Robust generalized canonical correlation analysis based on scatter matrices

IF 1.5 3区数学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computational Statistics & Data Analysis Pub Date : 2025-01-10 DOI:10.1016/j.csda.2025.108126

Nadia L. Kudraszow , Alejandra V. Vahnovan , Julieta Ferrario , M. Victoria Fasano

引用次数: 0

Abstract

Generalized Canonical Correlation Analysis (GCCA) is a powerful tool for analyzing and understanding linear relationships between multiple sets of variables. However, its classical estimations are highly sensitive to outliers, which can significantly affect the results of the analysis. A functional version of GCCA is proposed, based on scatter matrices, leading to robust and Fisher consistent estimators for appropriate choices of the scatter matrix. In cases where scatter matrices are ill-conditioned, a modification based on an estimation of the precision matrix is introduced. A procedure to identify influential observations is also developed. A simulation study evaluates the finite-sample performance of the proposed methods under clean and contaminated samples. The advantages of the influential data detection approach are demonstrated through an application to a real dataset.

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来源期刊

Computational Statistics & Data Analysis 数学-计算机：跨学科应用

CiteScore

3.70

自引率

5.60%

发文量

167

审稿时长

60 days

期刊介绍： Computational Statistics and Data Analysis (CSDA), an Official Publication of the network Computational and Methodological Statistics (CMStatistics) and of the International Association for Statistical Computing (IASC), is an international journal dedicated to the dissemination of methodological research and applications in the areas of computational statistics and data analysis. The journal consists of four refereed sections which are divided into the following subject areas: I) Computational Statistics - Manuscripts dealing with: 1) the explicit impact of computers on statistical methodology (e.g., Bayesian computing, bioinformatics,computer graphics, computer intensive inferential methods, data exploration, data mining, expert systems, heuristics, knowledge based systems, machine learning, neural networks, numerical and optimization methods, parallel computing, statistical databases, statistical systems), and 2) the development, evaluation and validation of statistical software and algorithms. Software and algorithms can be submitted with manuscripts and will be stored together with the online article. II) Statistical Methodology for Data Analysis - Manuscripts dealing with novel and original data analytical strategies and methodologies applied in biostatistics (design and analytic methods for clinical trials, epidemiological studies, statistical genetics, or genetic/environmental interactions), chemometrics, classification, data exploration, density estimation, design of experiments, environmetrics, education, image analysis, marketing, model free data exploration, pattern recognition, psychometrics, statistical physics, image processing, robust procedures. [...] III) Special Applications - [...] IV) Annals of Statistical Data Science [...]