Principal Component Analysis with Missing Data and Its Application to Polyhedral Object Modeling

2001 ◽  
pp. 3-39 ◽  
Author(s):  
Harry Shum ◽  
Katsushi Ikeuchi ◽  
Raj Reddy
Keyword(s):  
Principal Component Analysis ◽  
Missing Data ◽  
Principal Component ◽  
Component Analysis ◽  
Object Modeling

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 Principal Component Analysis with Noisy and/or Missing Data

2012 ◽  
Vol 124 (919) ◽  
pp. 1015-1023 ◽  
Author(s):  
Stephen Bailey
Keyword(s):  
Principal Component Analysis ◽  
Missing Data ◽  
Principal Component ◽  
Component Analysis

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
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