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Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…

Optimization and Control · Mathematics 2022-02-22 Dimitris Bertsimas , Ryan Cory-Wright , Jean Pauphilet

Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional…

Statistics Theory · Mathematics 2014-01-08 T. Tony Cai , Zongming Ma , Yihong Wu

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

The article proposes and theoretically analyses a \emph{computationally efficient} multi-task learning (MTL) extension of popular principal component analysis (PCA)-based supervised learning schemes…

Machine Learning · Statistics 2021-11-02 Malik Tiomoko , Romain Couillet , Frédéric Pascal

Principal component analysis (PCA) is a key tool in the field of data dimensionality reduction. However, some applications involve heterogeneous data that vary in quality due to noise characteristics associated with each data sample.…

Machine Learning · Statistics 2026-03-18 Javier Salazar Cavazos , Jeffrey A. Fessler , Laura Balzano

Sparse principal component analysis (sparse PCA) is a widely used technique for dimensionality reduction in multivariate analysis, addressing two key limitations of standard PCA. First, sparse PCA can be implemented in high-dimensional low…

Methodology · Statistics 2025-10-07 Jan O. Bauer

Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…

Computer Vision and Pattern Recognition · Computer Science 2015-04-24 Nauman Shahid , Vassilis Kalofolias , Xavier Bresson , Michael Bronstein , Pierre Vandergheynst

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

Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…

Computation · Statistics 2010-06-04 Vladimir Rokhlin , Arthur Szlam , Mark Tygert

Principal component analysis (PCA) is an unsupervised method for learning low-dimensional features with orthogonal projections. Multilinear PCA methods extend PCA to deal with multidimensional data (tensors) directly via tensor-to-tensor…

Machine Learning · Statistics 2015-05-08 Qiquan Shi , Haiping Lu

We consider streaming, one-pass principal component analysis (PCA), in the high-dimensional regime, with limited memory. Here, $p$-dimensional samples are presented sequentially, and the goal is to produce the $k$-dimensional subspace that…

Machine Learning · Statistics 2013-07-02 Ioannis Mitliagkas , Constantine Caramanis , Prateek Jain

Spectral methods have been the mainstay in several domains such as machine learning and scientific computing. They involve finding a certain kind of spectral decomposition to obtain basis functions that can capture important structures for…

Machine Learning · Computer Science 2020-04-20 Majid Janzamin , Rong Ge , Jean Kossaifi , Anima Anandkumar

Many machine learning systems are vulnerable to small perturbations made to inputs either at test time or at training time. This has received much recent interest on the empirical front due to applications where reliability and security are…

Data Structures and Algorithms · Computer Science 2021-08-16 Pranjal Awasthi , Vaggos Chatziafratis , Xue Chen , Aravindan Vijayaraghavan

Principal Component Analysis (PCA) is a classical method for reducing the dimensionality of data by projecting them onto a subspace that captures most of their variation. Effective use of PCA in modern applications requires understanding…

Statistics Theory · Mathematics 2019-06-14 David Hong , Laura Balzano , Jeffrey A. Fessler

The CP decomposition for high dimensional non-orthogonal spiked tensors is an important problem with broad applications across many disciplines. However, previous works with theoretical guarantee typically assume restrictive incoherence…

Machine Learning · Statistics 2022-09-20 Yuefeng Han , Cun-Hui Zhang

Recently, introducing Tensor Decomposition (TD) techniques into unsupervised feature selection (UFS) has been an emerging research topic. A tensor structure is beneficial for mining the relations between different modes and helps relieve…

Machine Learning · Computer Science 2025-07-04 Junjing Zheng , Xinyu Zhang , Weidong Jiang , Xiangfeng Qiu , Mingjian Ren

Tensor Robust Principal Component Analysis (TRPCA) is a fundamental technique for decomposing multi-dimensional data into a low-rank tensor and an outlier tensor, yet existing methods relying on sparse outlier assumptions often fail under…

Numerical Analysis · Mathematics 2025-04-28 Yangyang Xu , Kexin Li , Li Yang , You-Wei Wen

We study efficient algorithms for Sparse PCA in standard statistical models (spiked covariance in its Wishart form). Our goal is to achieve optimal recovery guarantees while being resilient to small perturbations. Despite a long history of…

Machine Learning · Computer Science 2020-11-13 Tommaso d'Orsi , Pravesh K. Kothari , Gleb Novikov , David Steurer

We introduce primed-PCA (pPCA), a two-step algorithm for speeding up the approximation of principal components. This algorithm first runs any approximate-PCA method to get an initial estimate of the principal components (priming), and then…

Machine Learning · Computer Science 2022-05-23 Bálint Máté , François Fleuret

It is critical to deploy complicated neural network models on hardware with limited resources. This paper proposes a novel model quantization method, named the Low-Cost Proxy-Based Adaptive Mixed-Precision Model Quantization (LCPAQ), which…

Computer Vision and Pattern Recognition · Computer Science 2024-04-04 Junzhe Chen , Qiao Yang , Senmao Tian , Shunli Zhang