An efficient kernel matrix evaluation measure

Nguyen, Canh Hao; Ho, Tu Bao

doi:10.1016/j.patcog.2008.04.005

Cited by 51 publications

(23 citation statements)

References 3 publications

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“…Another technique is the feature space-based kernel matrix (FSM) evaluation measure [37]. Both KTA and FSM, however, may not work well for small sample sizes and have a tendency of overfitting [38].…”

Section: Other More General Methods For Estimating σmentioning

confidence: 99%

Cross-validatory framework for optimal parameter estimation of KPCA and KPLS models

Krüger

et al. 2017

Chemometrics and Intelligent Laboratory Systems

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Section: Other More General Methods For Estimating σmentioning

confidence: 99%

Cross-validatory framework for optimal parameter estimation of KPCA and KPLS models

Krüger

et al. 2017

Chemometrics and Intelligent Laboratory Systems

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“…This is because the formulation of the ideal kernel often requires a large set of labeled examples. Furthermore, it has been shown in [62] that it is possible for a kernel function to have a low alignment measure for a particular dataset and still run well for that dataset. Therefore, a new measure of kernel alignment is devised in [62] based on the distribution of data in the feature space.…”

Section: Kernel Alignment Measurementioning

confidence: 99%

A survey of the state of the art in learning the kernels

2011

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In recent years, the machine learning community has witnessed a tremendous growth in the development of kernel-based learning algorithms. However, the performance of this class of algorithms greatly depends on the choice of the kernel function. Kernel function implicitly represents the inner product between a pair of points of a dataset in a higher dimensional space. This inner product amounts to the similarity between points and provides a solid foundation for nonlinear analysis in kernel-based learning algorithms. The most important challenge in kernel-based learning is the selection of an appropriate kernel for a given dataset. To remedy this problem, algorithms to learn the kernel have recently been proposed. These methods formulate a learning algorithm that finds an optimal kernel for a given dataset. In this paper, we present an overview of these algorithms and provide a comparison of various approaches to find an optimal kernel. Furthermore, a list of pivotal issues that lead to efficient design of such algorithms will be presented.

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“…Previous "filter" based kernel matrix learning algorithm can tackle the scaling variation (K' u = tK u (t > 0)), but the translation variance could not be considered. KTA is invariant to scaling problem, but as (Nguyen and Ho, 2008) points out, KTA is not invariant under data translation in the feature space. (He, Chang and Xie, 2008) normalizes the sub-kernel K u by dividing K u by the largest absolute value of K u .…”

Section: Kernel Normalizationmentioning

confidence: 99%

Learning to Combine Kernels for Object Categorization

Zhang¹,

Liu²,

Sun³

et al. 2011

CIS

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Kernel classifiers based on the hand-crafted image descriptors proposed in the literature have achieved state-of-the-art results in several dataset and been widely used in image classification systems. Due to the high intra-class and inter-class variety of image categories, no single descriptor could be optimal in all situations. Combining multiple descriptors for a given task is a way to improve the accuracy of the image classification systems. In this paper, we propose a filter framework "Learning to Align the Kernel to its Ideal Form(LAKIF)" to automatically learn the optimal linear combination of multiple kernels. Given the image dataset and the kernels computed on the image descriptors, the optimal kernel weight is learned before the classification. Our method effectively learns the kernel weights by aligning the kernels to their ideal forms, leading to quadratic programming solution. The method takes into account the variation of kernel matrix and imbalanced dataset, which are common in real world image categorization tasks. Experimental results on Graz-01 and Caltech-101 image databases show the effectiveness and robustness of our method.

show abstract

An efficient kernel matrix evaluation measure

Cited by 51 publications

References 3 publications

Cross-validatory framework for optimal parameter estimation of KPCA and KPLS models

Cross-validatory framework for optimal parameter estimation of KPCA and KPLS models

A survey of the state of the art in learning the kernels

Learning to Combine Kernels for Object Categorization

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