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473
Mean shift: A robust approach toward feature space analysis
 In PAMI
, 2002
"... A general nonparametric technique is proposed for the analysis of a complex multimodal feature space and to delineate arbitrarily shaped clusters in it. The basic computational module of the technique is an old pattern recognition procedure, the mean shift. We prove for discrete data the convergence ..."
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Cited by 2395 (37 self)
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A general nonparametric technique is proposed for the analysis of a complex multimodal feature space and to delineate arbitrarily shaped clusters in it. The basic computational module of the technique is an old pattern recognition procedure, the mean shift. We prove for discrete data the convergence of a recursive mean shift procedure to the nearest stationary point of the underlying density function and thus its utility in detecting the modes of the density. The equivalence of the mean shift procedure to the Nadaraya–Watson estimator from kernel regression and the robust Mestimators of location is also established. Algorithms for two lowlevel vision tasks, discontinuity preserving smoothing and image segmentation are described as applications. In these algorithms the only user set parameter is the resolution of the analysis, and either gray level or color images are accepted as input. Extensive experimental results illustrate their excellent performance.
KernelBased Object Tracking
, 2003
"... A new approach toward target representation and localization, the central component in visual tracking of nonrigid objects, is proposed. The feature histogram based target representations are regularized by spatial masking with an isotropic kernel. The masking induces spatiallysmooth similarity fu ..."
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Cited by 900 (4 self)
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A new approach toward target representation and localization, the central component in visual tracking of nonrigid objects, is proposed. The feature histogram based target representations are regularized by spatial masking with an isotropic kernel. The masking induces spatiallysmooth similarity functions suitable for gradientbased optimization, hence, the target localization problem can be formulated using the basin of attraction of the local maxima. We employ a metric derived from the Bhattacharyya coefficient as similarity measure, and use the mean shift procedure to perform the optimization. In the presented tracking examples the new method successfully coped with camera motion, partial occlusions, clutter, and target scale variations. Integration with motion filters and data association techniques is also discussed. We describe only few of the potential applications: exploitation of background information, Kalman tracking using motion models, and face tracking. Keywords: nonrigid object tracking; target localization and representation; spatiallysmooth similarity function; Bhattacharyya coefficient; face tracking. 1
RealTime Tracking of NonRigid Objects using Mean Shift
 IEEE CVPR 2000
, 2000
"... A new method for realtime tracking of nonrigid objects seen from a moving camera isproposed. The central computational module is based on the mean shift iterations and nds the most probable target position in the current frame. The dissimilarity between the target model (its color distribution) an ..."
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Cited by 815 (19 self)
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A new method for realtime tracking of nonrigid objects seen from a moving camera isproposed. The central computational module is based on the mean shift iterations and nds the most probable target position in the current frame. The dissimilarity between the target model (its color distribution) and the target candidates is expressed by a metric derived from the Bhattacharyya coefficient. The theoretical analysis of the approach shows that it relates to the Bayesian framework while providing a practical, fast and efficient solution. The capability of the tracker to handle in realtime partial occlusions, significant clutter, and target scale variations, is demonstrated for several image sequences.
Locally weighted learning
 ARTIFICIAL INTELLIGENCE REVIEW
, 1997
"... This paper surveys locally weighted learning, a form of lazy learning and memorybased learning, and focuses on locally weighted linear regression. The survey discusses distance functions, smoothing parameters, weighting functions, local model structures, regularization of the estimates and bias, ass ..."
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Cited by 599 (51 self)
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This paper surveys locally weighted learning, a form of lazy learning and memorybased learning, and focuses on locally weighted linear regression. The survey discusses distance functions, smoothing parameters, weighting functions, local model structures, regularization of the estimates and bias, assessing predictions, handling noisy data and outliers, improving the quality of predictions by tuning t parameters, interference between old and new data, implementing locally weighted learning e ciently, and applications of locally weighted learning. A companion paper surveys how locally weighted learning can be used in robot learning and control.
ModelBased Clustering, Discriminant Analysis, and Density Estimation
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 2000
"... Cluster analysis is the automated search for groups of related observations in a data set. Most clustering done in practice is based largely on heuristic but intuitively reasonable procedures and most clustering methods available in commercial software are also of this type. However, there is little ..."
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Cited by 573 (29 self)
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Cluster analysis is the automated search for groups of related observations in a data set. Most clustering done in practice is based largely on heuristic but intuitively reasonable procedures and most clustering methods available in commercial software are also of this type. However, there is little systematic guidance associated with these methods for solving important practical questions that arise in cluster analysis, such as \How many clusters are there?", "Which clustering method should be used?" and \How should outliers be handled?". We outline a general methodology for modelbased clustering that provides a principled statistical approach to these issues. We also show that this can be useful for other problems in multivariate analysis, such as discriminant analysis and multivariate density estimation. We give examples from medical diagnosis, mineeld detection, cluster recovery from noisy data, and spatial density estimation. Finally, we mention limitations of the methodology, a...
When Is "Nearest Neighbor" Meaningful?
 In Int. Conf. on Database Theory
, 1999
"... . We explore the effect of dimensionality on the "nearest neighbor " problem. We show that under a broad set of conditions (much broader than independent and identically distributed dimensions), as dimensionality increases, the distance to the nearest data point approaches the distance ..."
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Cited by 408 (2 self)
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. We explore the effect of dimensionality on the "nearest neighbor " problem. We show that under a broad set of conditions (much broader than independent and identically distributed dimensions), as dimensionality increases, the distance to the nearest data point approaches the distance to the farthest data point. To provide a practical perspective, we present empirical results on both real and synthetic data sets that demonstrate that this effect can occur for as few as 1015 dimensions. These results should not be interpreted to mean that highdimensional indexing is never meaningful; we illustrate this point by identifying some highdimensional workloads for which this effect does not occur. However, our results do emphasize that the methodology used almost universally in the database literature to evaluate highdimensional indexing techniques is flawed, and should be modified. In particular, most such techniques proposed in the literature are not evaluated versus simple...
Survey of clustering data mining techniques
, 2002
"... Accrue Software, Inc. Clustering is a division of data into groups of similar objects. Representing the data by fewer clusters necessarily loses certain fine details, but achieves simplification. It models data by its clusters. Data modeling puts clustering in a historical perspective rooted in math ..."
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Cited by 408 (0 self)
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Accrue Software, Inc. Clustering is a division of data into groups of similar objects. Representing the data by fewer clusters necessarily loses certain fine details, but achieves simplification. It models data by its clusters. Data modeling puts clustering in a historical perspective rooted in mathematics, statistics, and numerical analysis. From a machine learning perspective clusters correspond to hidden patterns, the search for clusters is unsupervised learning, and the resulting system represents a data concept. From a practical perspective clustering plays an outstanding role in data mining applications such as scientific data exploration, information retrieval and text mining, spatial database applications, Web analysis, CRM, marketing, medical diagnostics, computational biology, and many others. Clustering is the subject of active research in several fields such as statistics, pattern recognition, and machine learning. This survey focuses on clustering in data mining. Data mining adds to clustering the complications of very large datasets with very many attributes of different types. This imposes unique
Refining Initial Points for KMeans Clustering
, 1998
"... Practical approaches to clustering use an iterative procedure (e.g. KMeans, EM) which converges to one of numerous local minima. It is known that these iterative techniques are especially sensitive to initial starting conditions. We present a procedure for computing a refined starting condition fro ..."
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Cited by 317 (5 self)
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Practical approaches to clustering use an iterative procedure (e.g. KMeans, EM) which converges to one of numerous local minima. It is known that these iterative techniques are especially sensitive to initial starting conditions. We present a procedure for computing a refined starting condition from a given initial one that is based on an efficient technique for estimating the modes of a distribution. The refined initial starting condition allows the iterative algorithm to converge to a "better" local minimum. The procedure is applicable to a wide class of clustering algorithms for both discrete and continuous data. We demonstrate the application of this method to the popular KMeans clustering algorithm and show that refined initial starting points indeed lead to improved solutions. Refinement run time is considerably lower than the time required to cluster the full database. The method is scalable and can be coupled with a scalable clustering algorithm to address the largescale cl...
The cost of diversity: The diversification discount and inefficient investment
, 2000
"... We model the distortions that internal power struggles can generate in the allocation of resources between divisions of a diversified firm. The model predicts that if divisions are similar in the level of their resources and opportunities, funds will be transferred from divisions with poor opportuni ..."
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Cited by 307 (17 self)
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We model the distortions that internal power struggles can generate in the allocation of resources between divisions of a diversified firm. The model predicts that if divisions are similar in the level of their resources and opportunities, funds will be transferred from divisions with poor opportunities to divisions with good opportunities. When diversity in resources and opportunities increases, however, resources can flow toward the most inefficient division, leading to more inefficient investment and less valuable firms. We test these predictions on a panel of diversified U.S. firms during the period from 1980 to 1993 and find evidence consistent with them.