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Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a…

Machine Learning · Computer Science 2014-07-01 Navin Goyal , Santosh Vempala , Ying Xiao

This paper describes a novel face identification method that combines the eigenfaces theory with the Neural Nets. We use the eigenfaces methodology in order to reduce the dimensionality of the input image, and a neural net classifier that…

Computer Vision and Pattern Recognition · Computer Science 2022-04-04 Virginia Espinosa-Duro , Marcos Faundez-Zanuy

Most of the current techniques for face recognition require the presence of a full face of the person to be recognized, and this situation is difficult to achieve in practice, the required person may appear with a part of his face, which…

Computer Vision and Pattern Recognition · Computer Science 2022-03-14 Osama R. Shahin , Rami Ayedi , Alanazi Rayan , Rasha M. Abd El-Aziz , Ahmed I. Taloba

Principal Component Analysis (PCA) is a powerful and popular dimensionality reduction technique. However, due to its linear nature, it often fails to capture the complex underlying structure of real-world data. While Kernel PCA (kPCA)…

Machine Learning · Computer Science 2026-02-05 Thomas Uriot , Elise Chung

The high-dimensional feature space of the hyperspectral imagery poses major challenges to the processing and analysis of the hyperspectral data sets. In such a case, dimensionality reduction is necessary to decrease the computational…

Image and Video Processing · Electrical Eng. & Systems 2024-06-06 Mustafa Ustuner

Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In…

Machine Learning · Statistics 2013-10-01 Gonzalo Mateos , Georgios B. Giannakis

The technology of face recognition has made some progress in recent years. After studying the PCA, 2DPCA, R1-PCA, L1-PCA, KPCA and KECA algorithms, in this paper ECA (2DECA) is proposed by extracting features in PCA (2DPCA) based on Renyi…

Computer Vision and Pattern Recognition · Computer Science 2019-12-24 Xing Liu , Xiao-Jun Wu , Zhen Liu , He-Feng Yin

Principal component analysis (PCA) is one of the most fundamental procedures in exploratory data analysis and is the basic step in applications ranging from quantitative finance and bioinformatics to image analysis and neuroscience.…

Data Structures and Algorithms · Computer Science 2019-05-13 Fedor V. Fomin , Petr A. Golovach , Fahad Panolan , Kirill Simonov

Classical Principal Component Analysis (PCA) approximates data in terms of projections on a small number of orthogonal vectors. There are simple procedures to efficiently compute various functions of the data from the PCA approximation. The…

Machine Learning · Statistics 2019-07-26 Guihong Wan , Crystal Maung , Haim Schweitzer

This paper compares two neural network input selection schemes, the Principal Component Analysis (PCA) and the Automatic Relevance Determination (ARD) based on Mac-Kay's evidence framework. The PCA takes all the input data and projects it…

Computational Engineering, Finance, and Science · Computer Science 2007-05-23 L. Mdlazi , T. Marwala , C. J. Stander , C. Scheffer , P. S. Heyns

Efficient representations of data are essential for processing, exploration, and human understanding, and Principal Component Analysis (PCA) is one of the most common dimensionality reduction techniques used for the analysis of large,…

Computation · Statistics 2023-11-06 Olga Dorabiala , Aleksandr Aravkin , J. Nathan Kutz

Principal component analysis (PCA), the most popular dimension-reduction technique, has been used to analyze high-dimensional data in many areas. It discovers the homogeneity within the data and creates a reduced feature space to capture as…

Methodology · Statistics 2026-03-24 Daning Bi , Le Chang , Yanrong Yang

Facial expression analysis is one of the popular fields of research in human computer interaction (HCI). It has several applications in next generation user interfaces, human emotion analysis, behavior and cognitive modeling. In this paper,…

Computer Vision and Pattern Recognition · Computer Science 2015-05-18 S. L. Happy , Anjith George , Aurobinda Routray

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

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an…

Machine Learning · Statistics 2011-06-23 Alfredo A. Kalaitzis , Neil D. Lawrence

Principal component analysis (PCA) is fundamental to statistical machine learning. It extracts latent principal factors that contribute to the most variation of the data. When data are stored across multiple machines, however, communication…

Computation · Statistics 2018-01-11 Jianqing Fan , Dong Wang , Kaizheng Wang , Ziwei Zhu

Principal component analysis is an important pattern recognition and dimensionality reduction tool in many applications. Principal components are computed as eigenvectors of a maximum likelihood covariance $\widehat{\Sigma}$ that…

Statistics Theory · Mathematics 2017-10-30 Raphael Hauser , Raul Kangro , Jüri Lember , Heinrich Matzinger

In this paper, we study the application of sparse principal component analysis (PCA) to clustering and feature selection problems. Sparse PCA seeks sparse factors, or linear combinations of the data variables, explaining a maximum amount of…

Artificial Intelligence · Computer Science 2008-10-08 Ronny Luss , Alexandre d'Aspremont

In recent times, functional data analysis (FDA) has been successfully applied in the field of high dimensional data classification. In this paper, we present a novel classification framework using functional data and classwise Principal…

Machine Learning · Statistics 2021-06-29 Avishek Chatterjee , Satyaki Mazumder , Koel Das

The paper will present a novel approach for solving face recognition problem. Our method combines 2D Principal Component Analysis (2DPCA), one of the prominent methods for extracting feature vectors, and Support Vector Machine (SVM), the…

Computer Vision and Pattern Recognition · Computer Science 2011-10-26 Thai Hoang Le , Len Bui