arXiv subjects

Jan Plavka

Publications and source records attributed to Jan Plavka.

4 recordsLinked to original sources

arXiv2021

Self-supervised deep convolutional neural network for chest X-ray classification

Chest radiography is a relatively cheap, widely available medical procedure that conveys key information for making diagnostic decisions. Chest X-rays are almost always used in the diagnosis of respiratory diseases such as pneumonia or the recent COVID-19. In this paper, we propose a self-supervised deep neural network that is pretrained on an unlabeled chest X-ray dataset. The learned representations are transferred to downstream task - the classification of respiratory diseases. The results obtained on four public datasets show that our approach yields competitive results without requiring large amounts of labeled training data.

eess.IV↗

arXiv2016

Reachability of eigenspaces for interval circulant matrices in max-algebra

A nonnegative matrix A is said to be strongly robust if its max-algebraic eigencone is universally reachable, i.e., if the orbit of any initial vector ends up with a max-algebraic eigenvector of A. Consider the case when the initial vector is restricted to an interval and A can be any matrix from a given interval of nonnegative circulant matrices. The main aim of this paper is to classify and characterize the six types of interval robustness in this situation. This naturally leads us also to study the max-algebraic spectral theory of circulant matrices and the relation of inclusion between attraction cones of circulant matrices in max-algebra.

math.RA↗

arXiv2015

X-simple image eigencones of tropical matrices

We investigate max-algebraic (tropical) one-sided systems $A\otimes x=b$ where $b$ is an eigenvector and $x$ lies in an interval $X$. A matrix $A$ is said to have $X$-simple image eigencone associated with an eigenvalue $\lambda$, if any eigenvector $x$ associated with $\lambda$ and belonging to the interval $X$ is the unique solution of the system $A\otimes y=\lambda x$ in $X$. We characterize matrices with $X$-simple image eigencone geometrically and combinatorially, and for some special cases, derive criteria that can be efficiently checked in practice.

math.RA↗

arXiv2014

Characterizing matrices with $X$-simple image eigenspace in max-min semiring

A matrix $A$ is said to have $X$-simple image eigenspace if any eigenvector $x$ belonging to the interval $X=\{x\colon \underline{x}\leq x\leq\overline{x}\}$ is the unique solution of the system $A\otimes y=x$ in $X$. The main result of this paper is a combinatorial characterization of such matrices in the linear algebra over max-min (fuzzy) semiring. The characterized property is related to and motivated by the general development of tropical linear algebra and interval analysis, as well as the notions of simple image set and weak robustness (or weak stability) that have been studied in max-min and max-plus algebras.

math.RA↗