A fast algorithm for particle simulations
Journal of Computational Physics
Applied numerical linear algebra
Applied numerical linear algebra
Efficient svm training using low-rank kernel representations
The Journal of Machine Learning Research
Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
Learning the Kernel Matrix with Semidefinite Programming
The Journal of Machine Learning Research
Learning a kernel matrix for nonlinear dimensionality reduction
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Predictive low-rank decomposition for kernel methods
ICML '05 Proceedings of the 22nd international conference on Machine learning
Semi-supervised graph clustering: a kernel approach
ICML '05 Proceedings of the 22nd international conference on Machine learning
Information-theoretic metric learning
Proceedings of the 24th international conference on Machine learning
Learning nonparametric kernel matrices from pairwise constraints
Proceedings of the 24th international conference on Machine learning
Proceedings of the 25th international conference on Machine learning
Rank minimization via online learning
Proceedings of the 25th international conference on Machine learning
Structured metric learning for high dimensional problems
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
SimpleNPKL: simple non-parametric kernel learning
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Learning the optimal neighborhood kernel for classification
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Similarity search on Bregman divergence: towards non-metric indexing
Proceedings of the VLDB Endowment
Non-parametric kernel ranking approach for social image retrieval
Proceedings of the ACM International Conference on Image and Video Retrieval
Tensor sparse coding for region covariances
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part IV
Online multiple kernel learning: algorithms and mistake bounds
ALT'10 Proceedings of the 21st international conference on Algorithmic learning theory
Riemannian Metric and Geometric Mean for Positive Semidefinite Matrices of Fixed Rank
SIAM Journal on Matrix Analysis and Applications
Learning similarity function for rare queries
Proceedings of the fourth ACM international conference on Web search and data mining
On Convergence of Kernel Learning Estimators
SIAM Journal on Optimization
Learning low-rank kernel matrices for constrained clustering
Neurocomputing
A Family of Simple Non-Parametric Kernel Learning Algorithms
The Journal of Machine Learning Research
Identifying nuclear phenotypes using semi-supervised metric learning
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Manifold-Regularized minimax probability machine
PSL'11 Proceedings of the First IAPR TC3 conference on Partially Supervised Learning
Metric and kernel learning using a linear transformation
The Journal of Machine Learning Research
ICAISC'12 Proceedings of the 11th international conference on Artificial Intelligence and Soft Computing - Volume Part II
Distance metric learning under covariate shift
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Online Multiple Kernel Classification
Machine Learning
Unsupervised non-parametric kernel learning algorithm
Knowledge-Based Systems
Efficient image and tag co-ranking: a bregman divergence optimization method
Proceedings of the 21st ACM international conference on Multimedia
Laplacian minimax probability machine
Pattern Recognition Letters
An information theoretic sparse kernel algorithm for online learning
Expert Systems with Applications: An International Journal
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Kernel learning plays an important role in many machine learning tasks. However, algorithms for learning a kernel matrix often scale poorly, with running times that are cubic in the number of data points. In this paper, we propose efficient algorithms for learning low-rank kernel matrices; our algorithms scale linearly in the number of data points and quadratically in the rank of the kernel. We introduce and employ Bregman matrix divergences for rank-deficient matrices---these divergences are natural for our problem since they preserve the rank as well as positive semi-definiteness of the kernel matrix. Special cases of our framework yield faster algorithms for various existing kernel learning problems. Experimental results demonstrate the effectiveness of our algorithms in learning both low-rank and full-rank kernels.