Abstract
Conventional principal component analysis operates using a correlation matrix that is defined in the space of real numbers. This study introduces a novel method—complex Hilbert principal component analysis—which analyzes data using a correlation matrix defined in the space of complex numbers. As a practical application, we examine 10 major categories from the Japanese Family Income and Expenditure Survey for the period between January 1, 2000 and June 30, 2023, paying special attention to the time periods preceding and following the onset of the novel coronavirus disease 2019 pandemic. By analyzing the mode signal’s peaks, we identify specific days that exhibit characteristics that are consistent with the events occurring before and after the pandemic.