Vector quantization and signal compression
Vector quantization and signal compression
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Least Squares Support Vector Machine Classifiers
Neural Processing Letters
Fast computation of low rank matrix approximations
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
An Efficient k-Means Clustering Algorithm: Analysis and Implementation
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Fast Monte-Carlo Algorithms for finding low-rank approximations
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Efficient svm training using low-rank kernel representations
The Journal of Machine Learning Research
Kernel independent component analysis
The Journal of Machine Learning Research
Spectral Grouping Using the Nyström Method
IEEE Transactions on Pattern Analysis and Machine Intelligence
Predictive low-rank decomposition for kernel methods
ICML '05 Proceedings of the 22nd international conference on Machine learning
Block-quantized kernel matrix for fast spectral embedding
ICML '06 Proceedings of the 23rd international conference on Machine learning
On the Nyström Method for Approximating a Gram Matrix for Improved Kernel-Based Learning
The Journal of Machine Learning Research
An experimental evaluation of a Monte-Carlo algorithm for singular value decomposition
PCI'01 Proceedings of the 8th Panhellenic conference on Informatics
Approximate Spectral Clustering
PAKDD '09 Proceedings of the 13th Pacific-Asia Conference on Advances in Knowledge Discovery and Data Mining
On sampling-based approximate spectral decomposition
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Prototype vector machine for large scale semi-supervised learning
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Robust Positive semidefinite L-Isomap Ensemble
Pattern Recognition Letters
On Learning and Cross-Validation with Decomposed Nyström Approximation of Kernel Matrix
Neural Processing Letters
Fast density-weighted low-rank approximation spectral clustering
Data Mining and Knowledge Discovery
Accelerating kernel neural gas
ICANN'11 Proceedings of the 21th international conference on Artificial neural networks - Volume Part I
Fast affinity propagation clustering: A multilevel approach
Pattern Recognition
Dynamic subspace update with incremental Nyström approximation
ACCV'10 Proceedings of the 2010 international conference on Computer vision - Volume part II
A simplified multi-class support vector machine with reduced dual optimization
Pattern Recognition Letters
Randomized Algorithms for Matrices and Data
Foundations and Trends® in Machine Learning
Approximation techniques for clustering dissimilarity data
Neurocomputing
Cluster indicator decomposition for efficient matrix factorization
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Sampling methods for the Nyström method
The Journal of Machine Learning Research
Sparse spectral clustering method based on the incomplete Cholesky decomposition
Journal of Computational and Applied Mathematics
Hierarchical kernel spectral clustering
Neural Networks
Multi-level Low-rank Approximation-based Spectral Clustering for image segmentation
Pattern Recognition Letters
Fast semantic image retrieval based on random forest
Proceedings of the 20th ACM international conference on Multimedia
Random forest for image annotation
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VI
Low-rank quadratic semidefinite programming
Neurocomputing
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
Local information-based fast approximate spectral clustering
Pattern Recognition Letters
Improving CUR matrix decomposition and the Nyström approximation via adaptive sampling
The Journal of Machine Learning Research
Sparse semi-supervised learning on low-rank kernel
Neurocomputing
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Low-rank matrix approximation is an effective tool in alleviating the memory and computational burdens of kernel methods and sampling, as the mainstream of such algorithms, has drawn considerable attention in both theory and practice. This paper presents detailed studies on the Nyström sampling scheme and in particular, an error analysis that directly relates the Nyström approximation quality with the encoding powers of the landmark points in summarizing the data. The resultant error bound suggests a simple and efficient sampling scheme, the k-means clustering algorithm, for Nyström low-rank approximation. We compare it with state-of-the-art approaches that range from greedy schemes to probabilistic sampling. Our algorithm achieves significant performance gains in a number of supervised/unsupervised learning tasks including kernel PCA and least squares SVM.