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132
Approximation Algorithms for Projective Clustering
 Proceedings of the ACM SIGMOD International Conference on Management of data, Philadelphia
, 2000
"... We consider the following two instances of the projective clustering problem: Given a set S of n points in R d and an integer k ? 0; cover S by k hyperstrips (resp. hypercylinders) so that the maximum width of a hyperstrip (resp., the maximum diameter of a hypercylinder) is minimized. Let w ..."
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Cited by 246 (21 self)
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We consider the following two instances of the projective clustering problem: Given a set S of n points in R d and an integer k ? 0; cover S by k hyperstrips (resp. hypercylinders) so that the maximum width of a hyperstrip (resp., the maximum diameter of a hypercylinder) is minimized. Let w be the smallest value so that S can be covered by k hyperstrips (resp. hypercylinders), each of width (resp. diameter) at most w : In the plane, the two problems are equivalent. It is NPHard to compute k planar strips of width even at most Cw ; for any constant C ? 0 [50]. This paper contains four main results related to projective clustering: (i) For d = 2, we present a randomized algorithm that computes O(k log k) strips of width at most 6w that cover S. Its expected running time is O(nk 2 log 4 n) if k 2 log k n; it also works for larger values of k, but then the expected running time is O(n 2=3 k 8=3 log 4 n). We also propose another algorithm that computes a c...
Topic Detection and Tracking Pilot Study Final Report
 IN PROCEEDINGS OF THE DARPA BROADCAST NEWS TRANSCRIPTION AND UNDERSTANDING WORKSHOP
, 1998
"... Topic Detection and Tracking (TDT) is a DARPAsponsored initiative to investigate the state of the art in finding and following new events in a stream of broadcast news stories. The TDT problem consists of three major tasks: (1) segmenting a stream of data, especially recognized speech, into distinc ..."
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Cited by 221 (27 self)
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Topic Detection and Tracking (TDT) is a DARPAsponsored initiative to investigate the state of the art in finding and following new events in a stream of broadcast news stories. The TDT problem consists of three major tasks: (1) segmenting a stream of data, especially recognized speech, into distinct stories; (2) identifying those news stories that are the first to discuss a new event occurring in the news; and (3) given a small number of sample news stories about an event, finding all following stories in the stream.
The Pilot Study ran from September 1996 through October 1997. The primary participants were DARPA, Carnegie Mellon University, Dragon Systems, and the University of Massachusetts at Amherst. This report summarizes the findings of the pilot study.
The TDT work continues in a new project involving larger training and test corpora, more active participants, and a more broadly defined notion of "topic" than was used in the pilot study.
Incremental Clustering and Dynamic Information Retrieval
, 1997
"... Motivated by applications such as document and image classification in information retrieval, we consider the problem of clustering dynamic point sets in a metric space. We propose a model called incremental clustering which is based on a careful analysis of the requirements of the information retri ..."
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Cited by 153 (5 self)
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Motivated by applications such as document and image classification in information retrieval, we consider the problem of clustering dynamic point sets in a metric space. We propose a model called incremental clustering which is based on a careful analysis of the requirements of the information retrieval application, and which should also be useful in other applications. The goal is to efficiently maintain clusters of small diameter as new points are inserted. We analyze several natural greedy algorithms and demonstrate that they perform poorly. We propose new deterministic and randomized incremental clustering algorithms which have a provably good performance. We complement our positive results with lower bounds on the performance of incremental algorithms. Finally, we consider the dual clustering problem where the clusters are of fixed diameter, and the goal is to minimize the number of clusters. 1 Introduction We consider the following problem: as a sequence of points from a metric...
A Study on Retrospective and OnLine Event Detection
, 1998
"... This paper investigates the use and extension of text retrieval and clustering techniques for event detection. The task is to automatically detect novel events from a temporallyordered stream of news stories, either retrospectively or as the stories arrive. We applied hierarchical and nonhierarchi ..."
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Cited by 132 (8 self)
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This paper investigates the use and extension of text retrieval and clustering techniques for event detection. The task is to automatically detect novel events from a temporallyordered stream of news stories, either retrospectively or as the stories arrive. We applied hierarchical and nonhierarchical document clustering algorithms to a corpus of 15,836 stories, focusing on the exploitation of both content and temporal information. We found the resulting cluster hierarchies highly informative for retrospective detection of previously unidentified events, effectively supporting both queryfree and querydriven retrieval. We also found that temporal distribution patterns of document clusters provide useful information for improvement in both retrospective detection and online detection of novel events. In an evaluation using manually labelled events to judge the systemdetected events, we obtained a result of 82% in the F1 measure for retrospective detection, and a F1 value of 42% for...
Improved fast Gauss transform and efficient kernel density estimation
 In ICCV
, 2003
"... Evaluating sums of multivariate Gaussians is a common computational task in computer vision and pattern recognition, including in the general and powerful kernel density estimation technique. The quadratic computational complexity of the summation is a significant barrier to the scalability of this ..."
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Cited by 103 (7 self)
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Evaluating sums of multivariate Gaussians is a common computational task in computer vision and pattern recognition, including in the general and powerful kernel density estimation technique. The quadratic computational complexity of the summation is a significant barrier to the scalability of this algorithm to practical applications. The fast Gauss transform (FGT) has successfully accelerated the kernel density estimation to linear running time for lowdimensional problems. Unfortunately, the cost of a direct extension of the FGT to higherdimensional problems grows exponentially with dimension, making it impractical for dimensions above 3. We develop an improved fast Gauss transform to efficiently estimate sums of Gaussians in higher dimensions, where a new multivariate expansion scheme and an adaptive space subdivision technique dramatically improve the performance. The improved FGT has been applied to the mean shift algorithm achieving linear computational complexity. Experimental results demonstrate the efficiency and effectiveness of our algorithm. 1
Fast construction of nets in lowdimensional metrics and their applications
 SIAM Journal on Computing
, 2006
"... We present a near linear time algorithm for constructing hierarchical nets in finite metric spaces with constant doubling dimension. This datastructure is then applied to obtain improved algorithms for the following problems: approximate nearest neighbor search, wellseparated pair decomposition, s ..."
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Cited by 98 (10 self)
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We present a near linear time algorithm for constructing hierarchical nets in finite metric spaces with constant doubling dimension. This datastructure is then applied to obtain improved algorithms for the following problems: approximate nearest neighbor search, wellseparated pair decomposition, spanner construction, compact representation scheme, doubling measure, and computation of the (approximate) Lipschitz constant of a function. In all cases, the running (preprocessing) time is near linear and the space being used is linear. 1
Efficient algorithms for geometric optimization
 ACM Comput. Surv
, 1998
"... We review the recent progress in the design of efficient algorithms for various problems in geometric optimization. We present several techniques used to attack these problems, such as parametric searching, geometric alternatives to parametric searching, pruneandsearch techniques for linear progra ..."
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Cited by 94 (12 self)
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We review the recent progress in the design of efficient algorithms for various problems in geometric optimization. We present several techniques used to attack these problems, such as parametric searching, geometric alternatives to parametric searching, pruneandsearch techniques for linear programming and related problems, and LPtype problems and their efficient solution. We then describe a variety of applications of these and other techniques to numerous problems in geometric optimization, including facility location, proximity problems, statistical estimators and metrology, placement and intersection of polygons and polyhedra, and ray shooting and other querytype problems.
NCApproximation Schemes for NP and PSPACEHard Problems for Geometric Graphs
, 1997
"... We present NC approximation schemes for a number of graph problems when restricted to geometric graphs including unit disk graphs and graphs drawn in a civilized manner. Our approximation schemes exhibit the same time versus performance tradeoff as the best known approximation schemes for planar gr ..."
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Cited by 93 (1 self)
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We present NC approximation schemes for a number of graph problems when restricted to geometric graphs including unit disk graphs and graphs drawn in a civilized manner. Our approximation schemes exhibit the same time versus performance tradeoff as the best known approximation schemes for planar graphs. We also define the concept of precision unit disk graphs and show that for such graphs the approximation schemes have a better time versus performance tradeoff than the approximation schemes for arbitrary unit disk graphs. Moreover, compared to unit disk graphs, we show that for precision unit disk graphs, many more graph problems have efficient approximation schemes. Our NC approximation schemes can also be extended to obtain efficient NC approximation schemes for several PSPACEhard problems on unit disk graphs specified using a restricted version of the hierarchical specification language of Bentley, Ottmann and Widmayer. The approximation schemes for hierarchically specified un...
Structured Importance Sampling of Environment Maps
, 2003
"... We introduce structured importance sampling, a new technique for efficiently rendering scenes illuminated by distant natural illumination given in an environment map. Our method handles occlusion, highfrequency lighting, and is significantly faster than alternative methods based on Monte Carlo samp ..."
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Cited by 81 (9 self)
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We introduce structured importance sampling, a new technique for efficiently rendering scenes illuminated by distant natural illumination given in an environment map. Our method handles occlusion, highfrequency lighting, and is significantly faster than alternative methods based on Monte Carlo sampling. We achieve this speedup as a result of several ideas. First, we present a new metric for stratifying and sampling an environment map taking into account both the illumination intensity as well as the expected variance due to occlusion within the scene. We then present a novel hierarchical stratification algorithm that uses our metric to automatically stratify the environment map into regular strata. This approach enables a number of rendering optimizations, such as preintegrating the illumination within each stratum to eliminate noise at the cost of adding bias, and sorting the strata to reduce the number of sample rays. We have rendered several scenes illuminated by natural lighting, and our results indicate that structured importance sampling is better than the best previous Monte Carlo techniques, requiring one to two orders of magnitude fewer samples for the same image quality.
Learning approaches for Detecting and Tracking News Events
 IEEE Intelligent Systems
, 1999
"... This paper studies the effective use of information retrieval and machine learning techniques in a new task, event detection and tracking. The objective is to automatically detect novel events from chronologicallyordered streams of news stories, and track events of interest over time. We extended e ..."
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Cited by 77 (6 self)
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This paper studies the effective use of information retrieval and machine learning techniques in a new task, event detection and tracking. The objective is to automatically detect novel events from chronologicallyordered streams of news stories, and track events of interest over time. We extended existing supervised learning and unsupervised clustering algorithms to allow document classification based on both information content and temporal aspects of events. A taskoriented evaluation was conducted using Reuters and CNN news stories. We found agglomerative document clustering highly effective (82% in the F 1 measure) for retrospective event detection, and singlepass clustering with time windowing a better choice for online alerting of novel events. We also observed robust learning behavior for knearest neighbor (kNN) classification and a decisiontree approach in event tracking, under the difficult condition when the number of positive training examples is extremely small. 1 Intr...