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Principal Component Analysis with Noisy and/or Missing Data
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Principal Component Analysis with Noisy and/or Missing Data
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We present a method for performing Principal Component Analysis (PCA) on noisy datasets with missing values. Estimates of the measurement error are used to weight the input data such that compared to classic PCA, the resulting eigenvectors are more sensitive to the true underlying signal variations rather than being pulled by heteroskedastic measurement noise. Missing data is simply the limiting case of weight=0. The underlying algorithm is a noise weighted Expectation Maximization (EM) PCA, which has additional benefits of implementation speed and flexibility for smoothing eigenvectors to reduce the noise contribution. We present applications of this method on simulated data and QSO spectra from the Sloan Digital Sky Survey.
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Cited by 1 Pith paper
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Robust Heteroskedastic Matrix Factorization: A Generalization of PCA that Flags Outliers and Handles Missing Data
A robust, heteroskedastic matrix factorization method generalizes PCA to handle per-feature uncertainties, missing data, and outlier detection via Student-t likelihood iterative reweighting.
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