In this paper, the diagonal majorization algorithm (DMA) has been investigated. The research focuses on the possibilities to increase the efficiency of the algorithm by disclosing its properties. The diagonal majorization algorithm is oriented at the multidimensional data visualization. The experiments have proved that, when visualizing large data set with DMA, it is possible to save the comput...

This paper aims to generalize and unify classical criteria for comparisons of balanced lattice designs, including fractional factorial designs, supersaturated designs and uniform designs. We present a general majorization framework for assessing designs, which includes a stringent criterion of majorization via pairwise coincidences and flexible surrogates via convex functions. Classical orthogo...

Use of an error correction code in a given transmission channel can be regarded as the statistical experiment. Therefore, powerful results from the theory of comparison of experiments can be applied to compare the performances of different error correction codes. We present results on the comparison of block error correction codes using the representation of error correction code as a linear ex...

This paper establishes a strong connection between evolutionary algorithms and majorization theory, using replicator models as a bridge. The relationship between replicator selection systems and majorization theory suggests new selection operators, convergence results and theoretical gains such as the availability of convergence results from the well developed theory of inhomogeneous doubly sto...

This letter describes algorithms for nonnegative matrix factorization (NMF) with the β-divergence (β-NMF). The β-divergence is a family of cost functions parameterized by a single shape parameter β that takes the Euclidean distance, the Kullback-Leibler divergence, and the Itakura-Saito divergence as special cases (β = 2, 1, 0 respectively). The proposed algorithms are based on a surrogate auxi...

We present a straightforward linear algebraic model of greed, based only on extensions of classical majorization and convexity theory. This gives an alternative to other models of greedy-solvable problems such as matroids, greedoids, submodular functions, etc., and it is able to express established examples of greedy-solvable optimization problems that they cannot. The linear algebraic approach...

The main objective of the paper is to develop an innovative idea bringing continuous and discrete inequalities into a unified form. desired thus obtained by embedding majorization theory with existing notion inequalities. These notions are applied latest generalized form inequalities, popularly known as Hermite–Hadamard–Jensen–Mercer Moreover, frequently-used Caputo fractional operators employe...

Robust matrix factorization (RMF), which uses the `1-loss, often outperforms standard matrix factorization using the `2loss, particularly when outliers are present. The state-of-theart RMF solver is the RMF-MM algorithm, which, however, cannot utilize data sparsity. Moreover, sometimes even the (convex) `1-loss is not robust enough. In this paper, we propose the use of nonconvex loss to enhance...

We prove a moment majorization principle for matrix-valued functions with domain {−1, 1}m, m ∈ N. The principle is an inequality between higher-order moments of a non-commutative multilinear polynomial with different random matrix ensemble inputs, where each variable has small influence and the variables are instantiated independently. This technical result can be interpreted as a noncommutativ...