Multilinear PageRank: Uniqueness, error bound and perturbation analysis

Multilinear PageRank

In this paper, we first extend the celebrated PageRank modification to a higher-order Markov chain. Although this system has attractive theoretical properties, it is computationally intractable for many interesting problems. We next study a computationally tractable approximation to the higher-order PageRank vector that involves a system of polynomial equations called multilinear PageRank. This...

Convergence and Error Bound for Perturbation ofLinear

In various penalty/smoothing approaches to solving a linear program, one regularizes the problem by adding to the linear cost function a separable nonlinear function multiplied by a small positive parameter. Popular choices of this nonlinearfunction include the quadraticfunction, the logarithm function, and the x ln(x)-entropy function. Furthermore, the solutions generated by such approaches ma...

A global error bound for quadratic perturbation of linear programs

Perturbation Analysis of a Generalization Error Estimator

Abstract– Estimating the generalization capability is one of the most important problems in supervised learning. Therefore, various generalization error estimators have been proposed so far, in the presence of noise in output values. On the other hand, noise often exists in input values as well as output values. In this paper, we therefore investigate the influence of input noise on a generaliz...

Traditional PageRank versus Network Capacity Bound

In a former paper [9] we simplified the proof of a theorem on personalized random walk that is fundamental to graph nodes clustering and generalized it to bipartite graphs for a specific case where the proobability of random jump was proprtional to the number of links of ”personally prefereed” nodes. In this paper we turn to the more complex issue of graphs in which the random jump follows unif...