35 A Matrix Factorization-Based Method for Solar Spectral Irradiance Missing Data Imputation

Oregon Convention Center 

Solar Spectral Irradiance (SSI) is an important quantity in geophysical research, but missing data due to instrument downtime poses challenges. Existing methods, such as matrix completion and linear interpolation, struggle with recovery, due to the absence of temporal smoothness and the accomodation of 11-year SSI cycle driven by periodic solar magnetic activity.

This paper introduces SoftImpute with Projected Auto-regressive regularization (SIPA), a matrix factorization-based algorithm addressing downtime missingness. SIPA combines matrix low-rank pursuit and temporal smoothness regularization, offering an efficient alternating algorithm. A projection to the Auto-regressive (AR) penalty term prevents disturbance on non-downtime entries.

We prove the algorithm's non-decreasing property, analyze convergence rates, and design model assumptions for uncertainty quantification. An optimal sample splitting strategy for universal inference is given. Through simulated and real data, experimental validation demonstrates SIPA's superiority over existing methods in recovering downtime-induced missing Solar Spectral Irradiance data.

solar irradiance

vector time series

missing data imputation

matrix low-rank completion

alternating minimization

uncertainty quantification 

Section on Statistics and the Environment