Complementarity and nondegeneracy in semidefinite programming
Mathematical Programming: Series A and B
Convex Optimization
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
Multiple kernel learning, conic duality, and the SMO algorithm
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
Learning the Kernel Function via Regularization
The Journal of Machine Learning Research
Beyond the point cloud: from transductive to semi-supervised learning
ICML '05 Proceedings of the 22nd international conference on Machine learning
Least-Squares Covariance Matrix Adjustment
SIAM Journal on Matrix Analysis and Applications
Cover trees for nearest neighbor
ICML '06 Proceedings of the 23rd international conference on Machine learning
Learning low-rank kernel matrices
ICML '06 Proceedings of the 23rd international conference on Machine learning
Nonstationary kernel combination
ICML '06 Proceedings of the 23rd international conference on Machine learning
Learning the unified kernel machines for classification
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Large Scale Multiple Kernel Learning
The Journal of Machine Learning Research
Learning nonparametric kernel matrices from pairwise constraints
Proceedings of the 24th international conference on Machine learning
Training SVM with indefinite kernels
Proceedings of the 25th international conference on Machine learning
Localized multiple kernel learning
Proceedings of the 25th international conference on Machine learning
Proceedings of the 25th international conference on Machine learning
Fast solvers and efficient implementations for distance metric learning
Proceedings of the 25th international conference on Machine learning
Structure preserving embedding
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
More generality in efficient multiple kernel learning
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
SimpleNPKL: simple non-parametric kernel learning
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Low-Rank Kernel Learning with Bregman Matrix Divergences
The Journal of Machine Learning Research
Non-parametric kernel ranking approach for social image retrieval
Proceedings of the ACM International Conference on Image and Video Retrieval
B-Matching for spectral clustering
ECML'06 Proceedings of the 17th European conference on Machine Learning
Measuring statistical dependence with hilbert-schmidt norms
ALT'05 Proceedings of the 16th international conference on Algorithmic Learning Theory
Learning convex combinations of continuously parameterized basic kernels
COLT'05 Proceedings of the 18th annual conference on Learning Theory
Graph-Based Semi-Supervised Learning and Spectral Kernel Design
IEEE Transactions on Information Theory
Screening nonrandomized studies for medical systematic reviews: A comparative study of classifiers
Artificial Intelligence in Medicine
Semi-supervised learning with mixed knowledge information
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Integrating Spectral Kernel Learning and Constraints in Semi-Supervised Classification
Neural Processing Letters
Online Multiple Kernel Classification
Machine Learning
Online multi-modal distance learning for scalable multimedia retrieval
Proceedings of the sixth ACM international conference on Web search and data mining
Unsupervised non-parametric kernel learning algorithm
Knowledge-Based Systems
Semi-supervised learning with nuclear norm regularization
Pattern Recognition
Efficient kernel learning from side information using ADMM
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Previous studies of Non-Parametric Kernel Learning (NPKL) usually formulate the learning task as a Semi-Definite Programming (SDP) problem that is often solved by some general purpose SDP solvers. However, for N data examples, the time complexity of NPKL using a standard interior-point SDP solver could be as high as O(N6.5), which prohibits NPKL methods applicable to real applications, even for data sets of moderate size. In this paper, we present a family of efficient NPKL algorithms, termed "SimpleNPKL", which can learn non-parametric kernels from a large set of pairwise constraints efficiently. In particular, we propose two efficient SimpleNPKL algorithms. One is SimpleNPKL algorithm with linear loss, which enjoys a closed-form solution that can be efficiently computed by the Lanczos sparse eigen decomposition technique. Another one is SimpleNPKL algorithm with other loss functions (including square hinge loss, hinge loss, square loss) that can be re-formulated as a saddle-point optimization problem, which can be further resolved by a fast iterative algorithm. In contrast to the previous NPKL approaches, our empirical results show that the proposed new technique, maintaining the same accuracy, is significantly more efficient and scalable. Finally, we also demonstrate that the proposed new technique is also applicable to speed up many kernel learning tasks, including colored maximum variance unfolding, minimum volume embedding, and structure preserving embedding.