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high Technology Letters 2017年第2期23卷 179-184页

作者：李文法 Wang Gongming Li Ke Huang Su Beijing Key Laboratory of Information Service Engineering Beijing Union University National Laboratory of Biomacromolecules Institute of BiophysicsChinese Academy of Sciences

The performance of conventional similarity measurement methods is affected seriously by the curse of dimensionality of high-dimensional data.The reason is that data difference between sparse and noisy dimensionalities occupies a large proportion of the similarity,leading to the dissimilarities between any results.A similarity measurement method of high-dimensional data based on normalized net lattice subspace is proposed.The data range of each dimension is divided into several intervals,and the components in different dimensions are mapped onto the corresponding interval.Only the component in the same or adjacent interval is used to calculate the similarity.To validate this method,three data types are used,and seven common similarity measurement methods are compared.The experimental result indicates that the relative difference of the method is increasing with the dimensionality and is approximately two or three orders of magnitude higher than the conventional method.In addition,the similarity range of this method in different dimensions is [0,1],which is fit for similarity analysis after dimensionality reduction.

关键词： high-dimensional data the curse of dimensionality similarity normalization subspace NPsim

A Length-Adaptive Non-Dominated Sorting Genetic Algorithm for Bi-Objective high-dimensional Feature Selection

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IEEE/CAA Journal of Automatica Sinica 2023年第9期10卷 1834-1844页

作者： Yanlu Gong Junhai Zhou Quanwang Wu MengChu Zhou Junhao Wen College of Computer Science Chongqing UniversityChongqing 400044China IEEE Department of Electrical and Computer Engineering New Jersey Institute of TechnologyNewarkNJ 07102 USA College of Big data and Software Engineering Chongqing UniversityChongqing 400044China

As a crucial data preprocessing method in data mining,feature selection(FS)can be regarded as a bi-objective optimization problem that aims to maximize classification accuracy and minimize the number of selected features.Evolutionary computing(EC)is promising for FS owing to its powerful search capability.However,in traditional EC-based methods,feature subsets are represented via a length-fixed individual encoding.It is ineffective for high-dimensional data,because it results in a huge search space and prohibitive training time.This work proposes a length-adaptive non-dominated sorting genetic algorithm(LA-NSGA)with a length-variable individual encoding and a length-adaptive evolution mechanism for bi-objective highdimensional FS.In LA-NSGA,an initialization method based on correlation and redundancy is devised to initialize individuals of diverse lengths,and a Pareto dominance-based length change operator is introduced to guide individuals to explore in promising search space adaptively.Moreover,a dominance-based local search method is employed for further improvement.The experimental results based on 12 high-dimensional gene datasets show that the Pareto front of feature subsets produced by LA-NSGA is superior to those of existing algorithms.

关键词： Bi-objective optimization feature selection(FS) genetic algorithm high-dimensional data length-adaptive

high-dimensional Volatility Matrix Estimation with Cross-Sectional Dependent and Heavy-Tailed Microstructural Noise

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Journal of Systems Science & Complexity 2023年第5期36卷 2125-2154页

作者： LIANG Wanwan WU Ben FAN Xinyan JING Bingyi ZHANG Bo Center for Applied Statistics School of StatisticsInstitute of Probability and StatisticsRenmin University of ChinaBeijing 100086China Department of Statistics&data Science Southern University of Science and TechnologyShenzhen 518055China

The estimates of the high-dimensional volatility matrix based on high-frequency data play a pivotal role in many financial applications.However,most existing studies have been built on the sub-Gaussian and cross-sectional independence assumptions of microstructure noise,which are typically violated in the financial markets.In this paper,the authors proposed a new robust volatility matrix estimator,with very mild assumptions on the cross-sectional dependence and tail behaviors of the noises,and demonstrated that it can achieve the optimal convergence rate n-1/4.Furthermore,the proposed model offered better explanatory and predictive powers by decomposing the estimator into low-rank and sparse components,using an appropriate regularization procedure.Simulation studies demonstrated that the proposed estimator outperforms its competitors under various dependence structures of microstructure noise.Additionally,an extensive analysis of the high-frequency data for stocks in the Shenzhen Stock Exchange of China demonstrated the practical effectiveness of the estimator.

关键词： Cross-sectional dependence high-dimensional data high-frequency data integrated volatility matrix market microstructure noise

high-dimensional Tests for Mean Vector: Approaches without Estimating the Mean Vector Directly

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Acta Mathematicae Applicatae Sinica 2022年第1期38卷 78-86页

作者： Bo CHEN Hai-meng WANG School of Mathematics and Information Technology Jiangsu Second Normal UniversityNanjing 211200China

Several tests for multivariate mean vector have been proposed in the recent literature.Generally,these tests are directly concerned with the mean vector of a high-dimensional distribution.The paper presents two new test procedures for testing mean vector in large dimension and small samples.We do not focus on the mean vector directly,which is a different framework from the existing choices.The first test procedure is based on the asymptotic distribution of the test statistic,where the dimension increases with the sample size.The second test procedure is based on the permutation distribution of the test statistic,where the sample size is fixed and the dimension grows to infinity.Simulations are carried out to examine the finite-sample performance of the tests and to compare them with some popular nonparametric tests available in the literature.

关键词： asymptotic distribution high-dimensional data permutation test U-statistic testing mean vector

Nearly optimal stochastic approximation for online principal subspace estimation

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Science China Mathematics 2023年第5期66卷 1087-1122页

作者： Xin Liang Zhen-Chen Guo Li Wang Ren-Cang Li Wen-Wei Lin Yau Mathematical Sciences Center Tsinghua UniversityBeijing 100084China Yanqi Lake Beijing Institute of Mathematical Sciences and Applications Beijing 101408China Department of Mathematics Nanjing UniversityNanjing 210093China Department of Mathematics University of Texas at ArlingtonArlingtonTX 76019USA Department of Mathematics Hong Kong Baptist UniversityHong KongChina Nanjing Center for Applied Mathematics Nanjing 211135China Department of Applied Mathematics Yang Ming Chiao Tung UniversityHsinchu 300China

Principal component analysis(PCA) has been widely used in analyzing high-dimensional data. It converts a set of observed data points of possibly correlated variables into a set of linearly uncorrelated variables via an orthogonal transformation. To handle streaming data and reduce the complexities of PCA,(subspace)online PCA iterations were proposed to iteratively update the orthogonal transformation by taking one observed data point at a time. Existing works on the convergence of(subspace) online PCA iterations mostly focus on the case where the samples are almost surely uniformly bounded. In this paper, we analyze the convergence of a subspace online PCA iteration under more practical assumptions and obtain a nearly optimal finite-sample error bound. Our convergence rate almost matches the minimax information lower bound. We prove that the convergence is nearly global in the sense that the subspace online PCA iteration is convergent with high probability for random initial guesses. This work also leads to a simpler proof of the recent work on analyzing online PCA for the first principal component only.

关键词： principal component analysis principal component subspace stochastic approximation high-dimensional data online algorithm nite-sample analysis

A high-dimensional Test for Multivariate Analysis of Variance Under a Low-dimensional Factor Structure

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Communications in Mathematics and Statistics 2022年第4期10卷 581-597页

作者： Mingxiang Cao Yanling Zhao Kai Xu Daojiang He Xudong Huang Department of Statistics Anhui Normal UniversityWuhu 241000People’s Republic of China

In this paper,the problem of high-dimensional multivariate analysis of variance is investigated under a low-dimensional factor structure which violates some vital assumptions on covariance matrix in some existing literature.We propose a new test and derive that the asymptotic distribution of the test statistic is a weighted distribution of chi-squares of 1 degree of freedom under the null hypothesis and mild conditions.We provide numerical studies on both sizes and powers to illustrate performance of the proposed test.

关键词： high-dimensional data MANOVA Low-dimensional factor structure Chi-square distribution

VTwins:有限宏基因组样本推断疾病致病微生物特征

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Science Bulletin 2023年第22期68卷 2806-2816,M0006页

作者：孟庆仁周茜时硕肖景发马勤于军陈军康禹 CAS Key Laboratory of Genome Sciences and Information Beijing Institute of Genomics Chinese Academy of Sciences and China National Center for BioinformationBeijing 100101China School of Medicine Southern University of Science and TechnologyShenzhen 518055China National Clinical Research Center for Infectious Diseases The Third People’s Hospital of ShenzhenThe Second Affiliated Hospital of Southern University of Science and TechnologyShenzhen 518100China International Cancer Center Shenzhen University Medical SchoolShenzhen 518055China Department of Biomedical Informatics The Ohio State UniversityColumbus OH 43210USA University of Chinese Academy of Sciences Beijing 100190China

从高维、高变宏基因组数据中挖掘与疾病强关联的微生物特征是人体微生态研究的一大难题.受遗传学双生子研究的启发,本文开发了一种新型微生物特征挖掘算法——虚拟双胞胎(VTwins)算法.该算法通过将原始队列转化为具有相近的微生物组特... 详细信息

从高维、高变宏基因组数据中挖掘与疾病强关联的微生物特征是人体微生态研究的一大难题.受遗传学双生子研究的启发,本文开发了一种新型微生物特征挖掘算法——虚拟双胞胎(VTwins)算法.该算法通过将原始队列转化为具有相近的微生物组特征但分组不同的配对样本形成的配对队列来消除混淆因素的影响.结果显示,VTwins在识别因果特征的敏感性方面超过传统方法,并且将所需样本规模减小10倍,就可鉴定与疾病相关的微生物或代谢途径,并通过模拟和真实数据进行验证.与其他16种同类软件进行的基准测试进一步验证了VTwins在处理高维数据和挖掘宏基因组研究中的因果关系的能力和适用性.总体而言,VTwins可直接且强大地处理高变、高维数据,在宏基因组和其他组学数据的因果关系挖掘方面具有广阔的应用前景.VTwins的开源访问网址为https://***/mengqingren/VTwins.

关键词： Causality high-dimensional data Metagenome Differential abundance Paired cohort

An Ant Colony Optimization Based Dimension Reduction Method for high-dimensional datasets

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Journal of Bionic Engineering 2013年第2期10卷 231-241页

作者： Ying Li Gang Wang Huiling Chen Lian Shi Lei Qin College of Computer Science and Technology Jilin University Changchun 130012 P. R. China Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education Jilin University Changchun 130012 P. R. China College of Geo Exploration Science and Technology Jilin University Changchun 130026 P. R. China College of physics and electronic information Wenzhou University Wenzhou 325035 P. R. China

In this paper, a bionic optimization algorithm based dimension reduction method named Ant Colony Optimization -Selection （ACO-S） is proposed for high-dimensional datasets. Because microarray datasets comprise tens of thousands of features （genes）, they are usually used to test the dimension reduction techniques. ACO-S consists of two stages in which two well-known ACO algorithms, namely ant system and ant colony system, are utilized to seek for genes, respectively. In the first stage, a modified ant system is used to filter the nonsignificant genes from high-dimensional space, and a number of promising genes are reserved in the next step. In the second stage, an improved ant colony system is applied to gene selection. In order to enhance the search ability of ACOs, we propose a method for calculating priori available heuristic information and design a fuzzy logic controller to dynamically adjust the number of ants in ant colony system. Furthermore, we devise another fuzzy logic controller to tune the parameter （q0） in ant colony system. We evaluate the performance of ACO-S on five microarray datasets, which have dimensions varying from 7129 to 12000. We also compare the performance of ACO-S with the results obtained from four existing well-known bionic optimization algorithms. The comparison results show that ACO-S has a notable ability to＂ generate a gene subset with the smallest size and salient features while yielding high classification accuracy. The comparative results generated by ACO-S adopting different classifiers are also given. The proposed method is shown to be a promising and effective tool for mining high-dimension data and mobile robot navigation.

关键词： gene selection feature selection ant colony optimization high-dimensional data

Sparse recovery: from vectors to tensors

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National Science Review 2018年第5期5卷 756-767页

作者： Yao Wang Deyu Meng Ming Yuan School of Mathematics and Statistics Xi'an Jiaotong University Shenyang Institute of Automation Chinese Academy of Sciences Ministry of Education Key Lab of Intelligent Networks and Network Security Xi'an Jiaotong University Department of Statistics Columbia University

Recent advances in various fields such as telecommunications, biomedicine and economics, among others, have created enormous amount of data that are often characterized by their huge size and high dimensionality. It has become evident, from research in the past couple of decades, that sparsity is a flexible and powerful notion when dealing with these data, both from empirical and theoretical viewpoints. In this survey, we review some of the most popular techniques to exploit sparsity, for analyzing high-dimensional vectors, matrices and higher-order tensors.

关键词： high-dimensional data sparsity compressive sensing low-rank matrix recovery tensors