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17
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 1519 (34 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.
Estimating And Depicting The Structure Of A Distribution Of Random Functions
, 2000
"... . We suggest a nonparametric approach to making inference about the structure of distributions in a potentially infinitedimensional space, for example a function space, and displaying information about that structure. Our methodology is based on nonparametric density estimation, and draws inference ..."
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Cited by 9 (0 self)
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. We suggest a nonparametric approach to making inference about the structure of distributions in a potentially infinitedimensional space, for example a function space, and displaying information about that structure. Our methodology is based on nonparametric density estimation, and draws inference about the slope of the density. The latter step is implemented in a purely iterative way, using only elementary operations of addition and multiplication, and does not require any differentiation or dimensionreduction. Nevertheless it leads in a very simple and reliable manner to "curves" of steepest ascent up the "surface" defined by an estimate of the density of a potentially infinitedimensional distribution. The projections of these curves into the sample space are always onedimensional, or more properly oneparameter, structures, and so can be displayed visually even when the sample space is a class of functions. Also, the modes to which the sample space projections lead are themselv...
Modes and clustering for timewarped gene expression profile data
 Bioinformatics
, 2003
"... Motivation: The study of the dynamics of regulatory processes has led to increased interest for the analysis of temporal gene expression level data. To address the dynamics of regulation, expression data are collected repeatedly over time. It is difficult to statistically represent the resulting hig ..."
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Cited by 9 (4 self)
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Motivation: The study of the dynamics of regulatory processes has led to increased interest for the analysis of temporal gene expression level data. To address the dynamics of regulation, expression data are collected repeatedly over time. It is difficult to statistically represent the resulting highdimensional data. When regulatory processes determine gene expression, timewarping is likely to be present, i.e. the sample of gene expression trajectories reflects variation not only in terms of the expression amplitudes, but also in terms of the temporal structure of gene expression. Results: A nonparametric timesynchronized iterative mean updating technique is proposed to find an overall representation that corresponds to a mode of a sample of expression profiles, viewed as a random sample in function space. The proposed algorithm explores the application of previous work of Hall and Heckman to genomewide expression data and provides an extension that includes random timewarping with the aim to synchronize timescales across genes. The proposed algorithm is universally applicable for the construction of modes for functional data with timewarping. We demonstrate the construction of mode functions for a sample of Drosophila gene expression data. The algorithm can be applied to define clusters among the observed trajectories of gene expression, without any kind of prior nontimewarped clustering, as illustrated in the numerical example. Contact:
Robust fusion of uncertain information
 In Proc. Int’l Conf. Computer Vision and Pattern Recognition
, 2003
"... Abstract—A technique is presented to combine data points, each available with pointdependent uncertainty, when only a subset of these points come from sources, where is unknown. We detect the significant modes of the underlying multivariate probability distribution using a generalization of the non ..."
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Cited by 8 (3 self)
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Abstract—A technique is presented to combine data points, each available with pointdependent uncertainty, when only a subset of these points come from sources, where is unknown. We detect the significant modes of the underlying multivariate probability distribution using a generalization of the nonparametric mean shift procedure. The number of detected modes automaticallydefines, whilethe belongingof apoint to the basin of attraction of a mode provides the fusion rule. The robust data fusion algorithm was successfully applied to two computer vision problems: estimating the multiple affine transformations, and range image segmentation. Index Terms—Computer vision, information fusion, mean shift, robust analysis.
Compernolle, “Outlier correction for local distance measures in example based speech recognition
 in Proc. ICASSP
, 2007
"... Example based speech recognition is critically dependent on the quality of the acoustic distance measure between input and reference vectors. In the past, the commonly used Euclidean distance has been refined to take into account the covariance of the different sounds, resulting in a class dependent ..."
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Cited by 4 (3 self)
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Example based speech recognition is critically dependent on the quality of the acoustic distance measure between input and reference vectors. In the past, the commonly used Euclidean distance has been refined to take into account the covariance of the different sounds, resulting in a class dependent distance measure. However, using the same measure for the whole class is still too crude: vectors in the tails of the distribution (outliers) are unduly considered equally representative of the class as those in the centre. In this paper, we derive two techniques inspired by nonparametric density estimation that explicitly adjust the distance measure based on the position of the reference vector in its class. Experiments on three lowlevel acoustic tasks show that “data sharpening ” results in a substantial improvement, while “adaptive kernels ” have minimal effect. Index Terms — Example based recognition, DTW, Adaptive kernels, Nonparametric density estimates
F.: A clustering based denoising technique for range images of time of flight cameras
 In: CIMCA/IAWTIC/ISE
, 2008
"... A relatively new technique for measuring the 3D structure of visual scenes is provided by time of flight (TOF) cameras. Reflections of modulated light waves are recorded by a parallel pixel array structure. The time series at each pixel of the resulting image stream is used to estimate travelling ti ..."
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Cited by 3 (0 self)
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A relatively new technique for measuring the 3D structure of visual scenes is provided by time of flight (TOF) cameras. Reflections of modulated light waves are recorded by a parallel pixel array structure. The time series at each pixel of the resulting image stream is used to estimate travelling time and thus range information. This measuring technique results in pixel dependent noise levels with variances changing over several orders of magnitude dependent on the illumination and material parameters. This makes application of traditional (global) denoising techniques suboptimal. Using free aditional information from the camera and a clustering procedure we can get information about which pixels belong to the same object, and what their noise level is, which allows for locally adapted
CLUES: A nonparametric clustering method based on local shrinking
"... In this paper, we propose a novel nonparametric clustering method based on nonparametric local shrinking. Each data point is transformed in such a way that it moves a specific distance toward a cluster center. The direction and the associated size of each movement are determined by the median of i ..."
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Cited by 3 (0 self)
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In this paper, we propose a novel nonparametric clustering method based on nonparametric local shrinking. Each data point is transformed in such a way that it moves a specific distance toward a cluster center. The direction and the associated size of each movement are determined by the median of its Knearest neighbors. This process is repeated until a predefined convergence criterion is satisfied. The optimal value of the number of neighbors is determined by optimizing some commonly used index functions that measure the strengths of clusters generated by the algorithm. The number of clusters and the final partition are determined automatically without any input parameter except the stopping rule for convergence. Our experiments on simulated and real data sets suggest that that the proposed algorithm achieves relatively high accuracies when compared with classical clustering algorithms.
IMPOSING ECONOMIC CONSTRAINTS IN NONPARAMETRIC REGRESSION: SURVEY, IMPLEMENTATION AND EXTENSION
"... Abstract. Economic conditions such as convexity, homogeneity, homotheticity, and monotonicity are all important assumptions or consequences of assumptions of economic functionals to be estimated. Recent research has seen a renewed interest in imposing constraints in nonparametric regression. We surv ..."
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Cited by 1 (0 self)
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Abstract. Economic conditions such as convexity, homogeneity, homotheticity, and monotonicity are all important assumptions or consequences of assumptions of economic functionals to be estimated. Recent research has seen a renewed interest in imposing constraints in nonparametric regression. We survey the available methods in the literature, but focus on a particular estimator by Hall and Huang (2001) which is easily generalized to other nonparametric settings. We discuss its computational implementation in the face of linear constraints and how it can be extended to handle nonlinear constraints. Finally, we include a small simulation study to showcase the method. 1.
Smooth tail index estimation
, 2008
"... Both parametric distribution functions appearing in extreme value theory the generalized extreme value distribution and the generalized Pareto distribution have logconcave densities if the extreme value index γ ∈ [−1,0]. Replacing the order statistics in tail index estimators by their correspondi ..."
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Both parametric distribution functions appearing in extreme value theory the generalized extreme value distribution and the generalized Pareto distribution have logconcave densities if the extreme value index γ ∈ [−1,0]. Replacing the order statistics in tail index estimators by their corresponding quantiles from the distribution function that is based on the estimated logconcave density ̂ fn leads to novel smooth quantile and tail index estimators. These new estimators aim at estimating the tail index especially in small samples. Acting as a smoother of the empirical distribution function, the log–concave distribution function estimator reduces estimation variability to a much greater extent than it introduces bias. As a consequence, Monte Carlo simulations demonstrate that the smoothed version of the estimators are well superior to their nonsmoothed counterparts, in terms of mean squared error.