A review of Nyström methods for large-scale machine learning

Sun, Shiliang; Zhao, Jing; Zhu, Jiang

doi:10.1016/j.inffus.2015.03.001

Cited by 52 publications

(38 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Subsequently, it has been successfully employed for approximating the eigenvalues and eigenvectors of positive semi-definite matrices for kernel-based learning [16], [17], [18]. The standard Nyström method exploits a sub-matrix of the original kernel matrix K in order to determine its low-rank approximation.…”

Section: A Methods Exploiting Low-rank a Approximation Of Kmentioning

confidence: 99%

A review of approximate methods for kernel-based big media data analysis

Iosifidis

Tefas

Pitas

et al. 2016

2016 24th European Signal Processing Conference (EUSIPCO)

View full text Add to dashboard Cite

General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Abstract-With the increasing size of today's image and video data sets, standard pattern recognition approaches, like kernel based learning, need to face new challenges. Kernel-based methods require the storage and manipulation of the kernel matrix, having dimensions equal to the number of training samples. When the data set cardinality becomes large, the application of kernel methods becomes intractable. Approximate kernel-based learning approaches have been proposed in order to reduce the time and space complexities of kernel methods, while achieving satisfactory performance. In this paper, we provide a overview of such approximate kernel-based learning approaches finding application in media data analysis.

show abstract

Section: A Methods Exploiting Low-rank a Approximation Of Kmentioning

confidence: 99%

A review of approximate methods for kernel-based big media data analysis

Iosifidis

Tefas

Pitas

et al. 2016

2016 24th European Signal Processing Conference (EUSIPCO)

View full text Add to dashboard Cite

show abstract

“…It is of note that uniform sampling was adopted when the standard Nyström method was introduced [28]. It is a widely applied sampling method due to its low time consumption [26]. b) Random features approximation [20]: It computes a low-dimensional feature mapφ of dimension q such that φ (·),φ(·) =k(·, ·) k(·, ·).…”

Section: Background On Kernel Approximationmentioning

confidence: 99%

Deep Networks with Adaptive Nyström Approximation

Giffon

Ayache

Artières

et al. 2019

2019 International Joint Conference on Neural Networks (IJCNN)

View full text Add to dashboard Cite

Recent work has focused on combining kernel methods and deep learning to exploit the best of the two approaches. Here, we introduce a new architecture of neural networks in which we replace the top dense layers of standard convolutional architectures with an approximation of a kernel function by relying on the Nyström approximation. Our approach is easy and highly flexible. It is compatible with any kernel function and it allows exploiting multiple kernels. We show that our architecture has the same performance than standard architecture on datasets like SVHN and CIFAR100. One benefit of the method lies in its limited number of learnable parameters which makes it particularly suited for small training set sizes, e.g. from 5 to 20 samples per class.

show abstract

“…One evaluation of u k (x) requires sampling only one value of u k and the resulting eigenfunction is a discontinuous step function in physical space. The accuracy of u k (x) is improved by evaluation using an interpolating function provided in the Nyström method theory [10,11]:…”

Section: Numerical Solution Of the Kl Eigenspectrummentioning

confidence: 99%

Radiation Transport in Random Media With Large Fluctuations

2017

View full text Add to dashboard Cite

Neutral particle transport in media exhibiting large and complex material property spatial variation is modeled by representing cross sections as lognormal random functions of space and generated through a nonlinear memory-less transformation of a Gaussian process with covariance uniquely determined by the covariance of the cross section. A Karhunen-Loève decomposition of the Gaussian process is implemented to efficiently generate realizations of the random cross sections and Woodcock Monte Carlo used to transport particles on each realization and generate benchmark solutions for the mean and variance of the particle flux as well as probability densities of the particle reflectance and transmittance. A computationally efficient stochastic collocation method is implemented to directly compute the statistical moments such as the mean and variance, while a polynomial chaos expansion in conjunction with stochastic collocation provides a convenient surrogate model that also produces probability densities of output quantities of interest. Extensive numerical testing demonstrates that use of stochastic reduced-order modeling provides an accurate and cost-effective alternative to random sampling for particle transport in random media.

show abstract

A review of Nyström methods for large-scale machine learning

Cited by 52 publications

References 41 publications

A review of approximate methods for kernel-based big media data analysis

A review of approximate methods for kernel-based big media data analysis

Deep Networks with Adaptive Nyström Approximation

Radiation Transport in Random Media With Large Fluctuations

Contact Info

Product

Resources

About