A new class of geometric statistics for analyzing galaxy catalogs is presented. Filament statistics quantify filamentarity and planarity in large scale structure in a manner consistent with catalog visualizations. These statistics are based on sequences of spatial links which follow local high-density structures. From these link sequences we compute the discrete curvature, planarity, and torsio...

This paper provides a comparison study among a set of robust diffusion algorithms for processing optical flows. The proposed algorithms combine the smoothing ability of the heat kernel, modelled by the local Hessian, and the outlier rejection mechanisms of robust statistics algorithms. Smooth optical flow variation can be modelled very well using heat kernels. The diffusion kernel is considered...

In this paper we analyse the editing of ITV news bulletins using robust statistics to describe the distribution of shot lengths and its editing structure. Commonly cited statistics of film style such as the mean and variance do not accurately describe the style of a motion picture and reflect the influence of a small number of extreme values. Analysis based on such statistics will inevitably le...

• The Shewhart control charts, used for monitoring industrial processes, are the most popular tools in Statistical Process Control (SPC). They are usually developed under the assumption of independent and normally distributed data, an assumption rarely true in practice, and implemented with estimated control limits. But in general, we essentially want to control the process mean value and the p...

In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order statistics is associated with certain constraints. In particular, we derive an inequality on distribution for related order statistics. Moreover, we also propos...

The idea of Innovation Search, which was initially proposed for data clustering, recently used outlier detection. In the application Search detection, directions innovation were utilized to measure points. We study Values computed by algorithm under a quadratic cost function and it is proved that with new are equivalent Leverage Scores. This interesting connection establish several theoretical ...