A1218
Title: Hierarchical principal component analysis of high-dimensional spatial-temporal data
Authors: Chi Tim Ng - Hang Seng University of Hong Kong (Hong Kong) [presenting]
Abstract: Modern data collection technology allows researchers to obtain multivariate data from different geographical locations and different time points. For example, the Google search frequency of $P=100$ health-related keywords in N=52 states in the United States over a period of T=52 weeks. In large-scale tensor-valued datasets, P, T, N can be even greater. Traditional principal component analysis methods of data reduction are designed for the dataset represented as a two-dimensional array as the rows and columns of a spreadsheet. The extra dimension in the high-dimensional spatial-temporal data (P, T, N) gives new challenges to the researchers. The goal is to propose a hierarchical principal component analysis method for the tensor-valued data of three or even higher-dimensional arrays. By summarizing the huge dataset into relatively few driving forces, the massive dataset can be visualized through the changes in the influences of these driving forces over time and geographical regions. Empirical examples are used to illustrate the proposed hierarchical principal component analysis methods. The performances are evaluated through numerical simulation. This research was supported in part by the School Research Grant from the School of Decision Science, Hang Seng University of Hong Kong (No: SDSC-SRG036).
