Randomized algorithms
Fast computation of low rank matrix approximations
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Pass efficient algorithms for approximating large matrices
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Clustering Large Graphs via the Singular Value Decomposition
Machine Learning
Fast monte-carlo algorithms for finding low-rank approximations
Journal of the ACM (JACM)
Spectral techniques applied to sparse random graphs
Random Structures & Algorithms
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Adaptive sampling and fast low-rank matrix approximation
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Graph sparsification by effective resistances
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Bound for the L2 Norm of Random Matrix and Succinct Matrix Approximation
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part II
A note on element-wise matrix sparsification via a matrix-valued Bernstein inequality
Information Processing Letters
Local graph sparsification for scalable clustering
Proceedings of the 2011 ACM SIGMOD International Conference on Management of data
Subsampling mathematical relaxations and average-case complexity
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Low rank matrix-valued chernoff bounds and approximate matrix multiplication
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Adaptive sampling and fast low-rank matrix approximation
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Graph Sparsification by Effective Resistances
SIAM Journal on Computing
Sampling methods for the Nyström method
The Journal of Machine Learning Research
A matrix hyperbolic cosine algorithm and applications
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Simple and deterministic matrix sketching
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
Low rank approximation and regression in input sparsity time
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Sparsity lower bounds for dimensionality reducing maps
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We describe a simple random-sampling based procedure for producing sparse matrix approximations. Our procedure and analysis are extremely simple: the analysis uses nothing more than the Chernoff-Hoeffding bounds. Despite the simplicity, the approximation is comparable and sometimes better than previous work. Our algorithm computes the sparse matrix approximation in a single pass over the data. Further, most of the entries in the output matrix are quantized, and can be succinctly represented by a bit vector, thus leading to much savings in space.