Matrix computations (3rd ed.)
Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Latent semantic indexing: a probabilistic analysis
Journal of Computer and System Sciences - Special issue on the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose
IEEE Transactions on Pattern Analysis and Machine Intelligence
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 norm of random matrices
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Colibri: fast mining of large static and dynamic graphs
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
Numerical linear algebra in the streaming model
Proceedings of the forty-first annual ACM symposium on Theory of computing
Foundations and Trends® in Theoretical Computer Science
Spectral methods for matrices and tensors
Proceedings of the forty-second ACM symposium on Theory of computing
Matrix completion from a few entries
IEEE Transactions on Information Theory
Matrix Completion from Noisy Entries
The Journal of Machine Learning Research
Clustering coefficient queries on massive dynamic social networks
WAIM'10 Proceedings of the 11th international conference on Web-age information management
A Randomized Algorithm for Principal Component Analysis
SIAM Journal on Matrix Analysis and Applications
Fast Algorithms for Approximating the Singular Value Decomposition
ACM Transactions on Knowledge Discovery from Data (TKDD)
A note on element-wise matrix sparsification via a matrix-valued Bernstein inequality
Information Processing Letters
Proceedings of the ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
ACM SIGMETRICS Performance Evaluation Review - Performance evaluation review
XML documents clustering using a tensor space model
PAKDD'11 Proceedings of the 15th Pacific-Asia conference on Advances in knowledge discovery and data mining - Volume Part I
Descriptive matrix factorization for sustainability Adopting the principle of opposites
Data Mining and Knowledge Discovery
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
Randomized Algorithms for Matrices and Data
Foundations and Trends® in Machine Learning
Non-negative residual matrix factorization: problem definition, fast solutions, and applications
Statistical Analysis and Data Mining
Active spectral clustering via iterative uncertainty reduction
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
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
Column Subset Selection Problem is UG-hard
Journal of Computer and System Sciences
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Given a matrix A, it is often desirable to find a good approximation to A that has low rank. We introduce a simple technique for accelerating the computation of such approximations when A has strong spectral features, that is, when the singular values of interest are significantly greater than those of a random matrix with size and entries similar to A. Our technique amounts to independently sampling and/or quantizing the entries of A, thus speeding up computation by reducing the number of nonzero entries and/or the length of their representation. Our analysis is based on observing that the acts of sampling and quantization can be viewed as adding a random matrix N to A, whose entries are independent random variables with zero-mean and bounded variance. Since, with high probability, N has very weak spectral features, we can prove that the effect of sampling and quantization nearly vanishes when a low-rank approximation to A + N is computed. We give high probability bounds on the quality of our approximation both in the Frobenius and the 2-norm.