Alexander Kovačec

Deep learning networks for off-line handwritten signature recognition

Reliable identification and verification of off-line handwritten signatures from images is a difficult problem with many practical applications. This task is a difficult vision problem within the field of biometrics because a signature may change depending on psychological factors of the individual. Motivated by advances in brain science which describe how objects are represented in the visual cortex, advanced research on deep neural networks has been shown to work reliably on large image data sets. In this paper, we present a deep learning model for off-line handwritten signature recognition which is able to extract high-level representations. We also propose a two-step hybrid model for signature identification and verification improving the misclassification rate in the well-known GPDS database.

Young-type inequalities and their matrix analogues

We present several new Young-type inequalities for positive real numbers and we apply our results to obtain the matrix analogues. Among others, for real numbers , and , with and , we prove the inequalitieswhere and are, respectively, the (weighted) arithmetic and geometric means of the positive real numbers and with . In addition, we show that both bounds are sharp. An example of a matrix analogue for the case is the double-inequalityfor positive definite matrices . Our results extend some fresh inequalities established by Kittaneh, Manasrah, Hirzallah and Feng. Estimates for the quotient and its matrix analogues given by Furuichi and Minculete are also improved.

The Validity of the Marcus - de Oliveira Conjecture for Essentially Hermitian Matrices

Abstract Let X,Y be matrices of spectra x 1 ,…, x n and y 1 ,…, y n , respectively. For a wide class of pairs of essentially Hermitian matrices X,Y , we prove that the determinant of X+Y belongs to the convex hull of the n ! points п n i1 (x i +y σi ) (σ∈S n ).

On a conjecture of Marcus and de Oliveira

Abstract Let X , Y be two normal n × n matrices over C with respective spectra x 1 ,…, x n and y > 1 ,…, y n . Marcus and de Oliveira conjectured that the determinant of X + Y lies in the convex hull generated by the n ! complex points Π n i =1 ( x i + y ) σ ( i ) ), where σ ranges over the symmetric group S n . We prove the conjecture for the case that n −2 of the y i are equal. First the problem is reduced to the question of nonnegative solvability of a certain system of linear equations. Then the required nonnegative solvability is demonstrated by involving a measure theoretic generalization of the marriage lemma. Our main result forms a positive counterpart to a recent example given by Drury.

A bound for the determinant of the sum of two normal matrices

Hadamards determinant theorem is used to obtain an upper bound for the modulus of the determinant of the sum of two normal matrices in terms of their eigenvalues. This bound is compared with another given by M. E. Miranda.

A note on extrema of linear combinations of elementary symmetric functions

This note provides a new approach to a result of Foregger [T.H. Foregger, On the relative extrema of a linear combination of elementary symmetric functions, Linear Multilinear Algebra 20 (1987) pp. 377–385] and related earlier results by Keilson [J. Keilson, A theorem on optimum allocation for a class of symmetric multilinear return functions, J. Math. Anal. Appl. 15 (1966), pp. 269–272] and Eberlein [P.J. Eberlein, Remarks on the van der Waerden conjecture, II, Linear Algebra Appl. 2 (1969), pp. 311–320]. Using quite different techniques, we prove a more general result from which the others follow easily. Finally, we argue that the proof in [Foregger, 1987] is flawed.

Kolmogorov’s Theorem: From Algebraic Equations and Nomography to Neural Networks

We trace the developments around Hilbert’s thirteenth problem back to questions concerning algebraic equations.

Shaping graph pattern mining for financial risk

Abstract In recent years graph pattern mining took a prominent role in knowledge discovery in many scientific fields. From Web advertising to biology and finance, graph data is ubiquitous making pattern-based graph tools increasingly important. When it comes to financial settings, data is very complex and although many successful approaches have been proposed often they neglect the intertwined economic risk factors, which seriously affects the goodness of predictions. In this paper, we posit that financial risk analysis can be leveraged if structure can be taken into account by discovering financial motifs. We look at this problem from a graph-based perspective in two ways, by considering the structure in the inputs, the graphs themselves, and by taking into account the graph embedded structure of the data. In the first, we use gBoost combined with a substructure mining algorithm. In the second, we take a subspace learning graph embedded approach. In our experiments two datasets are used: a qualitative bankruptcy data benchmark and a real-world French database of corporate companies. Furthermore, we propose a graph construction algorithm to extract graph structure from feature vector data. Finally, we empirically show that in both graph-based approaches the financial motifs are crucial for the classification, thereby enhancing the prediction results.

The inequality of Milne and its converse II

We prove the following let, and be real numbers, and let be positive real numbers with. The inequalities hold for all real numbers if and only if and. Furthermore, we provide a matrix version. The first inequality (with and) is a discrete counterpart of an integral inequality published by E. A. Milne in 1925.

A formula for computing (1,2,3)-inverses of g-circulants

ABSTRACT Recent work on generalized inverses of linear operators centres around the construction of efficient algorithms for their computation. Here invariably structural properties of the operators and matrices involved are very convenient. As a contribution we obtain a rapidly evaluable explicit expression for (1, 2, 3)-inverses of singular g-circulants that originate in a nonsingular 1-circulant.