Complementarity and nondegeneracy in semidefinite programming
Mathematical Programming: Series A and B
Diffusion Kernels on Graphs and Other Discrete Input Spaces
ICML '02 Proceedings of the Nineteenth International Conference on Machine Learning
Convex Optimization
Learning the Kernel Matrix with Semidefinite Programming
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
Learning the unified kernel machines for classification
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Structured Prediction, Dual Extragradient and Bregman Projections
The Journal of Machine Learning Research
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
Fast solvers and efficient implementations for distance metric learning
Proceedings of the 25th international conference on Machine learning
Non-parametric kernel ranking approach for social image retrieval
Proceedings of the ACM International Conference on Image and Video Retrieval
Regression on Fixed-Rank Positive Semidefinite Matrices: A Riemannian Approach
The Journal of Machine Learning Research
Learning low-rank kernel matrices for constrained clustering
Neurocomputing
A Family of Simple Non-Parametric Kernel Learning Algorithms
The Journal of Machine Learning Research
Online Multiple Kernel Classification
Machine Learning
Online learning with multiple kernels: A review
Neural Computation
Unsupervised non-parametric kernel learning algorithm
Knowledge-Based Systems
Probabilistic non-linear distance metric learning for constrained clustering
Proceedings of the 4th MultiClust Workshop on Multiple Clusterings, Multi-view Data, and Multi-source Knowledge-driven Clustering
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Previous studies of Non-Parametric Kernel (NPK) learning usually reduce to solving some Semi-Definite Programming (SDP) problem by a standard SDP solver. However, time complexity of standard interior-point SDP solvers could be as high as O(n6.5). Such intensive computation cost prohibits NPK learning applicable to real applications, even for data sets of moderate size. In this paper, we propose an efficient approach to NPK learning from side information, referred to as SimpleNPKL, which can efficiently learn non-parametric kernels from large sets of pairwise constraints. In particular, we show that the proposed SimpleNPKL with linear loss has a closed-form solution that can be simply computed by the Lanczos algorithm. Moreover, we show that the SimpleNPKL with square hinge loss can be re-formulated as a saddle-point optimization task, which can be further solved by a fast iterative algorithm. In contrast to the previous approaches, our empirical results show that our new technique achieves the same accuracy, but is significantly more efficient and scalable.