Bi-criteria linear-time approximations for generalized k-mean/median/center
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Embeddings of surfaces, curves, and moving points in euclidean space
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Sampling-based dimension reduction for subspace approximation
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Efficient subspace approximation algorithms
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Fast dimension reduction using Rademacher series on dual BCH codes
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Sampling algorithms and coresets for ℓp regression
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Spectral clustering in telephone call graphs
Proceedings of the 9th WebKDD and 1st SNA-KDD 2007 workshop on Web mining and social network analysis
Tighter bounds for random projections of manifolds
Proceedings of the twenty-fourth annual symposium on Computational geometry
Dense Fast Random Projections and Lean Walsh Transforms
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Near Optimal Dimensionality Reductions That Preserve Volumes
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Spectral Clustering in Social Networks
Advances in Web Mining and Web Usage Analysis
Numerical linear algebra in the streaming model
Proceedings of the forty-first annual ACM symposium on Theory of computing
A fast and efficient algorithm for low-rank approximation of a matrix
Proceedings of the forty-first annual ACM symposium on Theory of computing
DOULION: counting triangles in massive graphs with a coin
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Foundations and Trends® in Theoretical Computer Science
Communications of the ACM
Spectral methods for matrices and tensors
Proceedings of the forty-second ACM symposium on Theory of computing
A sparse Johnson: Lindenstrauss transform
Proceedings of the forty-second ACM symposium on Theory of computing
Universal multi-dimensional scaling
Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining
Coresets and sketches for high dimensional subspace approximation problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
1-pass relative-error Lp-sampling with applications
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Streaming graph computations with a helpful advisor
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
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)
Blendenpik: Supercharging LAPACK's Least-Squares Solver
SIAM Journal on Scientific Computing
A unified framework for approximating and clustering data
Proceedings of the forty-third annual ACM symposium on Theory of computing
Fast moment estimation in data streams in optimal space
Proceedings of the forty-third annual ACM symposium on Theory of computing
Subspace embeddings for the L1-norm with applications
Proceedings of the forty-third annual ACM symposium on Theory of computing
Multiplicative approximations of random walk transition probabilities
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
SIAM Journal on Scientific Computing
Compressed matrix multiplication
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Sparser Johnson-Lindenstrauss transforms
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Optimal column-based low-rank matrix reconstruction
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Optimal bounds for Johnson-Lindenstrauss transforms and streaming problems with sub-constant error
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
An almost optimal unrestricted fast Johnson-Lindenstrauss transform
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
Column subset selection via sparse approximation of SVD
Theoretical Computer Science
Randomized Algorithms for Matrices and Data
Foundations and Trends® in Machine Learning
Fast matrix rank algorithms and applications
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
A GPU-based approximate SVD algorithm
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part I
An Almost Optimal Unrestricted Fast Johnson-Lindenstrauss Transform
ACM Transactions on Algorithms (TALG) - Special Issue on SODA'11
Optimal Bounds for Johnson-Lindenstrauss Transforms and Streaming Problems with Subconstant Error
ACM Transactions on Algorithms (TALG) - Special Issue on SODA'11
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
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
Compressed matrix multiplication
ACM Transactions on Computation Theory (TOCT) - Special issue on innovations in theoretical computer science 2012
Linear regression with random projections
The Journal of Machine Learning Research
Fast approximation of matrix coherence and statistical leverage
The Journal of Machine Learning Research
Fast matrix rank algorithms and applications
Journal of the ACM (JACM)
Sparser Johnson-Lindenstrauss Transforms
Journal of the ACM (JACM)
Column Subset Selection Problem is UG-hard
Journal of Computer and System Sciences
| Hi-index | 0.02 |
Recently several results appeared that show significant reduction in time for matrix multiplication, singular value decomposition as well as linear (\ell_ 2) regression, all based on data dependent random sampling. Our key idea is that low dimensional embeddings can be used to eliminate data dependence and provide more versatile, linear time pass efficient matrix computation. Our main contribution is summarized as follows. --Independent of the recent results of Har-Peled and of Deshpande and Vempala, one of the first -- and to the best of our knowledge the most efficient -- relative error (1 + \in) \parallel A - A_k \parallel _Fapproximation algorithms for the singular value decomposition of an m 脳 n matrix A with M non-zero entries that requires 2 passes over the data and runs in time O\left( {\left( {M(\frac{k} { \in } + k\log k) + (n + m)(\frac{k} { \in } + k\log k)^2 } \right)\log \frac{1} {\delta }} \right) --The first o(nd^{2}) time (1 + \in) relative error approximation algorithm for n 脳 d linear (\ell_2) regression. --A matrix multiplication and norm approximation algorithm that easily applies to implicitly given matrices and can be used as a black box probability boosting tool.