Bayesian principal component analysis

Mohamed Nounou, Bhavik R. Bakshi, Prem K. Goel, Xiaotong Shen

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

Principal component analysis (PCA) is a dimensionality reduction modeling technique that transforms a set of process variables by rotating their axes of representation. Maximum likelihood PCA (MLPCA) is an extension that accounts for different noise contributions in each variable. Neither PCA nor any of its extensions utilizes external information about the model or data, such as the range or distribution of the underlying measurements. Such prior information can be extracted from measured data and can be used to greatly enhance the model accuracy. This paper develops a Bayesian PCA (BPCA) modeling algorithm that improves the accuracy of estimating the parameters and measurements by incorporating prior knowledge about the data and model. The proposed approach integrates modeling and feature extraction by simultaneously solving parameter estimation and data reconciliation optimization problems. Methods for estimating the prior parameters from available data are discussed. Furthermore, BPCA reduces to PCA or MLPCA when a uniform prior is used. Several examples illustrate the benefits of BPCA versus existing methods even when the measurements violate the assumptions about their distribution.

Original languageEnglish
Pages (from-to)576-595
Number of pages20
JournalJournal of Chemometrics
Volume16
Issue number11
DOIs
Publication statusPublished - 1 Nov 2002
Externally publishedYes

Fingerprint

Bayesian Analysis
Principal component analysis
Principal Component Analysis
Maximum likelihood
Maximum Likelihood
Modeling
Reconciliation
Dimensionality Reduction
Prior Information
Violate
Prior Knowledge
Parameter estimation
Feature Extraction
Parameter Estimation
Feature extraction
Rotating
Integrate
Model
Transform
Optimization Problem

Keywords

  • Bayesian analysis
  • Filtering
  • Latent variables
  • Principal component analysis

ASJC Scopus subject areas

  • Analytical Chemistry
  • Applied Mathematics

Cite this

Nounou, M., Bakshi, B. R., Goel, P. K., & Shen, X. (2002). Bayesian principal component analysis. Journal of Chemometrics, 16(11), 576-595. https://doi.org/10.1002/cem.759

Bayesian principal component analysis. / Nounou, Mohamed; Bakshi, Bhavik R.; Goel, Prem K.; Shen, Xiaotong.

In: Journal of Chemometrics, Vol. 16, No. 11, 01.11.2002, p. 576-595.

Research output: Contribution to journalArticle

Nounou, M, Bakshi, BR, Goel, PK & Shen, X 2002, 'Bayesian principal component analysis', Journal of Chemometrics, vol. 16, no. 11, pp. 576-595. https://doi.org/10.1002/cem.759
Nounou, Mohamed ; Bakshi, Bhavik R. ; Goel, Prem K. ; Shen, Xiaotong. / Bayesian principal component analysis. In: Journal of Chemometrics. 2002 ; Vol. 16, No. 11. pp. 576-595.
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