### Understanding Crowd Collectivity: A Meta-Tracking Approach

"... Understanding pedestrian dynamics in crowded scenes is an important problem. Given highly fragmented tra-jectories as input, we present a novel, fully unsupervised approach to automatically infer the semantic regions in a scene. Once the semantic regions are learned, given a track-let of a person, o ..."

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Understanding pedestrian dynamics in crowded scenes is an important problem. Given highly fragmented tra-jectories as input, we present a novel, fully unsupervised approach to automatically infer the semantic regions in a scene. Once the semantic regions are learned, given a track-let of a person, our model predicts the pedestrian’s starting point and destination. The method is comprised of three steps. First, the spatial domain of the scene is quantized into hexagons and a 2D orientation distribution function (ODF) is learned for each hexagon. A Time Homogenous Markov Chain Meta-tracking method is used to automatically find the sources and sinks and later find the dominant paths in the scene. In the last step, using a 3-term based trajectory clustering method, we predict the source and sink for each pedestrian. Furthermore, we introduce a 2-step trajectory reconstruction method to infer the future behavior of each individual in the scene. Qualitative and quantitative experi-ments on a video surveillance dataset from New York Grand Central Station demonstrate the effectiveness of our method both in finding the semantic regions and grouping of frag-mented tracklets. 1.

### Infinite Shift-invariant Grouped Multi-task Learning for Gaussian Processes∗

"... Multi-task learning leverages shared information among data sets to improve the learning performance of individual tasks. The paper applies this framework for data where each task is a phase-shifted periodic time series. In particular, we develop a novel Bayesian nonparametric model capturing a mixt ..."

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Multi-task learning leverages shared information among data sets to improve the learning performance of individual tasks. The paper applies this framework for data where each task is a phase-shifted periodic time series. In particular, we develop a novel Bayesian nonparametric model capturing a mixture of Gaussian processes where each task is a sum of a group-specific function and a component capturing individual variation, in addition to each task being phase shifted. We develop an efficient em algorithm to learn the parameters of the model. As a special case we obtain the Gaussian mixture model and em algorithm for phased-shifted periodic time series. Furthermore, we extend the proposed model by using a Dirichlet Process prior and thereby leading to an infinite mixture model that is capable of doing automatic model selection. A Variational Bayesian approach is developed for inference in this model. Experiments in regression, classification and class discovery demonstrate the performance of the proposed models using both synthetic data and real-world time series data from astrophysics. Our methods are particularly useful when the time series are sparsely and non-synchronously sampled.

### ho, Gre Trajectory

"... clustering Sparse regression modeling fram an i ract. In ies into a maximum a posteriori approach, where the Expectation–Maximization (EM) algorithm is used deran such as ion-ba traffic bout a to such family which can be successfully applied when the assumptions made about the model of the motion ar ..."

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clustering Sparse regression modeling fram an i ract. In ies into a maximum a posteriori approach, where the Expectation–Maximization (EM) algorithm is used deran such as ion-ba traffic bout a to such family which can be successfully applied when the assumptions made about the model of the motion are adequately satisfied, including cases of occlusion. Alternatively, particle filters [4], including the condensation algorithm [5], are more general tracking methods without assuming any specific type of densities. this category. The above methods track only one object at a time. Other meth-ods that simultaneously track many objects have also been pro-posed [11,12]. In [13], multiple objects are tracked by using Graph Cuts [14] over some observations (i.e. possible locations of the object) which are extracted. Another approach is to employ le-vel-sets to represent each object to be tracked [15,16] which may also be useful to handle the case of multiple object tracking [17,18] by optimally grouping regions whose pixels have similar feature signatures. An application in vehicle tracking is presented in [19] where multiple vehicles are tracked by initially assigning q This paper has been recommended for acceptance by Y. Aloimonos. ⇑ Corresponding author.

### International Journal on Artificial Intelligence Tools c © World Scientific Publishing Company

, 2008

"... A regression mixture model with spatial constraints for clustering spatiotemporal data ..."

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A regression mixture model with spatial constraints for clustering spatiotemporal data