PCA model building with missing data: New proposals and a comparative study

[EN] This paper introduces new methods for building principal component analysis (PCA) models with missing data: projection to the model plane (PMP), known data regression (KDR), KDR with principal component regression (PCR), KDR with partial least squares regression (PLS) and trimmed scores regression (TSR). These methods are adapted from their PCA model exploitation version to deal with the more general problem of PCA model building when the training set has missing values. A comparative study is carried out comparing these new methods with the standard ones, such as the modified nonlinear iterative partial least squares (NIPALS), the it- erative algorithm (IA), the data augmentation method (DA) and the nonlinear programming approach (NLP). The performance is assessed using the mean squared prediction error of the reconstructed matrix and the cosines between the actual principal components and the ones extracted by each method. Four data sets, two simulated and two real ones, with several percentages of missing data, are used to perform the comparison. Guardar / Salir Siguiente >Research in this study was partially supported by the Spanish Ministry of Science and Innovation and FEDER funds from the European Union through grant DPI2011-28112-C04-02, and the Spanish Ministry of Economy and Competitiveness through grant ECO2013-43353-R. The authors gratefully acknowledge Salvador Garcia-Munoz for providing the Phi toolbox (version 1.7) to perform the nonlinear programming approach (NLP) method.Folch-Fortuny, A.; Arteaga Moreno, FJ.; Ferrer Riquelme, AJ. (2015). PCA model building with missing data: New proposals and a comparative study. Chemometrics and Intelligent Laboratory Systems. 146:77-88. https://doi.org/10.1016/j.chemolab.2015.05.006S778814

Robust PCA as Bilinear Decomposition with Outlier-Sparsity Regularization

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Airborne gravity and precise positioning for geologic applications

Airborne gravimetry has become an important geophysical tool primarily because of advancements in methodology and instrumentation made in the past decade. Airborne gravity is especially useful when measured in conjunction with other geophysical data, such as magnetics, radar, and laser altimetry. The aerogeophysical survey over the West Antarctic ice sheet described in this paper is one such interdisciplinary study. This paper outlines in detail the instrumentation, survey and data processing methodology employed to perform airborne gravimetry from the multiinstrumented Twin Otter aircraft. Precise positioning from carrier-phase Global Positioning System (GPS) observations are combined with measurements of acceleration made by the gravity meter in the aircraft to obtain the free-air gravity anomaly measurement at aircraft altitude. GPS data are processed using the Kinematic and Rapid Static (KARS) software program, and aircraft vertical acceleration and corrections for gravity data reduction are calculated from the GPS position solution. Accuracies for the free-air anomaly are determined from crossover analysis after significant editing (2.98 mGal rms) and from a repeat track (1.39 mGal rms). The aerogeophysical survey covered a 300,000 km2 region in West Antarctica over the course of five field seasons. The gravity data from the West Antarctic survey reveal the major geologic structures of the West Antarctic rift system, including the Whitmore Mountains, the Byrd Subglacial Basin, the Sinuous Ridge, the Ross Embayment, and Siple Dome. These measurements, in conjunction with magnetics and ice-penetrating radar, provide the information required to reveal the tectonic fabric and history of this important region

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