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Principal component analysis (PCA) is a fundamental technique for dimensionality reduction and denoising; however, its application to three-dimensional data with arbitrary orientations -- common in structural biology -- presents significant…

Signal Processing · Electrical Eng. & Systems 2025-10-22 Michael Fraiman , Paulina Hoyos , Tamir Bendory , Joe Kileel , Oscar Mickelin , Nir Sharon , Amit Singer

We study the distributed computing setting in which there are multiple servers, each holding a set of points, who wish to compute functions on the union of their point sets. A key task in this setting is Principal Component Analysis (PCA),…

Machine Learning · Computer Science 2014-12-24 Maria-Florina Balcan , Vandana Kanchanapally , Yingyu Liang , David Woodruff

Principal component analysis (PCA) has achieved great success in unsupervised learning by identifying covariance correlations among features. If the data collection fails to capture the covariance information, PCA will not be able to…

Computational Physics · Physics 2021-08-24 Ziming Liu , Sitian Qian , Yixuan Wang , Yuxuan Yan , Tianyi Yang

Photorealistic Codec Avatars (PCA), which generate high-fidelity human face renderings, are increasingly being used in Virtual Reality (VR) environments to enable immersive communication and interaction through deep learning-based…

Computer Vision and Pattern Recognition · Computer Science 2025-10-30 Mingzhi Zhu , Ding Shang , Sai Qian Zhang

Natural scene character recognition is challenging due to the cluttered background, which is hard to separate from text. In this paper, we propose a novel method for robust scene character recognition. Specifically, we first use robust…

Computer Vision and Pattern Recognition · Computer Science 2016-06-16 Zheng Zhang , Yong Xu , Cheng-Lin Liu

STEM XEDS spectrum images can be drastically denoised by application of the principal component analysis (PCA). This paper looks inside the PCA workflow step by step on an example of a complex semiconductor structure consisting of a number…

Image and Video Processing · Electrical Eng. & Systems 2019-10-16 Pavel Potapov , Axel Lubk

Principal component analysis (PCA) is an important tool in exploring data. The conventional approach to PCA leads to a solution which favours the structures with large variances. This is sensitive to outliers and could obfuscate interesting…

Methodology · Statistics 2015-06-16 A. A. Akinduko , A. N. Gorban

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

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 feature extraction method, but it may be adversely affected by outliers, resulting in inaccurate learning of the projection matrix. This paper proposes a robust method to estimate both the…

Machine Learning · Computer Science 2024-08-23 Yingzhuo Deng , Ke Hu , Bo Li , Yao Zhang

Methodologies for multidimensionality reduction aim at discovering low-dimensional manifolds where data ranges. Principal Component Analysis (PCA) is very effective if data have linear structure. But fails in identifying a possible…

Numerical Analysis · Mathematics 2021-01-14 Alberto García-González , Antonio Huerta , Sergio Zlotnik , Pedro Díez

Cellular Automata are discrete dynamical systems that evolve following simple and local rules. Despite of its local simplicity, knowledge discovery in CA is a NP problem. This is the main motivation for using data mining techniques for CA…

Discrete Mathematics · Computer Science 2007-05-23 Gilson A. Giraldi , Antonio A. F. Oliveira , Leonardo Carvalho

Principal Component Analysis (PCA) is a widely used technique in machine learning, data analysis and signal processing. With the increase in the size and complexity of datasets, it has become important to develop low-space usage algorithms…

Machine Learning · Computer Science 2023-03-09 Yichuan Deng , Zhao Song , Zifan Wang , Han Zhang

Factor analysis and principal component analysis (PCA) are used in many application areas. The first step, choosing the number of components, remains a serious challenge. Our work proposes improved methods for this important problem. One of…

Methodology · Statistics 2019-09-17 Edgar Dobriban , Art B. Owen

Generative Adversarial Networks (GAN) have been employed for face super resolution but they bring distorted facial details easily and still have weakness on recovering realistic texture. To further improve the performance of GAN based…

Computer Vision and Pattern Recognition · Computer Science 2020-08-31 Hao Dou , Chen Chen , Xiyuan Hu , Zuxing Xuan , Zhisen Hu , Silong Peng

In this paper we propose a new iterative algorithm to solve the fair PCA (FPCA) problem. We start with the max-min fair PCA formulation originally proposed in [1] and derive a simple and efficient iterative algorithm which is based on the…

Machine Learning · Statistics 2023-05-11 Prabhu Babu , Petre Stoica

Previous versions of sparse principal component analysis (PCA) have presumed that the eigen-basis (a $p \times k$ matrix) is approximately sparse. We propose a method that presumes the $p \times k$ matrix becomes approximately sparse after…

Machine Learning · Statistics 2023-08-07 Fan Chen , Karl Rohe

Artificial neural networks that learn to perform Principal Component Analysis (PCA) and related tasks using strictly local learning rules have been previously derived based on the principle of similarity matching: similar pairs of inputs…

Computation · Statistics 2018-11-06 Victor Minden , Cengiz Pehlevan , Dmitri B. Chklovskii

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the…

Machine Learning · Computer Science 2012-06-22 Alfredo Kalaitzis , Neil Lawrence

Principal component analysis (PCA) is an indispensable tool in many learning tasks that finds the best linear representation for data. Classically, principal components of a dataset are interpreted as the directions that preserve most of…

Optimization and Control · Mathematics 2018-03-13 Raphael A. Hauser , Armin Eftekhari , Heinrich F. Matzinger
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