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Analyzing GPS Datasets using Density Ranking

A traditional approach to analyze the distribution of a dataset is through estimating the underly probability density function. However, this approach fails in analyzing GPS data because the underlying probability density function does not exist. To handle this problem, we introduce the concept of density ranking. Density ranking is a quantity derived from ranking the relative probability intensity between points. We will show that density ranking is a powerful tool in analyzing GPS datasets and discuss how density ranking can be used to quantify human activity space. Moreover, to analyze multiple GPS datasets, we introduce geometric and topological summary curves. These curves summarize the density ranking using certain characteristics and provide useful information about each individual's activity space.