Robust Bilinear Probabilistic Principal Component Analysis

Principal component analysis (PCA) is one of the most popular tools in multivariate exploratory data analysis. Its probabilistic version (PPCA) based on the maximum likelihood procedure provides a probabilistic manner to implement dimension reduction. Recently, the bilinear PPCA (BPPCA) model, which...

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Autores principales:	Yaohang Lu, Zhongming Teng
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	2-D data probabilistic principal component analysis AECM algorithm matrix variate Gaussian distributions matrix variate <i>t</i> distributions outliers Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/a226d30d8ec741a4a23804bedfa1a54b
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id	oai:doaj.org-article:a226d30d8ec741a4a23804bedfa1a54b
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spelling	oai:doaj.org-article:a226d30d8ec741a4a23804bedfa1a54b2021-11-25T16:13:10ZRobust Bilinear Probabilistic Principal Component Analysis10.3390/a141103221999-4893https://doaj.org/article/a226d30d8ec741a4a23804bedfa1a54b2021-11-01T00:00:00Zhttps://www.mdpi.com/1999-4893/14/11/322https://doaj.org/toc/1999-4893Principal component analysis (PCA) is one of the most popular tools in multivariate exploratory data analysis. Its probabilistic version (PPCA) based on the maximum likelihood procedure provides a probabilistic manner to implement dimension reduction. Recently, the bilinear PPCA (BPPCA) model, which assumes that the noise terms follow matrix variate Gaussian distributions, has been introduced to directly deal with two-dimensional (2-D) data for preserving the matrix structure of 2-D data, such as images, and avoiding the curse of dimensionality. However, Gaussian distributions are not always available in real-life applications which may contain outliers within data sets. In order to make BPPCA robust for outliers, in this paper, we propose a robust BPPCA model under the assumption of matrix variate <i>t</i> distributions for the noise terms. The alternating expectation conditional maximization (AECM) algorithm is used to estimate the model parameters. Numerical examples on several synthetic and publicly available data sets are presented to demonstrate the superiority of our proposed model in feature extraction, classification and outlier detection.Yaohang LuZhongming TengMDPI AGarticle2-D dataprobabilistic principal component analysisAECM algorithmmatrix variate Gaussian distributionsmatrix variate <i>t</i> distributionsoutliersIndustrial engineering. Management engineeringT55.4-60.8Electronic computers. Computer scienceQA75.5-76.95ENAlgorithms, Vol 14, Iss 322, p 322 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	2-D data probabilistic principal component analysis AECM algorithm matrix variate Gaussian distributions matrix variate <i>t</i> distributions outliers Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95
spellingShingle	2-D data probabilistic principal component analysis AECM algorithm matrix variate Gaussian distributions matrix variate <i>t</i> distributions outliers Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95 Yaohang Lu Zhongming Teng Robust Bilinear Probabilistic Principal Component Analysis
description	Principal component analysis (PCA) is one of the most popular tools in multivariate exploratory data analysis. Its probabilistic version (PPCA) based on the maximum likelihood procedure provides a probabilistic manner to implement dimension reduction. Recently, the bilinear PPCA (BPPCA) model, which assumes that the noise terms follow matrix variate Gaussian distributions, has been introduced to directly deal with two-dimensional (2-D) data for preserving the matrix structure of 2-D data, such as images, and avoiding the curse of dimensionality. However, Gaussian distributions are not always available in real-life applications which may contain outliers within data sets. In order to make BPPCA robust for outliers, in this paper, we propose a robust BPPCA model under the assumption of matrix variate <i>t</i> distributions for the noise terms. The alternating expectation conditional maximization (AECM) algorithm is used to estimate the model parameters. Numerical examples on several synthetic and publicly available data sets are presented to demonstrate the superiority of our proposed model in feature extraction, classification and outlier detection.
format	article
author	Yaohang Lu Zhongming Teng
author_facet	Yaohang Lu Zhongming Teng
author_sort	Yaohang Lu
title	Robust Bilinear Probabilistic Principal Component Analysis
title_short	Robust Bilinear Probabilistic Principal Component Analysis
title_full	Robust Bilinear Probabilistic Principal Component Analysis
title_fullStr	Robust Bilinear Probabilistic Principal Component Analysis
title_full_unstemmed	Robust Bilinear Probabilistic Principal Component Analysis
title_sort	robust bilinear probabilistic principal component analysis
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/a226d30d8ec741a4a23804bedfa1a54b
work_keys_str_mv	AT yaohanglu robustbilinearprobabilisticprincipalcomponentanalysis AT zhongmingteng robustbilinearprobabilisticprincipalcomponentanalysis
_version_	1718413272790597632

Robust Bilinear Probabilistic Principal Component Analysis

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