Optimal algorithms for approximate clustering
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Vector quantization and signal compression
Vector quantization and signal compression
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
SIGMOD '95 Proceedings of the 1995 ACM SIGMOD international conference on Management of data
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Accelerating exact k-means algorithms with geometric reasoning
KDD '99 Proceedings of the fifth ACM SIGKDD international conference on Knowledge discovery and data mining
Evaluating a class of distance-mapping algorithms for data mining and clustering
KDD '99 Proceedings of the fifth ACM SIGKDD international conference on Knowledge discovery and data mining
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
An Efficient k-Means Clustering Algorithm: Analysis and Implementation
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Effect of the Input Density Distribution on Kernel-based Classifiers
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Spectral Grouping Using the Nyström Method
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Learning Spectral Clustering, With Application To Speech Separation
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
Sparsity preserving projections with applications to face recognition
Pattern Recognition
Simplifying mixture models through function approximation
IEEE Transactions on Neural Networks
Segmentation for SAR image based on a new spectral clustering algorithm
LSMS/ICSEE'10 Proceedings of the 2010 international conference on Life system modeling and simulation and intelligent computing, and 2010 international conference on Intelligent computing for sustainable energy and environment: Part III
Clustered Nyström method for large scale manifold learning and dimension reduction
IEEE Transactions on Neural Networks
Fast density-weighted low-rank approximation spectral clustering
Data Mining and Knowledge Discovery
Fast affinity propagation clustering: A multilevel approach
Pattern Recognition
Sampling methods for the Nyström method
The Journal of Machine Learning Research
Spectral clustering based on dictionary learning sampling for image segmentation
IScIDE'11 Proceedings of the Second Sino-foreign-interchange conference on Intelligent Science and Intelligent Data Engineering
Large scale online kernel classification
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
Local information-based fast approximate spectral clustering
Pattern Recognition Letters
Unsupervised images segmentation via incremental dictionary learning based sparse representation
Information Sciences: an International Journal
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The Nyström method is a well-known sampling-based technique for approximating the eigensystem of large kernel matrices. However, the chosen samples in the Nyström method are all assumed to be of equal importance, which deviates from the integral equation that defines the kernel eigenfunctions. Motivated by this observation, we extend the Nyström method to a more general, density-weighted version. We show that by introducing the probability density function as a natural weighting scheme, the approximation of the eigensystem can be greatly improved. An efficient algorithm is proposed to enforce such weighting in practice, which has the same complexity as the original Nyström method and hence is notably cheaper than several other alternatives. Experiments on kernel principal component analysis, spectral clustering, and image segmentation demonstrate the encouraging performance of our algorithm.