On Randomly Projected Hierarchical Clustering with Guarantees

Hierarchical clustering (HC) algorithms are generally limited to small data instances due to their runtime costs. Here we mitigate this shortcoming and explore fast HC algorithms based on random projections for single (SLC) and average (ALC) linkage clustering as well as for the minimum spanning tree problem (MST). We present a thorough adaptive analysis of our algorithms that improve prior work from $O(N^2)$ by up to a factor of $N/(\log N)^2$ for a dataset of $N$ points in Euclidean space. The algorithms maintain, with arbitrary high probability, the outcome of hierarchical clustering as well as the worst-case running-time guarantees. We also present parameter-free instances of our algorithms.Comment: This version contains the conference paper "On Randomly Projected Hierarchical Clustering with Guarantees'', SIAM International Conference on Data Mining (SDM), 2014 and, additionally, proofs omitted in the conference versio

Searching for Jets in Heavy Ion Collisions

Jet quenching measurements using leading particles and their correlations suffer from known biases, which can be removed via direct reconstruction of jets in central heavy ion collisions. In this talk, we discuss several modern jet reconstruction algorithms and background subtraction techniques that are appropriate to heavy ion collisions.Comment: Proceedings of the 24th Winter Workshop on Nuclear Dynamics, South Padre Island, Texas, 5-12 April 200

Pedestrian detection in uncontrolled environments using stereo and biometric information

A method for pedestrian detection from challenging real world outdoor scenes is presented in this paper. This technique is able to extract multiple pedestrians, of varying orientations and appearances, from a scene even when faced with large and multiple occlusions. The technique is also robust to changing background lighting conditions and effects, such as shadows. The technique applies an enhanced method from which reliable disparity information can be obtained even from untextured homogeneous areas within a scene. This is used in conjunction with ground plane estimation and biometric information,to obtain reliable pedestrian regions. These regions are robust to erroneous areas of disparity data and also to severe pedestrian occlusion, which often occurs in unconstrained scenarios

Beyond Hartigan Consistency: Merge Distortion Metric for Hierarchical Clustering

Hierarchical clustering is a popular method for analyzing data which associates a tree to a dataset. Hartigan consistency has been used extensively as a framework to analyze such clustering algorithms from a statistical point of view. Still, as we show in the paper, a tree which is Hartigan consistent with a given density can look very different than the correct limit tree. Specifically, Hartigan consistency permits two types of undesirable configurations which we term over-segmentation and improper nesting. Moreover, Hartigan consistency is a limit property and does not directly quantify difference between trees. In this paper we identify two limit properties, separation and minimality, which address both over-segmentation and improper nesting and together imply (but are not implied by) Hartigan consistency. We proceed to introduce a merge distortion metric between hierarchical clusterings and show that convergence in our distance implies both separation and minimality. We also prove that uniform separation and minimality imply convergence in the merge distortion metric. Furthermore, we show that our merge distortion metric is stable under perturbations of the density. Finally, we demonstrate applicability of these concepts by proving convergence results for two clustering algorithms. First, we show convergence (and hence separation and minimality) of the recent robust single linkage algorithm of Chaudhuri and Dasgupta (2010). Second, we provide convergence results on manifolds for topological split tree clustering