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Dimensionality reduction represents a critical preprocessing step in order to increase the efficiency and the performance of many hyperspectral imaging algorithms. However, dimensionality reduction algorithms, such as the Principal…

Machine Learning · Computer Science 2024-03-28 E. Martel , R. Lazcano , J. Lopez , D. Madroñal , R. Salvador , S. Lopez , E. Juarez , R. Guerra , C. Sanz , R. Sarmiento

Sparse Principal Components Analysis aims to find principal components with few non-zero loadings. We derive such sparse solutions by adding a genuine sparsity requirement to the original Principal Components Analysis (PCA) objective…

Methodology · Statistics 2014-08-19 Giovanni Maria Merola

We consider multi-class classification problems for high dimensional data. Following the idea of reduced-rank linear discriminant analysis (LDA), we introduce a new dimension reduction tool with a flavor of supervised principal component…

Methodology · Statistics 2017-03-28 Yue Selena Niu , Ning Hao , Bin Dong

Principal Component Analysis (PCA) is a workhorse of modern data science. While PCA assumes the data conforms to Euclidean geometry, for specific data types, such as hierarchical and cyclic data structures, other spaces are more…

Machine Learning · Statistics 2024-07-11 Puoya Tabaghi , Michael Khanzadeh , Yusu Wang , Sivash Mirarab

Principal component analysis (PCA) has been widely applied to dimensionality reduction and data pre-processing for different applications in engineering, biology and social science. Classical PCA and its variants seek for linear projections…

Machine Learning · Computer Science 2017-07-11 Xiaojun Chang , Feiping Nie , Yi Yang , Heng Huang

In this paper, we propose a novel approach named by Discriminative Principal Component Analysis which is abbreviated as Discriminative PCA in order to enhance separability of PCA by Linear Discriminant Analysis (LDA). The proposed method…

Computer Vision and Pattern Recognition · Computer Science 2019-03-13 Hanli Qiao

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 components analysis (PCA) is a widely used dimension reduction technique with an extensive range of applications. In this paper, an online distributed algorithm is proposed for recovering the principal eigenspaces. We further…

Machine Learning · Statistics 2019-05-20 Davoud Ataee Tarzanagh , Mohamad Kazem Shirani Faradonbeh , George Michailidis

Principal Component Analysis (PCA) is a cornerstone of dimensionality reduction, yet its classical formulation relies critically on second-order moments and is therefore fragile in the presence of heavy-tailed data and impulsive noise.…

Machine Learning · Computer Science 2026-05-05 Mario Sayde , Christopher Khater , Jihad Fahs , Ibrahim Abou-Faycal

Principal component analysis (PCA) is by far the most widespread tool for unsupervised learning with high-dimensional data sets. Its application is popularly studied for the purpose of exploratory data analysis and online process…

Applications · Statistics 2019-02-12 Stefania Russo , Guangyu Li , Kris Villez

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 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

Estimating intrinsic dimensionality of data is a classic problem in pattern recognition and statistics. Principal Component Analysis (PCA) is a powerful tool in discovering dimensionality of data sets with a linear structure; it, however,…

Computer Vision and Pattern Recognition · Computer Science 2010-02-11 Mingyu Fan , Nannan Gu , Hong Qiao , Bo Zhang

Sparse Principal Component Analysis (sPCA) is a popular matrix factorization approach based on Principal Component Analysis (PCA) that combines variance maximization and sparsity with the ultimate goal of improving data interpretation. When…

Machine Learning · Statistics 2020-11-19 J. Camacho , A. K. Smilde , E. Saccenti , J. A. Westerhuis

Principal Component Analysis (PCA) is a pivotal technique widely utilized in the realms of machine learning and data analysis. It aims to reduce the dimensionality of a dataset while minimizing the loss of information. In recent years,…

Cryptography and Security · Computer Science 2024-02-06 Xirong Ma

The literature provides strong evidence that stock prices can be predicted from past price data. Principal component analysis (PCA) is a widely used mathematical technique for dimensionality reduction and analysis of data by identifying a…

Mathematical Finance · Quantitative Finance 2018-03-15 Mahsa Ghorbani , Edwin K. P. Chong

The statistical analysis of tree structured data is a new topic in statistics with wide application areas. Some Principal Component Analysis (PCA) ideas were previously developed for binary tree spaces. In this study, we extend these ideas…

Methodology · Statistics 2012-02-14 Carlos A. Alfaro , Burcu Aydın , Elizabeth Bullitt , Alim Ladha , Carlos E. Valencia

Often the relation between the variables constituting a multivariate data space might be characterized by one or more of the terms: ``nonlinear'', ``branched'', ``disconnected'', ``bended'', ``curved'', ``heterogeneous'', or, more general,…

Astrophysics · Physics 2007-09-12 Jochen Einbeck , Ludger Evers , Coryn Bailer-Jones

Traditional principal component analysis (PCA) is well known in high-dimensional data analysis, but it requires to express data by a matrix with observations to be continuous. To overcome the limitations, a new method called flexible PCA…

Methodology · Statistics 2021-08-17 Tonglin Zhang , Baijian Yang , Qianqian Song , Jing Su

Principal component analysis (PCA) is a classical method for dimensionality reduction based on extracting the dominant eigenvectors of the sample covariance matrix. However, PCA is well known to behave poorly in the ``large $p$, small $n$''…

Statistics Theory · Mathematics 2009-08-26 Arash A. Amini , Martin J. Wainwright