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This paper presents a new method called the  functional distributional clustering algorithm  (FDCA) that seeks to identify spatially contiguous clusters and incorporate changes in temporal patterns across overcrowded networks. This method is motivated by a graph-based network composed of sensors arranged over space where recorded observations for each sensor represent a multi-modal distribution. The proposed method is fully non-parametric and generates clusters within an agglomerative hierarchical clustering approach based on a measure of distance that defines a cumulative distribution function over temporal changes for different locations in space. Traditional hierarchical clustering algorithms that are spatially adapted do not typically accommodate the temporal characteristics of the underlying data. The effectiveness of the FDCA is illustrated using an application to both empirical and simulated data from about 400 sensors in a 2.5 square miles network area in downtown San Francisco, California. The results demonstrate the superior ability of the the FDCA in identifying  true clusters  compared to functional only and distributional only algorithms  and similar performance to a model-based clustering algorithm .

Functional distributional clustering using spatio-temporal data