Matrix analysis
Computational methods for integral equations
Computational methods for integral equations
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Clustering in large graphs and matrices
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
Fast computation of low rank matrix approximations
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
Pass efficient algorithms for approximating large matrices
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Sparse Greedy Matrix Approximation for Machine Learning
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
The Effect of the Input Density Distribution on Kernel-based Classifiers
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Fast Monte-Carlo Algorithms for finding low-rank approximations
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Fast Monte-Carlo Algorithms for Approximate Matrix Multiplication
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Efficient svm training using low-rank kernel representations
The Journal of Machine Learning Research
Spectral Grouping Using the Nyström Method
IEEE Transactions on Pattern Analysis and Machine Intelligence
Learning a kernel matrix for nonlinear dimensionality reduction
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Fast Monte Carlo Algorithms for Matrices I: Approximating Matrix Multiplication
SIAM Journal on Computing
Fast Monte Carlo Algorithms for Matrices II: Computing a Low-Rank Approximation to a Matrix
SIAM Journal on Computing
SIAM Journal on Computing
Approximating a gram matrix for improved kernel-based learning
COLT'05 Proceedings of the 18th annual conference on Learning Theory
Sampling sub-problems of heterogeneous max-cut problems and approximation algorithms
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Block-quantized kernel matrix for fast spectral embedding
ICML '06 Proceedings of the 23rd international conference on Machine learning
Tensor-CUR decompositions for tensor-based data
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Subspace sampling and relative-error matrix approximation: column-row-based methods
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
AppProp: all-pairs appearance-space edit propagation
ACM SIGGRAPH 2008 papers
Improved Nyström low-rank approximation and error analysis
Proceedings of the 25th international conference on Machine learning
Modeling Transfer Relationships Between Learning Tasks for Improved Inductive Transfer
ECML PKDD '08 Proceedings of the 2008 European Conference on Machine Learning and Knowledge Discovery in Databases - Part I
Density-weighted nyström method for computing large kernel eigensystems
Neural Computation
Accuracy of suboptimal solutions to kernel principal component analysis
Computational Optimization and Applications
On sampling-based approximate spectral decomposition
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Learning Representation and Control in Markov Decision Processes: New Frontiers
Foundations and Trends® in Machine Learning
Learning representation and control in continuous Markov decision processes
AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
Fast Spectral Clustering with Random Projection and Sampling
MLDM '09 Proceedings of the 6th International Conference on Machine Learning and Data Mining in Pattern Recognition
Compact spectral bases for value function approximation using Kronecker factorization
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Weight-decay regularization in reproducing Kernel Hilbert spaces by variable-basis schemes
WSEAS Transactions on Mathematics
Learning relevant eye movement feature spaces across users
Proceedings of the 2010 Symposium on Eye-Tracking Research & Applications
Optimized fixed-size kernel models for large data sets
Computational Statistics & Data Analysis
Self-taught hashing for fast similarity search
Proceedings of the 33rd international ACM SIGIR conference on Research and development in information retrieval
Clustered Nyström method for large scale manifold learning and dimension reduction
IEEE Transactions on Neural Networks
Using an iterative linear solver in an interior-point method for generating support vector machines
Computational Optimization and Applications
Random Fourier approximations for skewed multiplicative histogram kernels
Proceedings of the 32nd DAGM conference on Pattern recognition
Robust Positive semidefinite L-Isomap Ensemble
Pattern Recognition Letters
Proceedings of the ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
Fast density-weighted low-rank approximation spectral clustering
Data Mining and Knowledge Discovery
ACM SIGMETRICS Performance Evaluation Review - Performance evaluation review
Approximate kernel k-means: solution to large scale kernel clustering
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
A large-scale manifold learning approach for brain tumor progression prediction
MLMI'11 Proceedings of the Second international conference on Machine learning in medical imaging
A simplified multi-class support vector machine with reduced dual optimization
Pattern Recognition Letters
Efficient combination of probabilistic sampling approximations for robust image segmentation
DAGM'06 Proceedings of the 28th conference on Pattern Recognition
Randomized Algorithms for Matrices and Data
Foundations and Trends® in Machine Learning
Active spectral clustering via iterative uncertainty reduction
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Nyström approximate model selection for LSSVM
PAKDD'12 Proceedings of the 16th Pacific-Asia conference on Advances in Knowledge Discovery and Data Mining - Volume Part I
Sampling methods for the Nyström method
The Journal of Machine Learning Research
Boosting multi-kernel locality-sensitive hashing for scalable image retrieval
SIGIR '12 Proceedings of the 35th international ACM SIGIR conference on Research and development in information retrieval
Multi-level Low-rank Approximation-based Spectral Clustering for image segmentation
Pattern Recognition Letters
Spectral demons --- image registration via global spectral correspondence
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part II
Separable approximate optimization of support vector machines for distributed sensing
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part II
Sparse hashing for fast multimedia search
ACM Transactions on Information Systems (TOIS)
Fast and scalable polynomial kernels via explicit feature maps
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
Multiple spectral kernel learning and a gaussian complexity computation
Neural Computation
Asymptotic error bounds for kernel-based Nyström low-rank approximation matrices
Journal of Multivariate Analysis
Beam search algorithms for multilabel learning
Machine Learning
Kernelizing the proportional odds model through the empirical kernel mapping
IWANN'13 Proceedings of the 12th international conference on Artificial Neural Networks: advances in computational intelligence - Volume Part I
Data analysis of (non-)metric proximities at linear costs
SIMBAD'13 Proceedings of the Second international conference on Similarity-Based Pattern Recognition
A scalable approach to column-based low-rank matrix approximation
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Reduced heteroscedasticity linear regression for Nyström approximation
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Deflation-based power iteration clustering
Applied Intelligence
Improving CUR matrix decomposition and the Nyström approximation via adaptive sampling
The Journal of Machine Learning Research
Large-scale SVD and manifold learning
The Journal of Machine Learning Research
Sparse semi-supervised learning on low-rank kernel
Neurocomputing
Column Subset Selection Problem is UG-hard
Journal of Computer and System Sciences
Efficient eigen-updating for spectral graph clustering
Neurocomputing
Spectral Log-Demons: Diffeomorphic Image Registration with Very Large Deformations
International Journal of Computer Vision
Hi-index | 0.00 |
A problem for many kernel-based methods is that the amount of computation required to find the solution scales as O(n3), where n is the number of training examples. We develop and analyze an algorithm to compute an easily-interpretable low-rank approximation to an n × n Gram matrix G such that computations of interest may be performed more rapidly. The approximation is of the form ~Gk = CWk+CT, where C is a matrix consisting of a small number c of columns of G and Wk is the best rank-k approximation to W, the matrix formed by the intersection between those c columns of G and the corresponding c rows of G. An important aspect of the algorithm is the probability distribution used to randomly sample the columns; we will use a judiciously-chosen and data-dependent nonuniform probability distribution. Let ||·||2 and ||·||F denote the spectral norm and the Frobenius norm, respectively, of a matrix, and let Gk be the best rank-k approximation to G. We prove that by choosing O(k/ε4) columns||G-CWk+CT||ξ ≤ ||G-Gk||ξ + ε Σi=1n Gii2 ,both in expectation and with high probability, for both ξ = 2, F, and for all k: 0 ≤ k ≤ rank(W). This approximation can be computed using O(n) additional space and time, after making two passes over the data from external storage. The relationships between this algorithm, other related matrix decompositions, and the Nyström method from integral equation theory are discussed.