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Learning with Uncertain kernel matrix Set

Journal of Computer Science & Technology 2010年第4期25卷 709-727页

作者：贾磊廖士中丁立中 School of Computer Science and Technology Tianjin University

We study support vector machines （SVM） for which the kernel matrix is not specified exactly and it is only known to belong to a given uncertainty set. We consider uncertainties that arise from two sources：（i） data measurement uncertainty, which stems from the statistical errors of input samples; （ii） kernel combination uncertainty, which stems from the weight of individual kernel that needs to be optimized in multiple kernel learning （MKL） problem. Much work has been studied, such as uncertainty sets that allow the corresponding SVMs to be reformulated as semi-definite programs （SDPs）, which is very computationally expensive however. Our focus in this paper is to identify uncertainty sets that allow the corresponding SVMs to be reformulated as second-order cone programs （SOCPs）, since both the worst case complexity and practical computational effort required to solve SOCPs is at least an order of magnitude less than that needed to solve SDPs of comparable size. In the main part of the paper we propose four uncertainty sets that meet this criterion. Experimental results are presented to confirm the validity of these SOCP reformulations.

关键词： support vector machine kernel matrix uncertainty second-order cone program

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On the Construction of the kernel matrix by Primitive BCH Codes for Polar Codes

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Communications and Network 2022年第1期14卷 23-35页

作者： Liping Lin College of Cyber Security Jinan University Guangzhou China

The polar codes defined by the kernel matrix are a class of codes with low coding-decoding complexity and can achieve the Shannon limit. In this paper, a novel method to construct the 2n-dimensional kernel matrix is proposed, that is based on primitive BCH codes that make use of the interception, the direct sum and adding a row and a column. For ensuring polarization of the kernel matrix, a solution is also put forward when the partial distances of the constructed kernel matrix exceed their upper bound. And the lower bound of exponent of the 2n-dimensional kernel matrix is obtained. The lower bound of exponent of our constructed kernel matrix is tighter than Gilbert-Varshamov (G-V) type, and the scaling exponent is better in the case of 16-dimensional.

关键词： Polar Code kernel matrix matrix Interception Partial Distance Exponent Scaling Exponent

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Unsupervised Nonlinear Adaptive Manifold Learning for Global and Local Information

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Tsinghua Science and Technology 2021年第2期26卷 163-171页

作者： Jiajun Gao Fanzhang Li Bangjun Wang Helan Liang School of Computer Science and Technology Soochow UniversitySuzhou 215006China Joint International Research Laboratory of Machine Learning and Neuromorphic Computing Provincial Key Laboratory for Computer Information Processing TechnologySoochow UniversitySuzhou 215006China

In this paper,we propose an Unsupervised Nonlinear Adaptive Manifold Learning method(UNAML)that considers both global and local *** this approach,we apply unlabeled training samples to study nonlinear manifold features,while considering global pairwise distances and maintaining local topology *** method aims at minimizing global pairwise data distance errors as well as local structural *** order to enable our UNAML to be more efficient and to extract manifold features from the external source of new data,we add a feature approximate error that can be used to learn a linear ***,we add a feature approximate error that can be used to learn a linear *** addition,we use a method of adaptive neighbor selection to calculate local structural *** paper uses the kernel matrix method to optimize the original *** algorithm proves to be more effective when compared with the experimental results of other feature extraction methods on real face-data sets and object data sets.

关键词： unsupervised manifold learning global and local information,adaptive neighbor selection method kernel matrix

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A centrality measure based on spectral optimization of modularity density

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Science China(Information Sciences) 2010年第9期53卷 1727-1737页

作者： FU LiDong1,2*,GAO Lin1 & MA XiaoKe1 1School of Computer Science and Engineering,Xidian University,Xi'an 710071,China 2College of Computer,Xi'an University of Science and Technology,Xi'an 710054,China School of Computer Science and Engineering Xidian University Xi’an China College of Computer Xi’an University of Science and Technology Xi’an China

Centrality analysis has been shown to be a valuable method for the structural analysis of complex *** is used to identify key elements within networks and to rank network elements such that experiments can be tailored to interesting *** this paper,we show that the optimization process of modularity density can be written in terms of the eigenspectrum of kernel *** on the eigenvectors belonging to the largest eigenvalue of kernel matrix,we present a new centrality measure that characterizes the contribution of each node to its assigned community in a network,called modularity density *** measure is illustrated and compared with the standard centrality measures by using respectively an artificial example and a classic network data *** statistical distribution of modularity density centrality is investigated by considering large computer generated graphs and two large networks from the real *** results show the significance of the proposed approach.

关键词： centrality modularity density centrality kernel matrix eigenspectrum

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