Applied numerical linear algebra
Applied numerical linear algebra
Convex Optimization
Learning the Kernel Matrix with Semidefinite Programming
The Journal of Machine Learning Research
Local Discriminant Embedding and Its Variants
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Local Fisher discriminant analysis for supervised dimensionality reduction
ICML '06 Proceedings of the 23rd international conference on Machine learning
Graph Embedding and Extensions: A General Framework for Dimensionality Reduction
IEEE Transactions on Pattern Analysis and Machine Intelligence
Learning Spectral Clustering, With Application To Speech Separation
The Journal of Machine Learning Research
Optimal dimensionality of metric space for classification
Proceedings of the 24th international conference on Machine learning
KPCA for semantic object extraction in images
Pattern Recognition
Preconditioning, randomization, solving linear systems, eigen-solving, and root-finding
Proceedings of the 2009 conference on Symbolic numeric computation
An efficient algorithm for local distance metric learning
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Link analysis, eigenvectors and stability
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 2
Generalized KPCA by adaptive rules in feature space
International Journal of Computer Mathematics
Discriminant Locally Linear Embedding With High-Order Tensor Data
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Effective Feature Extraction in High-Dimensional Space
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Regression on Fixed-Rank Positive Semidefinite Matrices: A Riemannian Approach
The Journal of Machine Learning Research
Effective diagnosis of Alzheimer's disease by means of distance metric learning and random forest
IWINAC'11 Proceedings of the 4th international conference on Interplay between natural and artificial computation: new challenges on bioinspired applications - Volume Part II
Effective diagnosis of alzheimer's disease by means of distance metric learning
HAIS'11 Proceedings of the 6th international conference on Hybrid artificial intelligent systems - Volume Part I
Metric and kernel learning using a linear transformation
The Journal of Machine Learning Research
Twin Mahalanobis distance-based support vector machines for pattern recognition
Information Sciences: an International Journal
Shape classification by manifold learning in multiple observation spaces
Information Sciences: an International Journal
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This paper focuses on developing a new framework of kernelizing Mahalanobis distance learners. The new KPCA trick framework offers several practical advantages over the classical kernel trick framework, e.g. no mathematical formulas and no reprogramming are required for a kernel implementation, a way to speed up an algorithm is provided with no extra work, the framework avoids troublesome problems such as singularity. Rigorous representer theorems in countably infinite dimensional spaces are given to validate our framework. Furthermore, unlike previous works which always apply brute force methods to select a kernel, we derive a kernel alignment formula based on quadratic programming which can efficiently construct an appropriate kernel for a given dataset.