Introduction to algorithms
Approximate nearest neighbors and the fast Johnson-Lindenstrauss transform
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Matrix Methods in Data Mining and Pattern Recognition (Fundamentals of Algorithms)
Matrix Methods in Data Mining and Pattern Recognition (Fundamentals of Algorithms)
Fast Computation of Fourier Integral Operators
SIAM Journal on Scientific Computing
The Mailman algorithm: A note on matrix--vector multiplication
Information Processing Letters
Efficient methods for grouping vectors into low-rank clusters
Journal of Computational Physics
| Hi-index | 31.45 |
We present an algorithm for detecting a low-rank cluster of vectors from within a much larger group of vectors. This algorithm relies on a basic geometric property of high-dimensional space: Most of the volume of a typical eccentric ellipsoid is confined to relatively few orthants within the ambient space. This simple fact can be used to quickly detect a collection of vectors with low numerical rank from amongst a larger group of vectors with higher numerical rank.