An Application of Proper Orthogonal Decomposition for Estimating Missing Data of Patients in Different Cause Groups

Norapon Sukuntee, Saifon Chaturantabut

Abstract

This work applies the notion of proper orthogonal decomposition(POD) to approximate missing data that represents the amount of in-patients from different cause groups, such as inuenza, malaria, HIV and alcoholic liver diseases, in Saraburi provice, Thailand. POD is used to construct a low-dimensional basis that extracts dominant trends of data from existing set of complete samples. The approximation of each missing data is obtained through an extension of POD called gappy POD (GPOD), which employs available data effciently and optimally in the least-squares sense. Due to the large variation among the numbers of in-patients in different categories, this work applies a normalization using mean and standard deviation to pre-process the data and introduces a possible range of each approximated missing value. The numerical tests demonstrate the accuracy of the estimation from GPOD using different numbers of complete samples. We also investigate the change in accuracy when the number of missing data in eachincomplete sample increases.