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 M-estimators of location is also established. Algorithms for two low-level 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.

Abstract—A technique is presented to combine data points, each available with point-dependent 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.

. We suggest a nonparametric approach to making inference about the structure of distributions in a potentially infinite-dimensional 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 dimension-reduction. 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 infinite-dimensional distribution. The projections of these curves into the sample space are always one-dimensional, or more properly one-parameter, 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...

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, time-warping 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 non-parametric time-synchronized 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 genome-wide 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 time-warping. 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 non-time-warped clustering, as illustrated in the numerical example. Contact:

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 non-parametric density estimation that explicitly adjust the distance measure based on the position of the reference vector in its class. Experiments on three low-level 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, Non-parametric density estimates

In this paper, we propose a novel non-parametric clustering method based on non-parametric 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 K-nearest neighbors. This process is repeated until a pre-defined 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.

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.

Both parametric distribution functions appearing in extreme value theory- the generalized extreme value distribution and the generalized Pareto distribution- have log-concave 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 log-concave 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 non-smoothed counterparts, in terms of mean squared error.