Open AccessProceedings Article
Data centering in feature space.
Marina Meila
- 03 Jan 2003
- pp 209-216
TL;DR: In this paper, a family of methods for data translation in feature space, to be used in conjunction with kernel machines, is presented, where the translations are performed using only kernel evaluations in input space.
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Abstract: This paper presents a family of methods for data translation in feature space, to be used in conjunction with kernel machines. The translations are performed using only kernel evaluations in input space. We use the methods to improve the numerical properties of kernel machines. Experiments with synthetic and real data demonstrate the effectivenes of data centering and highlight other interesting aspects of translation in feature space.
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Citations
•Journal Article
Algorithms for learning kernels based on centered alignment
TL;DR: The notion of centered alignment has been used as a similarity measure between kernels or kernel matrices as mentioned in this paper, which has been shown to consistently outperform the so-called uniform combination solution that has proven to be difficult to improve upon in the past.
Multiple kernel clustering based on centered kernel alignment
TL;DR: This paper proposes a novel MKC method that is different from those popular approaches, and an efficient two-step iterative algorithm is developed to solve the formulated optimization problem.
107
An efficient kernel matrix evaluation measure
Canh Hao Nguyen,Tu Bao Ho +1 more
TL;DR: This work proposes an efficient surrogate measure to evaluate the goodness of a kernel matrix based on the data distributions of classes in the feature space that not only overcomes the limitations of KTA but also possesses other properties like invariance, efficiency and an error bound guarantee.
61
•Proceedings Article
Kernel matrix evaluation
Canh Hao Nguyen,Tu Bao Ho +1 more
- 06 Jan 2007
TL;DR: This work proposes an efficient surrogate measure to evaluate the goodness of a kernel matrix based on the data distributions of classes in the feature space that not only overcomes the limitations of KTA, but also possesses other properties like invariance, efficiency and error bound guarantee.
Patent
Method of using kernel alignment to extract significant features from a large dataset
Nello Cristianini
- 12 Sep 2005
TL;DR: The spectral kernel machine as mentioned in this paper combines kernel functions and spectral graph theory for solving problems of machine learning, where data points in the dataset are placed in the form of a matrix known as a kernel matrix, or Gram matrix, containing all pairwise kernels between the data points.
24
References
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Chih-Chung Chang,Chih-Jen Lin +1 more
TL;DR: Issues such as solving SVM optimization problems theoretical convergence multiclass classification probability estimates and parameter selection are discussed in detail.
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Corinna Cortes,Vladimir Vapnik +1 more
TL;DR: High generalization ability of support-vector networks utilizing polynomial input transformations is demonstrated and the performance of the support- vector network is compared to various classical learning algorithms that all took part in a benchmark study of Optical Character Recognition.
Nonlinear component analysis as a kernel eigenvalue problem
TL;DR: A new method for performing a nonlinear form of principal component analysis by the use of integral operator kernel functions is proposed and experimental results on polynomial feature extraction for pattern recognition are presented.
Estimating the Support of a High-Dimensional Distribution
TL;DR: In this paper, the authors propose a method to estimate a function f that is positive on S and negative on the complement of S. The functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data; it is regularized by controlling the length of the weight vector in an associated feature space.
New Support Vector Algorithms
TL;DR: A new class of support vector algorithms for regression and classification that eliminates one of the other free parameters of the algorithm: the accuracy parameter in the regression case, and the regularization constant C in the classification case.
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