Alexander Kovačec

Bio: Alexander Kovačec is an academic researcher from University of Coimbra. The author has contributed to research in topics: Matrix (mathematics) & Positive-definite matrix. The author has an hindex of 7, co-authored 30 publications receiving 186 citations.

Positive semidefinite diagonal minus tail forms are sums of squares

Abstract: By a diagonal minus tail form (of even degree) we understand a real homogeneous polynomial F(x1, . . . , xn) = F(x) = D(x) − T(x), where the diagonal part D(x) is a sum of terms of the form \({b_i x_i^{2d}}\) with all bi ≥ 0 and the tail T(x) a sum of terms \({a_{i_1i_2\cdots i_n}x_1^{i_1}\cdots x_n^{i_n}}\) with \({a_{i_1i_2\cdots i_n} > 0}\) and at least two iν ≥ 1. We show that an arbitrary change of the signs of the tail terms of a positive semidefinite diagonal minus tail form will result in a sum of squares of polynomials. We also give an easily tested sufficient condition for a polynomial to be a sum of squares of polynomials (sos) and show that the class of polynomials passing this test is wider than the class passing Lasserre’s recent conditions. Another sufficient condition for a polynomial to be sos, like Lasserre’s piecewise linear in its coefficients, is also given.

Deep learning networks for off-line handwritten signature recognition

Abstract: 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

Abstract: 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.

An Introduction to Polynomial and Semi-Algebraic Optimization

Abstract: This is the first comprehensive introduction to the powerful moment approach for solving global optimization problems (and some related problems) described by polynomials (and even semi-algebraic functions). In particular, the author explains how to use relatively recent results from real algebraic geometry to provide a systematic numerical scheme for computing the optimal value and global minimizers. Indeed, among other things, powerful positivity certificates from real algebraic geometry allow one to define an appropriate hierarchy of semidefinite (SOS) relaxations or LP relaxations whose optimal values converge to the global minimum. Several extensions to related optimization problems are also described. Graduate students, engineers and researchers entering the field can use this book to understand, experiment with and master this new approach through the simple worked examples provided.

Deep Learning for Biometrics: A Survey

Abstract: In the recent past, deep learning methods have demonstrated remarkable success for supervised learning tasks in multiple domains including computer vision, natural language processing, and speech processing. In this article, we investigate the impact of deep learning in the field of biometrics, given its success in other domains. Since biometrics deals with identifying people by using their characteristics, it primarily involves supervised learning and can leverage the success of deep learning in other related domains. In this article, we survey 100 different approaches that explore deep learning for recognizing individuals using various biometric modalities. We find that most deep learning research in biometrics has been focused on face and speaker recognition. Based on inferences from these approaches, we discuss how deep learning methods can benefit the field of biometrics and the potential gaps that deep learning approaches need to address for real-world biometric applications.

Offline handwritten signature verification — Literature review

Abstract: The area of Handwritten Signature Verification has been broadly researched in the last decades, but remains an open research problem. The objective of signature verification systems is to discriminate if a given signature is genuine (produced by the claimed individual), or a forgery (produced by an impostor). This has demonstrated to be a challenging task, in particular in the offline (static) scenario, that uses images of scanned signatures, where the dynamic information about the signing process is not available. Many advancements have been proposed in the literature in the last 5–10 years, most notably the application of Deep Learning methods to learn feature representations from signature images. In this paper, we present how the problem has been handled in the past few decades, analyze the recent advancements in the field, and the potential directions for future research.