In this paper, we study the empirical spectral distribution of Spearman's rank correlation matrices, under assumption that observations are independent and identically distributed random vectors features correlated. We show limiting is generalized Mar\u{c}enko-Pastur law with covariance matrix observation after standardized transformation. With these results, compare several classical covarianc...

In contrast to SPD matrices, few tools exist perform Riemannian statistics on the open elliptope of full-rank correlation matrices. The quotient-affine metric was recently built as quotient affine-invariant by congruence action positive diagonal space matrices had always been thought a homogeneous space. contrast, we view in this work Lie group and left-invariant metric. This unexpected new vie...

In this article we describe a new Hermite series based sequential estimator for the Spearman rank correlation coefficient and provide algorithms applicable in both stationary non-stationary settings. To treat setting, introduce novel, exponentially weighted correlation, which allows local nonparametric of bivariate data stream to be tracked. best our knowledge is first algorithm proposed estima...

Although mixed-integer evolution strategies (MIES) have been successfully applied to optimization of mixed-integer problems, they may encounter challenges when fitness evaluations are time consuming. In this paper, we propose to use a radial-basis-function network (RBFN) trained based on the rank correlation coefficient distance metric to assist MIES. For the distance metric of the RBFN, we mod...

PageRank (PR) is an algorithm originally developed by Google to evaluate the importance of web pages. Considering how deeply rooted Google's PR algorithm is to gathering relevant information or to the success of modern businesses, the question of rank stability and choice of the damping factor (a parameter in the algorithm) is clearly important. We investigate PR as a function of the damping fa...