Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Kernel Matrix Completion by Semidefinite Programming
ICANN '02 Proceedings of the International Conference on Artificial Neural Networks
The Journal of Machine Learning Research
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
Learning the Kernel Function via Regularization
The Journal of Machine Learning Research
Generalized Discriminant Analysis Using a Kernel Approach
Neural Computation
Automatic basis function construction for approximate dynamic programming and reinforcement learning
ICML '06 Proceedings of the 23rd international conference on Machine learning
Learning sparse metrics via linear programming
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Fast solvers and efficient implementations for distance metric learning
Proceedings of the 25th international conference on Machine learning
Consistency of Trace Norm Minimization
The Journal of Machine Learning Research
Convex multi-task feature learning
Machine Learning
Kernel Regression with a Mahalanobis Metric for Short-Term Traffic Flow Forecasting
IDEAL '08 Proceedings of the 9th International Conference on Intelligent Data Engineering and Automated Learning
Distance Metric Learning for Large Margin Nearest Neighbor Classification
The Journal of Machine Learning Research
Semi-Supervised Multi-Task Regression
ECML PKDD '09 Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases: Part II
GSML: A Unified Framework for Sparse Metric Learning
ICDM '09 Proceedings of the 2009 Ninth IEEE International Conference on Data Mining
Joint covariate selection and joint subspace selection for multiple classification problems
Statistics and Computing
Nonlinear Combination of Multiple Kernels for Support Vector Machines
ICPR '10 Proceedings of the 2010 20th International Conference on Pattern Recognition
Sparse kernel regression for traffic flow forecasting
ISNN'11 Proceedings of the 8th international conference on Advances in neural networks - Volume Part II
The Selective Random Subspace Predictor for Traffic Flow Forecasting
IEEE Transactions on Intelligent Transportation Systems
Graph-Based Semi-Supervised Learning and Spectral Kernel Design
IEEE Transactions on Information Theory
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Kernel regression is a popular non-parametric fitting technique. It aims at learning a function which estimates the targets for test inputs as precise as possible. Generally, the function value for a test input is estimated by a weighted average of the surrounding training examples. The weights are typically computed by a distance-based kernel function and they strongly depend on the distances between examples. In this paper, we first review the latest developments of sparse metric learning and kernel regression. Then a novel kernel regression method involving sparse metric learning, which is called kernel regression with sparse metric learning KR_SML, is proposed. The sparse kernel regression model is established by enforcing a mixed 2,1-norm regularization over the metric matrix. It learns a Mahalanobis distance metric by a gradient descent procedure, which can simultaneously conduct dimensionality reduction and lead to good prediction results. Our work is the first to combine kernel regression with sparse metric learning. To verify the effectiveness of the proposed method, it is evaluated on 19 data sets for regression. Furthermore, the new method is also applied to solving practical problems of forecasting short-term traffic flows. In the end, we compare the proposed method with other three related kernel regression methods on all test data sets under two criterions. Experimental results show that the proposed method is much more competitive.