Article
Engineering, Aerospace
Kaushik Prabhu, Kyle T. Alfriend, Amir Rahmani, Fred Y. Hadaegh
Summary: Distributed least absolute deviations (D-LAD) estimator is developed for collaborative estimation in multi-agent systems, reducing communication costs, computational complexity, and memory requirements. The robustness of the D-LAD estimator prevents performance degradation in the presence of non-Gaussian measurement noise. The algorithm is implemented for linear systems and nonlinear orbit determination in a formation of spacecraft, and numerical simulations show its effectiveness.
JOURNAL OF GUIDANCE CONTROL AND DYNAMICS
(2023)
Article
Mathematics, Applied
Vasileios Charisopoulos, Austin R. Benson, Anil Damle
Summary: The study presents a communication-efficient distributed algorithm for computing the leading invariant subspace of a data matrix, utilizing a novel alignment scheme and requiring only a single round of communication. The algorithm demonstrates similar performance to a centralized estimator in problems like principal component analysis.
SIAM JOURNAL ON MATHEMATICS OF DATA SCIENCE
(2021)
Article
Engineering, Electrical & Electronic
HanQin Cai, Keaton Hamm, Longxiu Huang, Jiaqi Li, Tao Wang
Summary: IRCUR is a novel non-convex algorithm proposed for solving RPCA problems, which dramatically improves computational efficiency by using CUR decomposition. The algorithm is able to process only small submatrices, avoiding expensive computations on the entire matrix.
IEEE SIGNAL PROCESSING LETTERS
(2021)
Article
Engineering, Electrical & Electronic
Lucas P. Ramos, Dimas I. Alves, Leonardo T. Duarte, Mats I. Pettersson, Renato Machado
Summary: Robust principal component analysis (RPCA) and tensor RPCA (TRPCA) techniques are valuable for ground scene estimation (GSE) in synthetic aperture radar (SAR) imagery, improving the performance of change detection methods.
IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING
(2023)
Article
Engineering, Electrical & Electronic
Zhi Han, Shaojie Zhang, Zhiyu Liu, Yanmei Wang, Junping Yao, Yao Wang
Summary: Side information is introduced into RPCA to improve its performance, and studies on RPCA using tensor version have gained more attention. We propose three models based on tensor Singular Value Decomposition to solve the problem of Tensor RPCA with side information. Experimental studies show the superiority of our models over other state-of-the-arts.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY
(2023)
Article
Statistics & Probability
Feifei Guo, Shiqing Ling, Zichuan Mi
Summary: This paper proposes an automated approach using adaptive shrinkage techniques to determine the cointegrating rank and estimate the parameters in a vector error correction model with unknown order and heavy-tailed noise. The proposed method achieves accurate estimation and demonstrates good performance in simulations and empirical applications.
Article
Computer Science, Artificial Intelligence
Pei Li, Wenlin Zhang, Chengjun Lu, Rui Zhang, Xuelong Li
Summary: A novel robust kernel principal component analysis method with optimal mean (RKPCA-OM) is proposed to enhance the robustness of KPCA by automatically eliminating the optimal mean. The theoretical proof guarantees the convergence of the algorithm and the obtained optimal subspaces and means. Exhaustive experimental results validate the superiority of the proposed method.
Article
Computer Science, Artificial Intelligence
Kaixin Gao, Zheng-Hai Huang
Summary: This paper introduces the application of Tensor Robust Principal Component Analysis (TRPCA) in sparse noise removal. A novel nonconvex model TRPCAp is proposed and its error bound is established. The alternating direction method of multipliers is used to solve TRPCAp, and the effectiveness of the proposed method is demonstrated through extensive experiments.
SIAM JOURNAL ON IMAGING SCIENCES
(2023)
Article
Computer Science, Artificial Intelligence
Ziheng Li, Feiping Nie, Rong Wang, Xuelong Li
Summary: Matrix completion aims to estimate the missing entries of a low-rank and incomplete data matrix. Existing methods face problems with noise disturbance and the need for presetting a reasonable rank value. Therefore, this paper proposes a robust rank-one matrix completion method that divides the incomplete and noisy data matrix into two parts, approximates the low-rank part using a weighted rank-one matrix pursuit algorithm, and estimates the rank of the matrix using an adaptive weight vector. Experimental results demonstrate the performance of the proposed method for incomplete matrices disturbed by sparse noise.
PATTERN RECOGNITION
(2023)
Article
Statistics & Probability
Kangqiang Li, Han Bao, Lixin Zhang
Summary: This paper enhances the distributed PCA algorithm constructed by Fan et al. by utilizing robust covariance matrix estimators to handle heavy-tailed data. Theoretical results and extensive numerical trials indicate that the algorithm is robust to heavy-tailed data and outliers.
Article
Statistics & Probability
Jianqing Fan, Weichen Wang, Ziwei Zhu
Summary: This paper introduces a simple principle for robust statistical inference via shrinkage on the data, expanding the scope of high-dimensional techniques. Through an illustration of robust estimation of low-rank matrix, the proposed methodology shows similar statistical error rates under different conditions. Extensive simulations support the theoretical results, revealing the optimality of robust covariance estimator under high dimensions.
ANNALS OF STATISTICS
(2021)
Article
Chemistry, Multidisciplinary
Xin Sha, Naizhe Diao
Summary: In this study, a two-level feature extraction method based on 21-norm is proposed to remove noises and outliers in industrial data and extract key features. Extensive experiments demonstrate that this method is more effective than other state-of-the-art fault detection methods.
Article
Automation & Control Systems
Tony Cai, Hongzhe Li, Rong Ma
Summary: This paper presents a unified framework for the statistical analysis of various principal subspace estimation problems, revealing the interplay between the constraint set, signal-to-noise ratio, and dimensionality. The research results demonstrate interesting phase transition phenomena concerning the rates of convergence related to the signal-to-noise ratio and fundamental limit for consistent estimation.
JOURNAL OF MACHINE LEARNING RESEARCH
(2021)
Article
Mathematical & Computational Biology
Yu-Ying Zhao, Cui-Na Jiao, Mao-Li Wang, Jin-Xing Liu, Juan Wang, Chun-Hou Zheng
Summary: Clustering analysis of cancer genomics data has been a focus in recent years. A new method, HTRPCA, using tensor and hypergraph to represent and save geometric structure information, shows effectiveness in clustering samples and outperforms other advanced methods, as demonstrated in experiments on TCGA datasets.
INTERDISCIPLINARY SCIENCES-COMPUTATIONAL LIFE SCIENCES
(2022)
Article
Physics, Multidisciplinary
Antoine Maillard
Summary: This paper presents an analytical technique for computing the probability of rare events in random matrices where the largest eigenvalue is atypically large, and extends to the left tail of the smallest eigenvalue. The new technique does not require explicit knowledge of the eigenvalue law and can be applied to a wider range of random matrices, solving related problems and opening up possibilities for analyzing high-dimensional landscapes of complex inference models. The results are validated using importance sampling to effectively simulate events with extremely small probabilities (down to 10^(-100)).
Article
Statistics & Probability
Stanislav Minsker, Ying-Qi Zhao, Guang Cheng
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
(2016)
Article
Statistics & Probability
Stanislav Minsker
STATISTICS & PROBABILITY LETTERS
(2017)
Article
Computer Science, Information Systems
Larry Goldstein, Stanislav Minsker, Xiaohan Wei
IEEE TRANSACTIONS ON INFORMATION THEORY
(2018)
Article
Statistics & Probability
Stanislav Minsker
ANNALS OF STATISTICS
(2018)
Article
Automation & Control Systems
Mauro Maggioni, Stanislav Minsker, Nate Strawn
JOURNAL OF MACHINE LEARNING RESEARCH
(2016)
Proceedings Paper
Optics
Mauro Maggioni, Stanislav Minsker, Nate Strawn
WAVELETS AND SPARSITY XVI
(2015)