In this paper we address the problem of clustering trajectories, namely sets of short se quences of data measured as a function of a dependent variable such as time. Examples include storm path trajectories, longitudinal data such as drug therapy response, func tional expression data in computational biology, and movements of objects or individuals in video sequences. Our clustering algorithm is based on a principled method for probabilistic modelling of a set of trajectories as individual sequences of points generated from a finite mixture model consisting of regression model components. Unsupervised learning is carried out using maximum likelihood principles. Specifically, the EM algorithm is used to cope with the hidden data problem (i.e., the cluster memberships). We also develop general izations of the method to handle non-parametric (kernel) regression components as well as multi-dimensional outputs. Simulation results comparing our method with other clustering methods such as K-means and Gaussian mixtures are presented as well as experimental results on real data sets.
A probabilistic clustering technique is developed for classification of wintertime extratropical cyclone (ETC) tracks over the North Atlantic. We use a regression mixture model to describe the longitude-time and latitude-time propagation of the ETCs.A simple tracking algorithm is applied to 6-hourly mean sea-level pressure fields to obtain the tracks from either a general circulation model (GCM) or a reanalysis data set. Quadratic curves are found to provide the best description of the data.We select a three-cluster classification for both data sets, based on a mix of objective and subjective criteria. The track orientations in each of the clusters are broadly similar for the GCM and reanalyzed data; they are characterized by predominantly south-to-north (S-N), west-to-east (W-E), and southwest-to-northeast (SW-NE) tracking cyclones, respectively. The reanalysis cyclone tracks, however, are found to be much more tightly clustered geographically than those of the GCM. For the reanalysis data, a link is found between the occurrence of cyclones belonging to different clusters of trajectory-shape, and the phase of the North Atlantic Oscillation (NAO). The positive phase of the NAO is associated with the SW-NE oriented cluster, whose tracks are relatively straight and smooth (with cyclones that are typically faster, more intense, 2 and of longer duration). The negative NAO phase is associated with more-erratic W-E tracks, with typically weaker and slower-moving cyclones. The S-N cluster is accompanied by a more transient geopotential trough over the western North Atlantic. No clear associations are found in the case of the GCM composites.The GCM is able to capture cyclone tracks of quite realistic orientation, as well as subtle associated features of cyclone intensity, speed and lifetimes. The clustering clearly highlights, though, the presence of serious systematic errors in the GCM's simulation of ETC behavior.3
A new probabilistic clustering technique, based on a regression mixture model, is used to describe tropical cyclone trajectories in the western North Pacific. Each component of the mixture model consists of a quadratic regression curve of cyclone position against time. The best-track 1950-2002 dataset is described by seven distinct clusters. These clusters are then analyzed in terms of genesis location, trajectory, landfall, intensity, and seasonality.Both genesis location and trajectory play important roles in defining the clusters. Several distinct types of straight-moving, as well as recurving, trajectories are identified, thus enriching this main distinction found in previous studies. Intensity and seasonality of cyclones, though not used by the clustering algorithm, are both highly stratified from cluster to cluster. Three straight-moving trajectory types have very small withincluster spread, while the recurving types are more diffuse. Tropical cyclone landfalls over East and Southeast Asia are found to be strongly cluster dependent, both in terms of frequency and region of impact.The relationships of each cluster type with the large-scale circulation, sea surface temperatures, and the phase of the El Niño-Southern Oscillation are studied in a companion paper.
A new probabilistic clustering technique, based on a regression mixture model, is used to describe tropical cyclone trajectories in the western North Pacific. Each component of the mixture model consists of a quadratic regression curve of cyclone position against time. The best-track 1950-2002 dataset is described by seven distinct clusters. These clusters are then analyzed in terms of genesis location, trajectory, landfall, intensity, and seasonality.Both genesis location and trajectory play important roles in defining the clusters. Several distinct types of straight-moving, as well as recurving, trajectories are identified, thus enriching this main distinction found in previous studies. Intensity and seasonality of cyclones, though not used by the clustering algorithm, are both highly stratified from cluster to cluster. Three straight-moving trajectory types have very small withincluster spread, while the recurving types are more diffuse. Tropical cyclone landfalls over East and Southeast Asia are found to be strongly cluster dependent, both in terms of frequency and region of impact.The relationships of each cluster type with the large-scale circulation, sea surface temperatures, and the phase of the El Niño-Southern Oscillation are studied in a companion paper.
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