Pairwise classification has many applications including network prediction, entity resolution, and collaborative filtering. The pairwise kernel has been proposed for those purposes by several research groups independently, and has been used successfully in several fields. In this paper, we propose an efficient alternative which we call a Cartesian kernel. While the existing pairwise kernel (whi...

We present combinatorial operators for the expansion of the Kronecker product of irreducible representations of the symmetric group Sn. These combinatorial operators are defined in the ring of symmetric functions and act on the Schur functions basis. This leads to a combinatorial description of the Kronecker powers of the irreducible representations indexed with the partition (n − 1, 1) which s...

The fruitful relation between the theory of symmetric functions and that of D-finite power series was first introduced by Goulden and Jackson in 1980, and later extended by Gessel, who stated two important results that provide closure properties of D-finite symmetric series under the scalar and inner products. These products are very important from the computational and combinatorial points of ...

Multi-Input Multi-Output (MIMO) communication systems have become the center of public attention as alternative idea to overcome limitation of Single-Input Single-Output (SISO) [1]. There are three kind of analytic model on correlation-based : i.i.d. model, kronecker model and weichselberger model. In i.i.d. model, all elements of MIMO channel are uncorrelated, and we only need to know the vari...

A stochast Kronecker graph presents a generative model for the social and information networks. By means of EM algorithm with various version of MCMC samplings,we suggest a way to catch the potential Kronecker structure. This model allows us to infer how the latent part of graph is organized as well as to predict how the current graph evolves over time. General Terms Kronecker Graph

Kronecker-like forms of a system pencil are useful in solving many computational problems encountered in the analysis and synthesis of linear systems. The reduction of system pencils to various Kronecker-like forms can be performed by structure preserving 0(n 3) complexity numerically stable algorithms. The presented algorithms form the basis of a modular collection of LAPACK compatible FORTRAN...

For a family of multidimensional gambler models we provide formulas for the winning probabilities (in terms parameters system) and distribution game duration eigenvalues underlying one-dimensional games). These were known case - initially proofs purely analytical, later probabilistic construction has been given. Concerning duration, in many cases our approach yields sample-path constructions. W...

This paper investigates the Kronecker separability of the joint polarimetric angular power spectrum density (PSD) between the base station (BS) and mobile station (MS) of double directional measurements in an urban macrocell in Tokyo. A general form of the sum of channel polarization pair-wise Kronecker product approximation is proposed to be used to model a full channel correlation matrix. Its...