Principal Component Analysis in the Presence of Missing Data

2017 ◽  
pp. 47-70 ◽  
Author(s):  
Marco Geraci ◽  
Alessio Farcomeni
Keyword(s):  
Principal Component Analysis ◽  
Missing Data ◽  
Principal Component ◽  
Component Analysis

scholarly journals Extracting Common Mode Errors of Regional GNSS Position Time Series in the Presence of Missing Data by Variational Bayesian Principal Component Analysis

Sensors ◽  
2020 ◽  
Vol 20 (8) ◽  
pp. 2298 ◽  
Author(s):  
Wudong Li ◽  
Weiping Jiang ◽  
Zhao Li ◽  
Hua Chen ◽  
Qusen Chen ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Time Series ◽  
Missing Data ◽  
Principal Component ◽  
Component Analysis ◽  
Common Mode ◽  
Variational Bayesian ◽  
North East ◽  
Position Time Series ◽  
Gnss Position Time Series

Removal of the common mode error (CME) is very important for the investigation of global navigation satellite systems’ (GNSS) error and the estimation of an accurate GNSS velocity field for geodynamic applications. The commonly used spatiotemporal filtering methods normally process the evenly spaced time series without missing data. In this article, we present the variational Bayesian principal component analysis (VBPCA) to estimate and extract CME from the incomplete GNSS position time series. The VBPCA method can naturally handle missing data in the Bayesian framework and utilizes the variational expectation-maximization iterative algorithm to search each principal subspace. Moreover, it could automatically select the optimal number of principal components for data reconstruction and avoid the overfitting problem. To evaluate the performance of the VBPCA algorithm for extracting CME, 44 continuous GNSS stations located in Southern California were selected. Compared to previous approaches, VBPCA could achieve better performance with lower CME relative errors when more missing data exists. Since the first principal component (PC) extracted by VBPCA is remarkably larger than the other components, and its corresponding spatial response presents nearly uniform distribution, we only use the first PC and its eigenvector to reconstruct the CME for each station. After filtering out CME, the interstation correlation coefficients are significantly reduced from 0.43, 0.46, and 0.38 to 0.11, 0.10, and 0.08, for the north, east, and up (NEU) components, respectively. The root mean square (RMS) values of the residual time series and the colored noise amplitudes for the NEU components are also greatly suppressed, with average reductions of 27.11%, 28.15%, and 23.28% for the former, and 49.90%, 54.56%, and 49.75% for the latter. Moreover, the velocity estimates are more reliable and precise after removing CME, with average uncertainty reductions of 51.95%, 57.31%, and 49.92% for the NEU components, respectively. All these results indicate that the VBPCA method is an alternative and efficient way to extract CME from regional GNSS position time series in the presence of missing data. Further work is still required to consider the effect of formal errors on the CME extraction during the VBPCA implementation.

scholarly journals Sequential projection pursuit principal component analysis – dealing with missing data associated with new -omics technologies

BioTechniques ◽  
2013 ◽  
Vol 54 (3) ◽  
Author(s):  
Bobbie-Jo M. Webb-Robertson ◽  
Melissa M. Matzke ◽  
Thomas O. Metz ◽  
Jason E. McDermott ◽  
Hyunjoo Walker ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Missing Data ◽  
Projection Pursuit ◽  
Principal Component ◽  
Component Analysis ◽  
Omics Technologies

Process Monitoring of Filter Press in Hydrometallurgy Based on PCA

2015 ◽  
Vol 738-739 ◽  
pp. 844-848
Author(s):  
Qing Kai Wang ◽  
Xiao Yu Zou ◽  
Shu Wang ◽  
Da Kuo He ◽  
Yang Zhou ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Data Analysis ◽  
Missing Data ◽  
Process Monitoring ◽  
Test Data ◽  
Principal Component ◽  
Sampling Period ◽  
Component Analysis ◽  
Filter Press ◽  
Metallurgical Technology

Hydrometallurgy is a popular metallurgical technology. Filter press is common but vital to the production of hydrometallurgy. Hence, the process monitoring of filter press is of great significance for hydrometallurgy. Due to data analysis and related knowledge of filter press, Principal component analysis (PCA) is applied to process monitoring of the filter press via two traditional statistics. However, modeling and test data collected from actual production suffers from outliers, missing data, inconsistent sampling period between variables. Based on these practical problems, corresponding data proceeding technique is proposed. The final application simulation illustrates the validity of the proposed method.

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