Novel approaches in Extended Principal Component Analysis to compare spatio-temporal patterns among multiple image time series

Extended Principal Component Analysis (EPCA) aims to examine the patterns of variability shared among multiple datasets. In image time series analysis, this is conventionally done by virtually extending the spatial dimension of the time series by spatially concatenating the different time series and then performing S-mode PCA. In S-mode analysis, samples in space are the statistical variables and samples in time are the statistical observations. This paper introduces the concept of temporal concatenation of multiple image time series to perform EPCA. EPCA can also be done with a T-mode orientation in which samples in time are the statistical variables and samples in space are the statistical observations. This leads to a total of four orientations in which EPCA can be carried out. This research explores these four orientations and their implications in investigating spatio-temporal relationships among multiple time series. This research demonstrates that EPCA carried out with temporal concatenation of the multiple time series with T-mode (tT) is able to identify similar spatial patterns among multiple time series. The conventional S-mode EPCA with spatial concatenation (sS) identifies similar temporal patterns among multiple time series. The other two modes, namely T-mode with spatial concatenation (sT) and S-mode with temporal concatenation (tS), are able to identify patterns which share consistent temporal phase relationships and consistent spatial phase relationships with each other, respectively. In a case study using three sets of precipitation time series data from GPCP, CMAP and NCEP-DOE, the results show that examination of all four modes provides an effective basis for comparison of the series.