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Robust probabilistic PCA with missing data and contribution analysis for outlier detection

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  • Chen, Tao
  • Martin, Elaine
  • Montague, Gary

Abstract

Principal component analysis (PCA) is a widely adopted multivariate data analysis technique, with interpretation being established on the basis of both classical linear projection and a probability model (i.e. probabilistic PCA (PPCA)). Recently robust PPCA models, by using the multivariate t-distribution, have been proposed to consider the situation where there may be outliers within the data set. This paper presents an overview of the robust PPCA technique, and further discusses the issue of missing data. An expectation-maximization (EM) algorithm is presented for the maximum likelihood estimation of the model parameters in the presence of missing data. When applying robust PPCA for outlier detection, a contribution analysis method is proposed to identify which variables contribute the most to the occurrence of outliers, providing valuable information regarding the source of outlying data. The proposed technique is demonstrated on numerical examples, and the application to outlier detection and diagnosis in an industrial fermentation process.

Suggested Citation

  • Chen, Tao & Martin, Elaine & Montague, Gary, 2009. "Robust probabilistic PCA with missing data and contribution analysis for outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3706-3716, August.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:10:p:3706-3716
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    References listed on IDEAS

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    1. Michael E. Tipping & Christopher M. Bishop, 1999. "Probabilistic Principal Component Analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 611-622.
    2. Tao Chen & Julian Morris & Elaine Martin, 2006. "Probability density estimation via an infinite Gaussian mixture model: application to statistical process monitoring," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(5), pages 699-715, November.
    3. Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
    4. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549, September.
    5. Liu, Chuanhai, 1997. "ML Estimation of the MultivariatetDistribution and the EM Algorithm," Journal of Multivariate Analysis, Elsevier, vol. 63(2), pages 296-312, November.
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    2. Sang-Mok Lee & So-Won Choi & Eul-Bum Lee, 2023. "Prediction Modeling of Flue Gas Control for Combustion Efficiency Optimization for Steel Mill Power Plant Boilers Based on Partial Least Squares Regression (PLSR)," Energies, MDPI, vol. 16(19), pages 1-33, September.
    3. Boente, Graciela & Pires, Ana M. & Rodrigues, Isabel M., 2010. "Detecting influential observations in principal components and common principal components," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2967-2975, December.
    4. Efstathios Panayi & Gareth Peters & Ioannis Kosmidis, 2014. "Liquidity commonality does not imply liquidity resilience commonality: A functional characterisation for ultra-high frequency cross-sectional LOB data," Papers 1406.5486, arXiv.org.
    5. Dorota Toczydlowska & Gareth W. Peters, 2018. "Financial Big Data Solutions for State Space Panel Regression in Interest Rate Dynamics," Econometrics, MDPI, vol. 6(3), pages 1-45, July.

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