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Background foreground separation (BFS) is a popular computer vision problem where dynamic foreground objects are separated from the static background of a scene. Typically, this is performed using consumer cameras because of their low cost,…

Image and Video Processing · Electrical Eng. & Systems 2021-08-16 Spencer Markowitz , Corey Snyder , Yonina C. Eldar , Minh N. Do

Principal components analysis (PCA) is the optimal linear auto-encoder of data, and it is often used to construct features. Enforcing sparsity on the principal components can promote better generalization, while improving the…

Machine Learning · Computer Science 2015-02-25 Malik Magdon-Ismail , Christos Boutsidis

Fourier ptychography is a recently explored imaging method for overcoming the diffraction limit of conventional cameras with applications in microscopy and yielding high-resolution images. In order to splice together low-resolution images…

Image and Video Processing · Electrical Eng. & Systems 2020-03-18 Yican Chen , Zhi Luo , Xia Wu , Huidong Yang , Bo Huang

The robust PCA of covariance matrices plays an essential role when isolating key explanatory features. The currently available methods for performing such a low-rank plus sparse decomposition are matrix specific, meaning, those algorithms…

Machine Learning · Statistics 2023-06-07 Calypso Herrera , Florian Krach , Anastasis Kratsios , Pierre Ruyssen , Josef Teichmann

In this brief note, we formulate Principal Component Analysis (PCA) over datasets consisting not of points but of distributions, characterized by their location and covariance. Just like the usual PCA on points can be equivalently derived…

Machine Learning · Statistics 2023-06-26 Vlad Niculae

Semantic segmentation of functional magnetic resonance imaging (fMRI) makes great sense for pathology diagnosis and decision system of medical robots. The multi-channel fMRI provides more information of the pathological features. But the…

Computer Vision and Pattern Recognition · Computer Science 2017-07-12 Lei Tai , Haoyang Ye , Qiong Ye , Ming Liu

Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…

Data Structures and Algorithms · Computer Science 2021-06-07 Agniva Chowdhury , Petros Drineas , David P. Woodruff , Samson Zhou

Principal component analysis (PCA) is a standard dimensionality reduction technique used in various research and applied fields. From an algorithmic point of view, classical PCA can be formulated in terms of operations on a multivariate…

Methodology · Statistics 2022-11-08 Ayisha Fayomi , Yannis Pantazis , Michail Tsagris , Andrew T. A. Wood

In this work, we develop a novel principal component analysis (PCA) for semimartingales by introducing a suitable spectral analysis for the quadratic variation operator. Motivated by high-dimensional complex systems typically found in…

Statistics Theory · Mathematics 2016-03-10 Alberto Ohashi , Alexandre B Simas

Principal Component Analysis (PCA) aims to find subspaces spanned by the so-called principal components that best represent the variance in the dataset. The deflation method is a popular meta-algorithm that sequentially finds individual…

Machine Learning · Computer Science 2024-05-30 Fangshuo Liao , Junhyung Lyle Kim , Cruz Barnum , Anastasios Kyrillidis

We extend the principal component analysis (PCA) to second-order stationary vector time series in the sense that we seek for a contemporaneous linear transformation for a $p$-variate time series such that the transformed series is segmented…

Methodology · Statistics 2018-12-21 Jinyuan Chang , Bin Guo , Qiwei Yao

Uncertainty quantification is crucial for the deployment of image restoration models in safety-critical domains, like autonomous driving and biological imaging. To date, methods for uncertainty visualization have mainly focused on per-pixel…

Computer Vision and Pattern Recognition · Computer Science 2023-11-07 Elias Nehme , Omer Yair , Tomer Michaeli

We study distributed principal component analysis (PCA) in high-dimensional settings under the spiked model. In such regimes, sample eigenvectors can deviate significantly from population ones, introducing a persistent bias. Existing…

Methodology · Statistics 2025-05-29 Weiming Li , Zeng Li , Siyu Wang , Yanqing Yin , Junpeng Zhu

Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…

Machine Learning · Statistics 2017-05-19 Xianghui Luo , Robert J. Durrant

Functional Principal Component Analysis (FPCA) has become a widely-used dimension reduction tool for functional data analysis. When additional covariates are available, existing FPCA models integrate them either in the mean function or in…

Methodology · Statistics 2022-04-13 Ci-Ren Jiang , Eardi Lila , John AD Aston , Jane-Ling Wang

Probabilistic principal component analysis (PCA) and its Bayesian variant (BPCA) are widely used for dimension reduction in machine learning and statistics. The main advantage of probabilistic PCA over the traditional formulation is…

Machine Learning · Statistics 2025-05-23 Arghya Datta , Philippe Gagnon , Florian Maire

Sparse principal component analysis (PCA) is a well-established dimensionality reduction technique that is often used for unsupervised feature selection (UFS). However, determining the regularization parameters is rather challenging, and…

Machine Learning · Computer Science 2025-04-07 Long Chen , Xianchao Xiu

Principal Component Analysis (PCA) is a popular method for dimension reduction and has attracted an unfailing interest for decades. More recently, kernel PCA (KPCA) has emerged as an extension of PCA but, despite its use in practice, a…

Machine Learning · Computer Science 2023-01-25 Maxime Haddouche , Benjamin Guedj , John Shawe-Taylor

We introduce a novel algorithm that computes the $k$-sparse principal component of a positive semidefinite matrix $A$. Our algorithm is combinatorial and operates by examining a discrete set of special vectors lying in a low-dimensional…

Machine Learning · Statistics 2014-05-09 Dimitris S. Papailiopoulos , Alexandros G. Dimakis , Stavros Korokythakis

Principal component analysis (PCA) is a popular dimension reduction technique for vector data. Factored PCA (FPCA) is a probabilistic extension of PCA for matrix data, which can substantially reduce the number of parameters in PCA while…

Machine Learning · Statistics 2023-12-19 Xuan Ma , Jianhua Zhao , Yue Wang