Asymptotic theory of finite dimensional normed spaces
Asymptotic theory of finite dimensional normed spaces
Randomized algorithms
Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Authoritative sources in a hyperlinked environment
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Approximating the bandwidth via volume respecting embeddings
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Fast computation of low rank matrix approximations
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Shape dimension and approximation from samples
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Improved Testing Algorithms for Monotonicity
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
Fast Monte-Carlo Algorithms for finding low-rank approximations
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Combinatorial feature selection problems
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Algorithmic Applications of Low-Distortion Geometric Embeddings
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Information and Computation
Improved algorithms for quantum identification of Boolean oracles
Theoretical Computer Science
Triangulation and embedding using small sets of beacons
Journal of the ACM (JACM)
Improved algorithms for quantum identification of boolean oracles
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
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Data dimensionality is a crucial issue in a variety of settings, where it is desirable to determine whether a data set given in a high-dimensional space adheres to a low-dimensional structure. We study this problem in the framework of property testing: Given a query access to a data set S, we wish to determine whether S is low-dimensional, or whether it should be modified significantly in order to have the property. Allowing a constant probability of error, we aim at algorithms whose complexity does not depend on the size of S.We present algorithms for testing the low-dimensionality of a set of vectors and for testing whether a matrix is of low rank. We then address low-dimensionality in metric spaces. For vectors in the metric space l1, we show that low-dimensionality is not testable. For l2, we show that a data set can be tested for having a low-dimensional structure, but that the property of approximately having such a structure is not testable.