Progressive Scattered Data Filtering
نویسنده
چکیده
Given a finite point set Z ⊂ R, the covering radius of a nonempty subset X ⊂ Z is the minimum distance rX,Z such that every point in Z is at a distance of at most rX,Z from some point in X. This paper concerns the construction of a sequence of subsets of decreasing sizes, such that their covering radii are small. To this end, a method for progressive data reduction, referred to as scattered data filtering, is proposed. The resulting scheme is a composition of greedy Thinning, a recursive point removal strategy, and Exchange, a postprocessing local optimization procedure. The paper proves adaptive a priori lower bounds on the minimal covering radii, which allows us to control for any current subset the deviation of its covering radius from the optimal value at run time. Important computational aspects of greedy Thinning and Exchange are discussed. The good performance of the proposed filtering scheme is finally shown by numerical examples.
منابع مشابه
Enhancement in Data Mining Technique for Scattered Document Using Clustering
Clustering is a widely studied data mining problem in the text documents. The problem finds numerous applications in customer segmentation, classification, collaborative filtering, visualization, document organization, and indexing. In this paper, we will provide a detailed survey of the problem of text clustering. We will study the key challenges of the clustering problem, as it applies to the...
متن کاملThinning and Approximation of Large Sets of Scattered Data
Having various concrete industrial applications in mind we focus on surface fitting to large scattered data sets. We describe a general method for modelling data which incorporates both filtering using triangulations, and hierarchical interpolation based on compactly supported radial basis functions. The uniformity of the data points plays a significant role. The utility of the method is confir...
متن کاملDigital Total Variation Filtering as Postprocessing for Radial Basis Function Approximation Methods
Digital total variation (DTV) filtering techniques, that originated in the field of image processing, are adapted to postprocess Radial Basis Function approximations of piecewise continuous functions. Through numerical examples, we show that DTV filtering is a fast, robust, postprocessing method that can be used to remove Gibbs oscillations while sharply resolving discontinuities. The method is...
متن کاملA Framework for Real-time Volume Visualization of Streaming Scattered Data
Visualization of scattered data over a volumetric spatial domain is often done by reconstructing a trivariate function on some grid using scattered data interpolation methods and visualizing the function using standard visualization techniques. Scattered data reconstruction algorithms are often computationally expensive and difficult to implement. In order to visualize streaming scattered data,...
متن کامل