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作者：张建军江南大学

学位级别：硕士

21世纪我们进入了信息时代,随之而来的高维数据越来越多。由于这些高维数据中存在很多冗余信息,或者我们只关心数据中的一部分重要的特征信息。此时对数据进行降维也越发地重要。同时,在对有类别标签的高维数据进行降维的时候,对降维的... 详细信息

21世纪我们进入了信息时代,随之而来的高维数据越来越多。由于这些高维数据中存在很多冗余信息,或者我们只关心数据中的一部分重要的特征信息。此时对数据进行降维也越发地重要。同时,在对有类别标签的高维数据进行降维的时候,对降维的要求也就更高,在提取数据集中重要属性信息的同时,要保证数据集的类别属性。由于环境的不可预知性,采集,保存,流通过程中,数据集或多或少的惨入了噪声,噪声的引入给降维的工作带来很大的不便,得到的结果也有很大的偏差。当然可以先利用各种去除噪音的方法先对数据集进行预处理,但是考量一个降维与分类算法的重要方面是看算法的抗造性能。普通的降维分类算法如PCA,lPP等都使用利用数据点之间的距离平方来度量数据点的相似度,放大了噪音点对降维结果的影响,l1-norm则采用了绝对值距离,不会放大噪音的影响。本文研究了l1-norm的一般特点,然后改进现有的降维算法,通过一系列的实验对这算法的抗噪性进行验证,实验证明,经过l1-norm改进后的降维算法与传统的降维算法相比,抗噪性能都有了较大程度的提高。同时,不仅仅只在降维的时候要考虑噪声的影响。在模糊聚类领域,通常能够将数据点到聚类中心点的距离作为衡量该点属于哪一类的重要指标,然而通常的聚类算法都使用的是欧式距离,由于欧式距离对噪声敏感的原因,我们可以利用对噪声不敏感的距离进行组合作为样本间的相似度量度,这样不仅可以在对样本集结构缺乏了解的情况下,对数据集进行有效的聚类,而且具有抗噪性。同样,我们发现在分类领域里,尤其是在迁移学习中,抗噪同样很值得研究。数据集随着时间的改变而不断地发生着微小的改变,对变化后的数据集进行分类的时候,如果这个微小的改变正是变化在最优分割面附近的话,分类的向量会发生很大变化,这样的结果显然是不合理的。本文提出了ESVM算法,在对缓慢变化后的数据集进行分类的时候,考虑到原来数据集的概率分布信息,使得分类结果在分类合理的情况下,有效地继承原数据集的经验,分割面不会变化很大,从而在一定程度上,体现了ESVM算法的抗噪性能。

关键词：降维分类聚类迁移学习抗噪 l1-norm 绝对值距离

ASYMPTOTICS OF THE “MINIMUM l_1-norm”ESTIMATES IN A PARTlY lINEAR MODEl

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Systems Science and Mathematical Sciences 1994年第1期7卷 67-77页

作者： SHI Peide lI Guoying(Institute of Systems Science, Academia Sinica, Beijing 100080, China) 中科院系统科学所北京

ＡＳＹＭＰＴＯＴＩＣＳＯＦＴＨＥ“ＭＩＮＩＭＵＭＬ＿１－ＮＯＲＭ”ＥＳＴＩＭＡＴＥＳＩＮＡＰＡＲＴＬＹＬＩＮＥＡＲＭＯＤＥＬ￥ＳＨＩＰｅｉｄｅ；ＬＩＧｕｏｙｉｎｇ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，... 详细信息

ＡＳＹＭＰＴＯＴＩＣＳＯＦＴＨＥ“ＭＩＮＩＭＵＭＬ＿１－ＮＯＲＭ”ＥＳＴＩＭＡＴＥＳＩＮＡＰＡＲＴＬＹＬＩＮＥＡＲＭＯＤＥＬ￥ＳＨＩＰｅｉｄｅ；ＬＩＧｕｏｙｉｎｇ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅ...

关键词： Partly linear model global rate of convergence piecewise polynomial, l1-norm estimates.

ROBUST NONPARAMETRIC REGRESSION BASED ON l_1-norm AND B-SPlINES

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Systems Science and Mathematical Sciences 1995年第2期8卷 187-192页

作者： SHI Peide(Department of Probability and Statistics, Peking University, Beijing 100871,China)ZHANG Zhengjun(School Of Management,Beijing University of Aeronautics and Astronautics,Beijing 100083, China) 北京大学概率统计系北京北京航空航天大学管理学院北京

ＲＯＢＵＳＴＮＯＮＰＡＲＡＭＥＴＲＩＣＲＥＧＲＥＳＳＩＯＮＢＡＳＥＤＯＮＬ＿１－ＮＯＲＭＡＮＤＢ－ＳＰＬＩＮＥＳＳＨＩＰｅｉｄｅ（ＤｅｐａｒｔｍｅｎｔｏｆＰｒｏｂａｂｉｌｉｔｙａｎｄＳｔａｔｉｓｔｉｃｓ，Ｐｅｋｉｎｇ... 详细信息

ＲＯＢＵＳＴＮＯＮＰＡＲＡＭＥＴＲＩＣＲＥＧＲＥＳＳＩＯＮＢＡＳＥＤＯＮＬ＿１－ＮＯＲＭＡＮＤＢ－ＳＰＬＩＮＥＳＳＨＩＰｅｉｄｅ（ＤｅｐａｒｔｍｅｎｔｏｆＰｒｏｂａｂｉｌｉｔｙａｎｄＳｔａｔｉｓｔｉｃｓ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎ...

关键词： B-spline function l1-norm estimator TURBO nonparametric regression

A NEURAl-BASED NONlINEAR l_1-norm OPTIMIZATION AlGORITHM FOR DIAGNOSIS OF NETWORKS*

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Journal of Electronics(China) 1998年第4期15卷 365-371页

作者： He Yigang (Department of Electrical Engineering, Hunan University, Changsha 410082)luo Xianjue Qiu Guanyuan(School of Electrical Engineering, Xi’an Jiaotong University, Xi’an 710049)

Based on exact penalty function, a new neural network for solving the l1-norm optimization problem is proposed. In comparison with Kennedy and Chua’s network(1988), it has better *** on Bandler’s fault location method(1982), a new nonlinearly constrained l1-norm problem is developed. It can be solved with less computing time through only one optimization processing. The proposed neural network can be used to solve the analog diagnosis l1 problem. The validity of the proposed neural networks and the fault location l1 method are illustrated by extensive computer simulations.

关键词： Fault diagnosis l1-norm Neural optimization

Association RuleMining Frequent-Pattern-Based Intrusion Detection in Network

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Computer Systems Science & Engineering 2023年第2期44卷 1617-1631页

作者： S.Sivanantham V.Mohanraj Y.Suresh J.Senthilkumar Department of Information Technology Adhiyamaan College of EngineeringHosurTamilnaduIndia Department of Information Technology Sona College of TechnologySalemTamilnaduIndia

In the network security system,intrusion detection plays a signiﬁcant *** network security system detects the malicious actions in the network and also conforms the availability,integrity and conﬁdentiality of data informa-tion *** identiﬁcation system can easily detect the false positive *** large number of false positive alerts are created then it makes intrusion detection system as difﬁcult to differentiate the false positive alerts from genuine *** research works have been *** issues in the existing algo-rithms are more memory space and need more time to execute the transactions of *** paper proposes a novel framework of network security Intrusion Detection System(IDS)using Modiﬁed Frequent Pattern(MFP-Tree)via K-means *** accuracy rate of Modiﬁed Frequent Pattern Tree(MFPT)-K means method inﬁnding the various attacks are normal 94.89%,for DoS based attack 98.34%,for User to Root(U2R)attacks got 96.73%,Remote to local(R2l)got 95.89%and Probe attack got 92.67%and is optimal when it is compared with other existing algorithms of K-Means and APRIORI.

关键词： IDS K-means frequent pattern tree false alert mining l1-norm

Robust latent Factor Analysis for Precise Representation of High-Dimensional and Sparse Data

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IEEE/CAA Journal of Automatica Sinica 2021年第4期8卷 796-805页

作者： Di Wu Xin luo the Chongqing Key laboratory of Big Data and Intelligent Computing Chongqing Institute of Green and Intelligent TechnologyChinese Academy of SciencesChongqing 400714 the Chongqing School University of Chinese Academy of SciencesChongqing 400714China

High-dimensional and sparse(HiDS)matrices commonly arise in various industrial applications,e.g.,recommender systems(RSs),social networks,and wireless sensor *** they contain rich information,how to accurately represent them is of great significance.A latent factor(lF)model is one of the most popular and successful ways to address this *** lF models mostly adopt l2-norm-oriented loss to represent an HiDS matrix,i.e.,they sum the errors between observed data and predicted ones with *** l2-norm is sensitive to outlier ***,outlier data usually exist in such *** example,an HiDS matrix from RSs commonly contains many outlier ratings due to some heedless/malicious *** address this issue,this work proposes a smooth l1-norm-oriented latent factor(Sl-lF)*** main idea is to adopt smooth l1-norm rather than l2-norm to form its loss,making it have both strong robustness and high accuracy in predicting the missing data of an HiDS *** results on eight HiDS matrices generated by industrial applications verify that the proposed Sl-lF model not only is robust to the outlier data but also has significantly higher prediction accuracy than state-of-the-art models when they are used to predict the missing data of HiDS matrices.

关键词： High-dimensional and sparse matrix l1-norm l2 norm latent factor model recommender system smooth l1-norm

Feature selection for probabilistic load forecasting via sparse penalized quantile regression

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Journal of Modern Power Systems and Clean Energy 2019年第5期7卷 1200-1209页

作者： Yi WANG Dahua GAN Ning ZHANG le XIE Chongqing KANG Department of Electrical Engineering Tsinghua UniversityBeijingChina Department of Electrical and Computer Engineering Texas A&M UniversityUvaldeTXUSA

Probabilistic load forecasting(PlF)is able to present the uncertainty information of the future *** is the basis of stochastic power system planning and *** works on PlF mainly focus on how to develop and combine forecasting models,while the feature selection issue has not been thoroughly investigated for *** paper fills the gap by proposing a feature selection method for PlF via sparse l1-norm penalized quantile *** can be viewed as an extension from point forecasting-based feature selection to probabilistic forecasting-based feature *** both the number of training samples and the number of features to be selected are very large,the feature selection process is casted as a large-scale convex optimization *** alternating direction method of multipliers is applied to solve the problem in an efficient *** conduct case studies on the open datasets of ten *** results show that the proposed feature selection method can improve the performance of the probabilistic forecasting and outperforms traditional least absolute shrinkage and selection operator method.

关键词： Probabilistic load forecasting Feature selection Alternating direction method of multipliers(ADMM) Quantile regression l1-norm penalty

Coherence of Superposition States

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Communications in Theoretical Physics 2019年第9期71卷 1084-1088页

作者：宇文珊珊邵连合席政军 College of Computer Science Shaanxi Normal UniversityXi'an710062China School of Computer Science Xi'an Polytechnic UniversityXi'an710048China

We find tight upper bound on the coherence of a superposition of two states in terms of the coherence of the two states constituting the superposition with l1-norm of coherence. Our upper bound is tighter than the one presented by liu, et al. [Quantum Inf. Process. 15(2016) 4209.] We also generalize the results to the case that the superposition is constituted with more than two states in high dimension, and we give the corresponding upper bounds.

关键词： quantum coherence superposition states l1-norm of coherence

Dynamics of Cohering and Decohering Power under Markovian Channels

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Communications in Theoretical Physics 2017年第11期67卷 571-579页

作者：陈明明罗宇邵连合李永明 School of Mathematics and Information Science Shaanxi normal University College of Computer Science Shaanxi normal University

In this paper, we investigate the cohering and decohering power of the one-qubit Markovian channels with respect to coherence measures based on the l1-norm, the R′enyi α-relative entropy and the Tsallis α-relative entropy of coherence, respectively. The amplitude damping channel, phase damping channel, depolarizing channel, and flip channels are analytically calculated. It shows that the decohering power of the amplitude damping channel on the x, y, and z basis is equal to each other. The same phenomenon can be seen for the phase damping channel and the flip *** cohering power for the phase damping channel and the flip channels on the x, y basis also equals to that on the z basis. However, the cohering and decohering power of the depolarizing channel is independent to the reference *** the cohering power of the amplitude damping channel on the x, y basis is different to that on the z basis.

关键词： l1-norm Rnyi α-relative entropy Tsallis α-relative entropy single-qubit state Markovian channels cohering and decohering power