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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

The goal of this investigation is to quantify to what extent computer vision methods can correctly classify facial expressions on a sign language dataset. We extend our experiments by recognizing expressions using only the upper or lower…

Computer Vision and Pattern Recognition · Computer Science 2025-07-29 Fabrizio Nunnari , Alakshendra Jyotsnaditya Ramkrishna Singh , Patrick Gebhard

Facial Expression Recognition is a commercially-important application, but one under-appreciated limitation is that such applications require making predictions on out-of-sample distributions, where target images have different properties…

Computer Vision and Pattern Recognition · Computer Science 2023-03-10 Varsha Suresh , Gerard Yeo , Desmond C. Ong

This chapter describes gene expression analysis by Singular Value Decomposition (SVD), emphasizing initial characterization of the data. We describe SVD methods for visualization of gene expression data, representation of the data using a…

Biological Physics · Physics 2007-05-23 Michael E. Wall , Andreas Rechtsteiner , Luis M. Rocha

A system with many degrees of freedom can be characterized by a covariance matrix; principal components analysis (PCA) focuses on the eigenvalues of this matrix, hoping to find a lower dimensional description. But when the spectrum is…

Biological Physics · Physics 2017-04-26 Serena Bradde , William Bialek

Regularized variants of Principal Components Analysis, especially Sparse PCA and Functional PCA, are among the most useful tools for the analysis of complex high-dimensional data. Many examples of massive data, have both sparse and…

Machine Learning · Statistics 2019-08-21 Genevera I. Allen , Michael Weylandt

The idea of representation has been used in various fields of study from data analysis to political science. In this paper, we define representativeness and describe a method to isolate data points that can represent the entire data set.…

Information Retrieval · Computer Science 2016-10-20 Ashwinkumar Ganesan , Tim Oates , Matt Schmill

We develop a practical semidefinite programming (SDP) facial reduction procedure that utilizes computationally efficient approximations of the positive semidefinite cone. The proposed method simplifies SDPs with no strictly feasible…

Optimization and Control · Mathematics 2017-11-30 Frank Permenter , Pablo Parrilo

Principal component analysis (PCA) is a widely used unsupervised dimensionality reduction technique in machine learning, applied across various fields such as bioinformatics, computer vision and finance. However, when the response variables…

Applications · Statistics 2025-06-25 Theodosios Papazoglou , Guosheng Yin

Face detection and recognition has been prevalent with research scholars and diverse approaches have been incorporated till date to serve purpose. The rampant advent of biometric analysis systems, which may be full body scanners, or iris…

Computer Vision and Pattern Recognition · Computer Science 2017-01-31 Smriti Tikoo , Nitin Malik

Principal component analysis (PCA) is a statistical technique commonly used in multivariate data analysis. However, PCA can be difficult to interpret and explain since the principal components (PCs) are linear combinations of the original…

Mathematical Software · Computer Science 2013-12-24 W. Liu , H. Zhang , D. Tao , Y. Wang , K. Lu

In this paper, a novel method for representation and recognition of the facial expressions in two-dimensional image sequences is presented. We apply a variation of two-dimensional heteroscedastic linear discriminant analysis (2DHLDA)…

Computer Vision and Pattern Recognition · Computer Science 2012-07-23 Mahmoud Khademi , Mohammad H. Kiapour , Mehran Safayani , Mohammad T. Manzuri , M. Shojaei

In this paper, an Eigenvector based system has been presented to recognize facial expressions from digital facial images. In the approach, firstly the images were acquired and cropping of five significant portions from the image was…

Computer Vision and Pattern Recognition · Computer Science 2013-03-05 Jeemoni Kalita , Karen Das

Recognizing facial expressions from static images or video sequences is a widely studied but still challenging problem. The recent progresses obtained by deep neural architectures, or by ensembles of heterogeneous models, have shown that…

Computer Vision and Pattern Recognition · Computer Science 2018-10-25 Lisa Graziani , Stefano Melacci , Marco Gori

Privacy-preserving data mining has become an important topic. People have built several multi-party-computation (MPC)-based frameworks to provide theoretically guaranteed privacy, the poor performance of real-world algorithms have always…

Cryptography and Security · Computer Science 2021-05-18 Xiaoyu Fan , Guosai Wang , Kun Chen , Xu He , Wei Xu

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

Principal component analysis (PCA) is routinely used in population genetics to assess genetic structure. With chromosomal reference genomes and population-scale whole genome-sequencing becoming increasingly accessible, contemporary studies…

Populations and Evolution · Quantitative Biology 2025-01-22 L. Moritz Blumer , Jeffrey M. Good , Richard Durbin

Human eyes concentrate different facial regions during distinct cognitive activities. We study utilising facial visual saliency maps to classify different facial expressions into different emotions. Our results show that our novel method of…

Computer Vision and Pattern Recognition · Computer Science 2018-11-13 Zhenyue Qin , Jie Wu

Automated facial expression analysis has a variety of applications in human-computer interaction. Traditional methods mainly analyze prototypical facial expressions of no more than eight discrete emotions as a classification task. However,…

Computer Vision and Pattern Recognition · Computer Science 2018-05-04 Feng Zhou , Shu Kong , Charless Fowlkes , Tao Chen , Baiying Lei

Face recognition has been an active research area in the past few decades. In general, face recognition can be very challenging due to variations in viewpoint, illumination, facial expression, etc. Therefore it is essential to extract…

Computer Vision and Pattern Recognition · Computer Science 2017-12-04 Shervin Minaee , Amirali Abdolrashidi , Yao Wang