Principal Component Analysis with Noisy and/or Missing Data

TL;DR

This paper introduces a noise-weighted EM PCA method that effectively handles noisy and missing data, improving the extraction of true signal variations in datasets like astronomical spectra.

Contribution

It proposes a novel noise-weighted EM PCA algorithm that enhances PCA performance on noisy and incomplete data, with applications demonstrated on simulated and real astronomical datasets.

Findings

Improved eigenvector sensitivity to true signals over noise.

Effective handling of missing data as zero-weight cases.

Enhanced speed and smoothing capabilities of the algorithm.

Abstract

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.