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TextRank is a variant of PageRank typically used in graphs that represent documents, and where vertices denote terms and edges denote relations between terms. Quite often the relation between terms is simple term co-occurrence within a…

A classical problem in matrix computations is the efficient and reliable approximation of a given matrix by a matrix of lower rank. The truncated singular value decomposition (SVD) is known to provide the best such approximation for any…

In this article, we describe the regression test process to test and verify the changes made on software. A developed technique use the automation test based on decision tree and test selection process in order to reduce the testing cost is…

Several problems in machine learning, statistics, and other fields rely on computing eigenvectors. For large scale problems, the computation of these eigenvectors is typically performed via iterative schemes such as subspace iteration or…

The prevalence of e-learning systems and on-line courses has made educational material widely accessible to students of varying abilities and backgrounds. There is thus a growing need to accommodate for individual differences in e-learning…

Deep learning is rapidly becoming a go-to tool for many artificial intelligence problems due to its ability to outperform other approaches and even humans at many problems. Despite its popularity we are still unable to accurately predict…

We use simple equations in order to compare the basins of attraction on the complex plane, corresponding to a large collection of numerical methods, of several order. Two cases are considered, regarding the total number of the roots, which…

Traditional numerical methods for calculating matrix eigenvalues are prohibitively expensive for high-dimensional problems. Iterative random sparsification methods allow for the estimation of a single dominant eigenvalue at reduced cost by…

We devise and analyze algorithms for the empirical policy evaluation problem in reinforcement learning. Our algorithms explore backward from high-cost states to find high-value ones, in contrast to forward approaches that work forward from…

We consider the problem of computing ratings using the results of games played between a set of n players, and show how this problem can be reduced to computing the positive eigenvectors corresponding to the dominant eigenvalues of certain…

There has recently been a growing interest in the development of statistical methods to compare medical costs between treatment groups. When cumulative cost is the outcome of interest, right-censoring poses the challenge of informative…

Approximating ground and a fixed number of excited state energies, or equivalently low order Hamiltonian eigenvalues, is an important but computationally hard problem. Typically, the cost of classical deterministic algorithms grows…

PageRank (PR) is a fundamental tool for assessing the relative importance of the nodes in a network. In this paper, we propose a measure, weighted PageRank (WPR), extended from the classical PR for weighted, directed networks with possible…

Value iteration is a commonly used and empirically competitive method in solving many Markov decision process problems. However, it is known that value iteration has only pseudo-polynomial complexity in general. We establish a somewhat…

We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…

Evaluating how well a whole system or set of subsystems performs is one of the primary objectives of performance testing. We can tell via performance assessment if the architecture implementation meets the design objectives. Performance…

Learning-based approaches for solving large sequential decision making problems have become popular in recent years. The resulting agents perform differently and their characteristics depend on those of the underlying learning approach.…

Efficiency, the basic concept of multi-objective optimization is investigated for the class of pairwise comparison matrices. A weight vector is called efficient if no alternative weight vector exists such that every pairwise ratio of the…

We describe two algorithms for the eigenvalue, eigenvector problem which, on input a Gaussian matrix with complex entries, finish with probability 1 and in average polynomial time.

In this paper we introduce an iterative voting algorithm and then use it to obtain a rating method which is very robust against collusion attacks as well as random and biased raters. Unlike the previous iterative methods, our method is not…