We describe here a new method to estimate copula measure. From N observations of two variables X and Y , we draw a huge number m of subsamples (size n < N), and we compute the joint ranks in these subsamples. Then, for p, q ≤ n, the density in (p/n, q/n) is estimated as 1 mn Pm s=1 Pn i=1 {Ri,s=p,Si,s=q} where Ri,s (respectively Si,s) is the rank in X (resp. Y ) of the i observation of the s sa...

This work addresses the problem of detecting clusters in a weighted, undirected, graph by using kernel-based clustering methods, directly partitioning the graph according to a welldefined similarity measure between the nodes (a kernel on a graph). The proposed algorithms are based on a two-step procedure. First, a kernel or similarity matrix, providing a meaningful similarity measure between an...

In this note, a new proof for the positivity of Dunkl’s intertwining operator in the crystallographic case is given. It is based on an asymptotic relationship between the Opdam-Cherednik kernel and the Dunkl kernel as recently observed by M. de Jeu, and on positivity results of S. Sahi for the Heckman-Opdam polynomials and their nonsymmetric counterparts. 2000 AMS Subject Classification: 33C52,...

The Z2s -additive codes are subgroups of Z n 2s , and can be seen as a generalization of linear codes over Z2 and Z4. A Z2s -linear Hadamard code is a binary Hadamard code which is the Gray map image of a Z2s additive code. It is known that the dimension of the kernel can be used to give a complete classification of the Z4-linear Hadamard codes. In this paper, the kernel of Z2s -linear Hadamard...

This report describes how to implement protocols in the x-kernel. It gives the x-kernel’s programming interface, describes how to configure an x-kernel that contains a certain collection of protocols, and demonstrates how to run and debug an x-kernel. The x-kernel can be run in several environments: as a user program on a Sun SparcStation running SunOS4.1, as a user program on SGI systems runni...

This short note deals with approximation order of spaces spanned by (x;), x 2 X, with a positive deenite kernel on a sphere and X a given set of nodes. We estimate both the L 2-and the L 1-error, if the function to be approximated is assumed to be rather smooth, thus deviating from the usual assumption that the function stems from thèna-tive space' of the kernel. It is of interest that, based o...

We give the first algorithm for kernel Nyström approximation that runs in linear time in the number of training points and is provably accurate for all kernel matrices, without dependence on regularity or incoherence conditions. The algorithm projects the kernel onto a set of s landmark points sampled by their ridge leverage scores, requiring just O(ns) kernel evaluations and O(ns) additional r...