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- Ding-Xuan Zhou

Discipline name
H-index
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
39
Citations
6,606
126
World Ranking
1065
National Ranking
52

- Mathematical analysis
- Statistics
- Machine learning

His primary areas of study are Reproducing kernel Hilbert space, Discrete mathematics, Kernel embedding of distributions, Applied mathematics and Kernel. As a member of one scientific family, Ding-Xuan Zhou mostly works in the field of Reproducing kernel Hilbert space, focusing on Polynomial kernel and, on occasion, Regularization perspectives on support vector machines. His Discrete mathematics research includes themes of Function, Invariant subspace, Spectral radius and Hilbert space.

His study in Applied mathematics is interdisciplinary in nature, drawing from both Probability distribution and Uniform convergence. His Kernel course of study focuses on Regularization and Disjoint sets, Eigenfunction, Polynomial, Statistical classification and Round-off error. As a part of the same scientific study, Ding-Xuan Zhou usually deals with the Kernel method, concentrating on Sample and frequently concerns with Algorithm and Mathematical optimization.

- Learning Theory: An Approximation Theory Viewpoint (447 citations)
- Learning Theory Estimates via Integral Operators and Their Approximations (431 citations)
- The covering number in learning theory (262 citations)

The scientist’s investigation covers issues in Applied mathematics, Mathematical analysis, Reproducing kernel Hilbert space, Mathematical optimization and Algorithm. His research investigates the connection with Applied mathematics and areas like Empirical risk minimization which intersect with concerns in Lipschitz continuity and Deep learning. His Mathematical analysis research includes elements of Wavelet, Pure mathematics and Joint spectral radius.

His Reproducing kernel Hilbert space research is multidisciplinary, incorporating perspectives in Function, Kernel embedding of distributions and Discrete mathematics. Ding-Xuan Zhou usually deals with Mathematical optimization and limits it to topics linked to Learning theory and Algorithmic learning theory. His work investigates the relationship between Algorithm and topics such as Support vector machine that intersect with problems in Probability distribution.

- Applied mathematics (24.10%)
- Mathematical analysis (23.59%)
- Reproducing kernel Hilbert space (21.03%)

- Artificial intelligence (12.82%)
- Deep learning (7.69%)
- Algorithm (17.44%)

His primary areas of investigation include Artificial intelligence, Deep learning, Algorithm, Artificial neural network and Learning theory. The various areas that Ding-Xuan Zhou examines in his Algorithm study include Semi-supervised learning, Stochastic gradient descent, Kernel, Support vector machine and Gradient descent. The Kernel study combines topics in areas such as Regularization, Hilbert space, Applied mathematics and Probability measure.

His work on Polynomial kernel is typically connected to Bottleneck as part of general Support vector machine study, connecting several disciplines of science. The concepts of his Learning theory study are interwoven with issues in Kaczmarz method, Linear system and Rotation. His Smoothness study integrates concerns from other disciplines, such as Discrete mathematics and Combinatorics.

- Universality of deep convolutional neural networks (86 citations)
- Distributed Kernel-Based Gradient Descent Algorithms (45 citations)
- Towards Understanding the Spectral Bias of Deep Learning (41 citations)

- Mathematical analysis
- Statistics
- Machine learning

Ding-Xuan Zhou mostly deals with Artificial intelligence, Deep learning, Artificial neural network, Algorithm and Convolutional neural network. The study incorporates disciplines such as Semi-supervised learning, Kernel, Gradient descent, Computational learning theory and Loss functions for classification in addition to Algorithm. The various areas that Ding-Xuan Zhou examines in his Semi-supervised learning study include Empirical risk minimization, Hinge loss, Reproducing kernel Hilbert space, Regularization perspectives on support vector machines and Kernel embedding of distributions.

His study looks at the intersection of Kernel and topics like Kernel with Rate of convergence. Many of his studies involve connections with topics such as Discrete mathematics and Rate of convergence. Within one scientific family, Ding-Xuan Zhou focuses on topics pertaining to Approximation theory under Convolutional neural network, and may sometimes address concerns connected to Operator.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Learning Theory: An Approximation Theory Viewpoint

Felipe Cucker;Ding Xuan Zhou.

**(2007)**

679 Citations

Learning Theory Estimates via Integral Operators and Their Approximations

Steve Smale;Ding-Xuan Zhou.

Constructive Approximation **(2007)**

550 Citations

The covering number in learning theory

Ding-Xuan Zhou.

Journal of Complexity **(2002)**

390 Citations

Shannon sampling and function reconstruction from point values

Steve Smale;Ding-Xuan Zhou.

Bulletin of the American Mathematical Society **(2004)**

335 Citations

ESTIMATING THE APPROXIMATION ERROR IN LEARNING THEORY

Steve Smale;Ding-Xuan Zhou.

Analysis and Applications **(2003)**

323 Citations

Capacity of reproducing kernel spaces in learning theory

Ding-Xuan Zhou.

IEEE Transactions on Information Theory **(2003)**

318 Citations

Support Vector Machine Soft Margin Classifiers: Error Analysis

Di-Rong Chen;Qiang Wu;Yiming Ying;Ding-Xuan Zhou.

Journal of Machine Learning Research **(2004)**

269 Citations

Learning Rates of Least-Square Regularized Regression

Qiang Wu;Yiming Ying;Ding-Xuan Zhou.

Foundations of Computational Mathematics **(2006)**

253 Citations

Shannon sampling II: Connections to learning theory

Steve Smale;Ding-Xuan Zhou.

Applied and Computational Harmonic Analysis **(2005)**

248 Citations

Learning Theory: An Approximation Theory Viewpoint (Cambridge Monographs on Applied & Computational Mathematics)

Felipe Cucker;Ding Xuan Zhou.

**(2007)**

213 Citations

Mathematical Foundations of Computing

Analysis and Applications

(Impact Factor: 1.956)

Journal of Complexity

(Impact Factor: 1.333)

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