The nature of statistical learning theory
The nature of statistical learning theory
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Machine Learning
A Tutorial on Support Vector Machines for Pattern Recognition
Data Mining and Knowledge Discovery
Large scale genomic sequence SVM classifiers
ICML '05 Proceedings of the 22nd international conference on Machine learning
Learning Bounds for Kernel Regression Using Effective Data Dimensionality
Neural Computation
Statistical properties of kernel principal component analysis
Machine Learning
Accurate Error Bounds for the Eigenvalues of the Kernel Matrix
The Journal of Machine Learning Research
Structural risk minimization over data-dependent hierarchies
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
On the eigenspectrum of the gram matrix and the generalization error of kernel-PCA
IEEE Transactions on Information Theory
Input space versus feature space in kernel-based methods
IEEE Transactions on Neural Networks
An introduction to kernel-based learning algorithms
IEEE Transactions on Neural Networks
The Journal of Machine Learning Research
Colored subspace analysis: dimension reduction based on a signal's autocorrelation structure
IEEE Transactions on Circuits and Systems Part I: Regular Papers
A Cure for Variance Inflation in High Dimensional Kernel Principal Component Analysis
The Journal of Machine Learning Research
TAKES: a fast method to select features in the kernel space
Proceedings of the 20th ACM international conference on Information and knowledge management
Kernel Analysis of Deep Networks
The Journal of Machine Learning Research
Non-sparse multiple kernel fisher discriminant analysis
The Journal of Machine Learning Research
Security analysis of online centroid anomaly detection
The Journal of Machine Learning Research
Kernelizing the proportional odds model through the empirical kernel mapping
IWANN'13 Proceedings of the 12th international conference on Artificial Neural Networks: advances in computational intelligence - Volume Part I
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We show that the relevant information of a supervised learning problem is contained up to negligible error in a finite number of leading kernel PCA components if the kernel matches the underlying learning problem in the sense that it can asymptotically represent the function to be learned and is sufficiently smooth. Thus, kernels do not only transform data sets such that good generalization can be achieved using only linear discriminant functions, but this transformation is also performed in a manner which makes economical use of feature space dimensions. In the best case, kernels provide efficient implicit representations of the data for supervised learning problems. Practically, we propose an algorithm which enables us to recover the number of leading kernel PCA components relevant for good classification. Our algorithm can therefore be applied (1) to analyze the interplay of data set and kernel in a geometric fashion, (2) to aid in model selection, and (3) to denoise in feature space in order to yield better classification results.