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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

Principal Component Analysis (PCA) is a foundational technique in machine learning for dimensionality reduction of high-dimensional datasets. However, PCA could lead to biased outcomes that disadvantage certain subgroups of the underlying…

Machine Learning · Computer Science 2025-03-04 Junhui Shen , Aaron J. Davis , Ding Lu , Zhaojun Bai

Dimension reduction is useful for exploratory data analysis. In many applications, it is of interest to discover variation that is enriched in a "foreground" dataset relative to a "background" dataset. Recently, contrastive principal…

Methodology · Statistics 2021-05-04 Didong Li , Andrew Jones , Barbara Engelhardt

Principal Component Analysis (PCA) is the most common nonparametric method for estimating the volatility structure of Gaussian interest rate models. One major difficulty in the estimation of these models is the fact that forward rate curves…

Statistical Finance · Quantitative Finance 2014-08-28 Marcio Laurini , Alberto Ohashi

This paper introduces a robust estimation strategy for the spatial functional linear regression model using dimension reduction methods, specifically functional principal component analysis (FPCA) and functional partial least squares…

Methodology · Statistics 2024-10-28 Ufuk Beyaztas , Abhijit Mandal , Han Lin Shang

Principal component analysis (PCA) is a popular dimension reduction technique often used to visualize high-dimensional data structures. In genomics, this can involve millions of variables, but only tens to hundreds of observations.…

Statistics Theory · Mathematics 2020-06-11 Kristoffer Hellton , Magne Thoresen

Functional data analysis (FDA) is a part of modern multivariate statistics that analyses data providing information about curves, surfaces or anything else varying over a certain continuum. In economics and empirical finance we often have…

Methodology · Statistics 2019-10-25 Daniel Kosiorowski , Jerzy P. Rydlewski , Małgorzata Snarska

In this paper we address the problem of feature selection when the data is functional, we study several statistical procedures including classification, regression and principal components. One advantage of the blinding procedure is that it…

Methodology · Statistics 2023-12-29 Ricardo Fraiman , Yanina Gimenez , Marcela Svarc

This paper describes some applications of an incremental implementation of the principal component analysis (PCA). The algorithm updates the transformation coefficients matrix on-line for each new sample, without the need to keep all the…

Machine Learning · Statistics 2019-08-14 Vittorio Lippi , Giacomo Ceccarelli

Software testing uses wide range of different tools to enhance the complicated process of defining quality of the system under test. Formal Concept Analysis (FCA) provides us with algorithms of deriving formal ontology from a set of objects…

Software Engineering · Computer Science 2015-05-07 Fedor Strok

Principal component analysis (PCA) is often used to analyze multivariate data together with cluster analysis, which depends on the number of principal components used. It is therefore important to determine the number of significant…

Applications · Statistics 2024-09-19 Joshua C. Macdonald , Javier Blanco-Portillo , Marcus W. Feldman , Yoav Ram

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

A powerful study design in the fields of genomics and metabolomics is the 'replicated time course experiment' where individual time series are observed for a sample of biological units, such as human patients, termed replicates. Standard…

Methodology · Statistics 2011-12-02 Maurice Berk , Giovanni Montana

Principal component analysis (PCA) is a dimensionality reduction method in data analysis that involves diagonalizing the covariance matrix of the dataset. Recently, quantum algorithms have been formulated for PCA based on diagonalizing a…

Quantum Physics · Physics 2022-10-26 Max Hunter Gordon , M. Cerezo , Lukasz Cincio , Patrick J. Coles

An improved mixture of probabilistic principal component analysis (PPCA) has been introduced for nonlinear data-driven process monitoring in this paper. To realize this purpose, the technique of a mixture of probabilistic principal…

Methodology · Statistics 2020-12-15 Jingxin Zhang , Hao Chen , Songhang Chen , Xia Hong

A data table which is arranged according to two factors can often be considered as a compositional table. An example is the number of unemployed people, split according to gender and age classes. Analyzed as compositions, the relevant…

Methodology · Statistics 2019-04-12 Julie Rendlová , Karel Hron , Kamila Fačevicová , Peter Filzmoser

The robust PCA problem, wherein, given an input data matrix that is the superposition of a low-rank matrix and a sparse matrix, we aim to separate out the low-rank and sparse components, is a well-studied problem in machine learning. One…

Machine Learning · Computer Science 2017-07-06 U. N. Niranjan , Arun Rajkumar , Theja Tulabandhula

Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain…

Machine Learning · Computer Science 2017-10-27 Gang Wang , Jia Chen , Georgios B. Giannakis

This work obtains novel finite sample guarantees for Principal Component Analysis (PCA). These hold even when the corrupting noise is non-isotropic, and a part (or all of it) is data-dependent. Because of the latter, in general, the noise…

Machine Learning · Statistics 2017-09-20 Namrata Vaswani , Praneeth Narayanamurthy

Functional data analysis, which handles data arising from curves, surfaces, volumes, manifolds and beyond in a variety of scientific fields, is a rapidly developing area in modern statistics and data science in the recent decades. The…

Methodology · Statistics 2020-08-21 Xiaoke Zhang , Wu Xue , Qiyue Wang