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It is well known that Principal Component Analysis (PCA) is strongly affected by outliers and a lot of effort has been put into robustification of PCA. In this paper we present a new algorithm for robust PCA minimizing the trimmed…

Machine Learning · Statistics 2015-06-02 Anastasia Podosinnikova , Simon Setzer , Matthias Hein

This paper is concerned with the computation of the principal components for a general tensor, known as the tensor principal component analysis (PCA) problem. We show that the general tensor PCA problem is reducible to its special case…

Optimization and Control · Mathematics 2013-11-19 Bo Jiang , Shiqian Ma , Shuzhong Zhang

We study robust PCA for the fully observed setting, which is about separating a low rank matrix $\boldsymbol{L}$ and a sparse matrix $\boldsymbol{S}$ from their sum $\boldsymbol{D}=\boldsymbol{L}+\boldsymbol{S}$. In this paper, a new…

Information Theory · Computer Science 2021-06-29 HanQin Cai , Jian-Feng Cai , Ke Wei

In this work, we address the problem of outlier detection for robust motion estimation by using modern sparse-low-rank decompositions, i.e., Robust PCA-like methods, to impose global rank constraints. Robust decompositions have shown to be…

Computer Vision and Pattern Recognition · Computer Science 2014-10-23 German Ros , Jose Alvarez , Julio Guerrero

Robust Principal Component Analysis (RPCA) is a widely used method for recovering low-rank structure from data matrices corrupted by significant and sparse outliers. These corruptions may arise from occlusions, malicious tampering, or other…

Methodology · Statistics 2023-10-31 Xiaojun Zheng , Simon Mak , Liyan Xie , Yao Xie

Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some…

Machine Learning · Computer Science 2021-06-29 Zhao Kang , Hongfei Liu , Jiangxin Li , Xiaofeng Zhu , Ling Tian

Robust tensor recovery plays an instrumental role in robustifying tensor decompositions for multilinear data analysis against outliers, gross corruptions and missing values and has a diverse array of applications. In this paper, we study…

Machine Learning · Statistics 2014-08-26 Donald Goldfarb , Zhiwei Qin

Recommendation systems, social network analysis, medical imaging, and data mining often involve processing sparse high-dimensional data. Such high-dimensional data are naturally represented as tensors, and they cannot be efficiently…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-10-22 Weiyun Jiang , Kaiqi Zhang , Colin Yu Lin , Feng Xing , Zheng Zhang

Outlier based Robust Principal Component Analysis (RPCA) requires centering of the non-outliers. We show a "bias trick" that automatically centers these non-outliers. Using this bias trick we obtain the first RPCA algorithm that is optimal…

Machine Learning · Computer Science 2019-11-20 Baokun He , Guihong Wan , Haim Schweitzer

When synthesizing multi-source high-dimensional data, a key objective is to extract low-dimensional representations that effectively approximate the original features across different sources. Such representations facilitate the discovery…

Machine Learning · Computer Science 2026-03-10 Zhenyu Wang , Molei Liu , Jing Lei , Francis Bach , Zijian Guo

In this paper, a new method is proposed for sparse PCA based on the recursive divide-and-conquer methodology. The main idea is to separate the original sparse PCA problem into a series of much simpler sub-problems, each having a closed-form…

Computer Vision and Pattern Recognition · Computer Science 2012-12-03 Qian Zhao , Deyu Meng , Zongben Xu

Robust Principal Component Analysis (RPCA) aims at recovering a low-rank subspace from grossly corrupted high-dimensional (often visual) data and is a cornerstone in many machine learning and computer vision applications. Even though RPCA…

Computer Vision and Pattern Recognition · Computer Science 2017-03-29 Niannan Xue , Yannis Panagakis , Stefanos Zafeiriou

Comparing tensors and identifying their (dis)similar structures is fundamental in understanding the underlying phenomena for complex data. Tensor decomposition methods help analysts extract tensors' essential characteristics and aid in…

Human-Computer Interaction · Computer Science 2025-07-29 Naoki Okami , Kazuki Miyake , Naohisa Sakamoto , Jorji Nonaka , Takanori Fujiwara

This work studies the recursive robust principal components' analysis (PCA) problem. Here, "robust" refers to robustness to both independent and correlated sparse outliers, although we focus on the latter. A key application where this…

Information Theory · Computer Science 2011-06-17 Chenlu Qiu , Namrata Vaswani

Commonly used in computer vision and other applications, robust PCA represents an algorithmic attempt to reduce the sensitivity of classical PCA to outliers. The basic idea is to learn a decomposition of some data matrix of interest into…

Computer Vision and Pattern Recognition · Computer Science 2016-10-10 Tae-Hyun Oh , Yasuyuki Matsushita , In So Kweon , David Wipf

Tensor decompositions are promising tools for big data analytics as they bring multiple modes and aspects of data to a unified framework, which allows us to discover complex internal structures and correlations of data. Unfortunately most…

Numerical Analysis · Computer Science 2014-12-30 Guoxu Zhou , Andrzej Cichocki , Shengli Xie

We propose a robust principal component analysis (RPCA) framework to recover low-rank and sparse matrices from temporal observations. We develop an online version of the batch temporal algorithm in order to process larger datasets or…

Machine Learning · Statistics 2022-08-04 Hong-Lan Botterman , Julien Roussel , Thomas Morzadec , Ali Jabbari , Nicolas Brunel

Deep unfolded neural networks are designed by unrolling the iterations of optimization algorithms. They can be shown to achieve faster convergence and higher accuracy than their optimization counterparts. This paper proposes a new…

Machine Learning · Computer Science 2020-10-05 Huynh Van Luong , Boris Joukovsky , Yonina C. Eldar , Nikos Deligiannis

Nonnegative Tucker decomposition (NTD) is a powerful tool for the extraction of nonnegative parts-based and physically meaningful latent components from high-dimensional tensor data while preserving the natural multilinear structure of…

Machine Learning · Computer Science 2015-09-17 Guoxu Zhou , Andrzej Cichocki , Qibin Zhao , Shengli Xie

Due to their transient nature, clouds represent anomalies relative to the underlying landscape of interest. Hence, the challenge of cloud identification can be considered a specific case in the more general problem of anomaly detection. The…

Geophysics · Physics 2024-01-15 Christopher Small , Daniel Sousa