Finding Representative Points in Multivariate Data Using PCA

Abstract: The idea of representation has been used in various fields of study from data analysis to political science. In this paper, we define representativeness and describe a method to isolate data points that can represent the entire data set. Also, we show how the minimum set of representative data points can be generated. We use data from GLOBE (a project to study the effects on Land Change based on a set of parameters that include temperature, forest cover, human population, atmospheric parameters and many other variables) to test & validate the algorithm. Principal Component Analysis (PCA) is used to reduce the dimensions of the multivariate data set, so that the representative points can be generated efficiently and its Representativeness has been compared against Random Sampling of points from the data set.