computing
Principal Direction Divisive Partitioning
Data Mining and Knowledge Discovery
Data mining tasks and methods: Classification: nearest-neighbor approaches
Handbook of data mining and knowledge discovery
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Think globally, fit locally: unsupervised learning of low dimensional manifolds
The Journal of Machine Learning Research
The CMU Pose, Illumination, and Expression Database
IEEE Transactions on Pattern Analysis and Machine Intelligence
Divide-and-Conquer Algorithm for Creating Neighborhood Graph for Clustering
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 1 - Volume 01
Acquiring Linear Subspaces for Face Recognition under Variable Lighting
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Agglomerative Clustering Using a k-Nearest Neighbor Graph
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nearest-Neighbor Methods in Learning and Vision: Theory and Practice (Neural Information Processing)
Nearest-Neighbor Methods in Learning and Vision: Theory and Practice (Neural Information Processing)
Distributed computation of the knn graph for large high-dimensional point sets
Journal of Parallel and Distributed Computing
A fast all nearest neighbor algorithm for applications involving large point-clouds
Computers and Graphics
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast algorithms for the all nearest neighbors problem
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Optimal parallel all-nearest-neighbors using the well-separated pair decomposition
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Practical construction of k-nearest neighbor graphs in metric spaces
WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
On the computational complexity of the LBG and PNN algorithms
IEEE Transactions on Image Processing
Multilevel manifold learning with application to spectral clustering
CIKM '10 Proceedings of the 19th ACM international conference on Information and knowledge management
Hubs in Space: Popular Nearest Neighbors in High-Dimensional Data
The Journal of Machine Learning Research
Efficient k-nearest neighbor graph construction for generic similarity measures
Proceedings of the 20th international conference on World wide web
The role of hubness in clustering high-dimensional data
PAKDD'11 Proceedings of the 15th Pacific-Asia conference on Advances in knowledge discovery and data mining - Volume Part I
CoNLL '11 Proceedings of the Fifteenth Conference on Computational Natural Language Learning
Fast approximate similarity search based on degree-reduced neighborhood graphs
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
Hubness-based fuzzy measures for high-dimensional k-nearest neighbor classification
MLDM'11 Proceedings of the 7th international conference on Machine learning and data mining in pattern recognition
A nonparametric classification method based on K-associated graphs
Information Sciences: an International Journal
Hubness-Aware shared neighbor distances for high-dimensional k-nearest neighbor classification
HAIS'12 Proceedings of the 7th international conference on Hybrid Artificial Intelligent Systems - Volume Part II
Fast approximate nearest-neighbor search with k-nearest neighbor graph
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Query-driven iterated neighborhood graph search for large scale indexing
Proceedings of the 20th ACM international conference on Multimedia
Sequential spectral learning to hash with multiple representations
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part V
Information Sciences: an International Journal
Class imbalance and the curse of minority hubs
Knowledge-Based Systems
Technical Section: EXOD: A tool for building and exploring a large graph of open datasets
Computers and Graphics
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Nearest neighbor graphs are widely used in data mining and machine learning. A brute-force method to compute the exact kNN graph takes Θ(dn2) time for n data points in the d dimensional Euclidean space. We propose two divide and conquer methods for computing an approximate kNN graph in Θ(dnt) time for high dimensional data (large d). The exponent t ∈ (1,2) is an increasing function of an internal parameter α which governs the size of the common region in the divide step. Experiments show that a high quality graph can usually be obtained with small overlaps, that is, for small values of t. A few of the practical details of the algorithms are as follows. First, the divide step uses an inexpensive Lanczos procedure to perform recursive spectral bisection. After each conquer step, an additional refinement step is performed to improve the accuracy of the graph. Finally, a hash table is used to avoid repeating distance calculations during the divide and conquer process. The combination of these techniques is shown to yield quite effective algorithms for building kNN graphs.