Cross-validation methods in principal component analysis: A comparison

Diana, Giancarlo; Tommasi, Chiara

doi:10.1007/bf02511446

Cited by 88 publications

(35 citation statements)

References 15 publications

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“…Selecting an appropriate number of PCs introduces a good performance of PCA in terms of processes monitoring. Several methods for determining the number of PCs have been proposed such as; the Scree plot [15], the cumulative percent variance (CPV), the cross validation [16], and the profile likelihood [17]. In this study herein, the cumulative percent variance method is utilized to come up with the optimum number of retained principal components.…”

Section: Principal Component Analysis (Pca)mentioning

confidence: 99%

Enhanced Monitoring of Environmental Processes

Mansouri¹,

Destain²,

Nounou³

et al. 2016

IJESD

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Abstract-The process monitoring systems are often utilized in environmental process operations. Many practical applications used for scheduling, planning or operator training are often complex for direct usage in process monitoring. In this paper, it is proposed to use the generalized likelihood ratio (GLR) based principal components analysis (PCA) for process monitoring and fault detection of environmental processes. The objective is to combine the GLR test with PCA model in order to improve the fault detection performance. GLR-based PCA is a multivariate statistical technique used in multivariate statistical process monitoring and fault detection. PCA reduces the dimensionality of the original data by projecting it onto a space with significantly fewer dimensions. It obtains the principal events of variability in a process. If some of these events change, it can be due to a fault in the process. The data are collected from the crop model in order to calculate the PCA model and the thresholds; Hotelling statistic, 2 T , Q statistic and GLR test statistic are used in order to detect the faults. It is demonstrated that the performance of faults detection can be improved by combining GLR test and PCA.

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Section: Principal Component Analysis (Pca)mentioning

confidence: 99%

Enhanced Monitoring of Environmental Processes

Mansouri¹,

Destain²,

Nounou³

et al. 2016

IJESD

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“…n pc is commonly chosen by means of crossvalidation techniques [30]. In this work leave-one-out cross-validation [31] was used. Note that usually n pc ⌧ JK w due to the presence of high correlation amongst the process variables.…”

Section: Model Identificationmentioning

confidence: 99%

Trajectory tracking of batch product quality using intermittent measurements and moving window estimation

Wan

Marjanovic

Lennox

2012

Proceedings of 2012 UKACC International Conference on Control

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In order to meet tight product quality specifications for batch/semi-batch processes, it is vital to monitor and control product quality throughout the batch duration. The ideal strategy is to achieve end-product quality specifications through trajectory tracking control during a batch run. However, due to the lack of in-situ sensors for continuous monitoring of batch product quality, the measurements are usually implemented by laboratory assays and are inherently intermittent. Therefore, direct trajectory tracking of batch product quality is challenging in such applications. This paper proposes a practical approach to realise trajectory tracking control of batch product quality in those situations where only intermittent measurements are available. The first step of the approach consists in identifying a projection to latent structures (PLS) model to identify a relationship between readily measured process variable trajectories and intermittently measured batch product quality. Then the identified PLS-based prediction model is transformed into recursive formulation by utilising missing data imputation algorithms. Such recursive formulation allows identified PLS-based model to be readily incorporated as a predictor into standard model predictive control (MPC) framework. Case study employing simulated fed-batch fermentation process used to manufacture penicillin was employed to illustrate the principle and the e↵ectiveness of the proposed approach.

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“…Many algorithms for selecting principal components have been put forward, such as, cumulative percent variance (CPV) Jiang and Yan (2012), variance of reconstruction error (VℝE) Lu et al (2004) and cross validation (CV) Diana and Tommasi (2002). CPV selects the first several PCs that represent the major variance information of original data.…”

Section: Introductionmentioning

confidence: 99%

“…CV is a method that is not based on the eigenvalues of the sample covariance matrix but on the predictive of different PC models. The basic idea of CV is the use of different data sets for estimation and validation of each PC model Diana and Tommasi (2002), Qin and Dunia (2000). Generally, most of the classical algorithms just consider normal operational observations and select the first several PCs with larger variance.…”

Section: Introductionmentioning

confidence: 99%