Authors:
Telmo J. P. Pires
and
Mário A. T. Figueiredo
Affiliation:
Instituto de Telecomunições and Instituto Superior Técnico, Portugal
Keyword(s):
Unsupervised Learning, Directional Statistics, k-means, EM Algorithm, Nonnegative Matrix Factorization, Trajectory Clustering.
Related
Ontology
Subjects/Areas/Topics:
Applications
;
Bayesian Models
;
Clustering
;
Computer Vision, Visualization and Computer Graphics
;
Human-Computer Interaction
;
Matrix Factorization
;
Methodologies and Methods
;
Model Selection
;
Motion and Tracking
;
Motion, Tracking and Stereo Vision
;
Pattern Recognition
;
Physiological Computing Systems
;
Shape Representation
;
Software Engineering
;
Sparsity
;
Theory and Methods
Abstract:
Automatic trajectory classification has countless applications, ranging from the natural sciences, such as zoology and meteorology, to urban planning, sports analysis, and surveillance, and has generated great research interest. This paper proposes and evaluates three new methods for trajectory clustering, strictly based on the trajectory shapes, thus invariant under changes in spatial position and scale (and, optionally, orientation). To extract shape information, the trajectories are first uniformly resampled using splines, and then described by the sequence of tangent angles at the resampled points. Dealing with angular data is challenging, namely due to its periodic nature, which needs to be taken into account when designing any clustering technique. In this context, we propose three methods: a variant of the k-means algorithm, based on a dissimilarity measure that is adequate for angular data; a finite mixture of multivariate Von Mises distributions, which is fitted using an EM
algorithm; sparse nonnegative matrix factorization, using complex representation of the angular data. Methods for the automatic selection of the number of clusters are also introduced. Finally, these techniques are tested and compared on both real and synthetic data, demonstrating their viability.
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