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.
The authors have applied multivariate cluster analysis to a variety of environmental science domains, including ecological regionalization; environmental monitoring network design; analysis of satellite-, airborne-, and ground-based remote sensing, and climate model-model and model-measurement intercomparison. The clustering methodology employs a k-means statistical clustering algorithm that has been implemented in a highly scalable, parallel high performance computing (HPC) application. Because of its efficiency and use of HPC platforms, the clustering code may be applied as a data mining tool to analyze and compare very large data sets of high dimensionality, such as very long or high frequency resolution time series measurements or model output. The method was originally applied across geographic space and called Multivariate Ge- ographic Clustering (MGC). Now applied across space and through time, the environmental data mining method is called Multivariate Spatio-Temporal Clustering (MSTC). Described here are the clustering algorithm, recent code improvements that significantly reduce the time-to-solution, and a new parallel principal components analysis (PCA) tool that can analyze very large data sets. Finally, a sampling of the authors' applications of MGC and MSTC to problems in the environ- mental sciences are presented.