Kristian Sabo

 

ksabo web

Full Professor
Department of Mathematics
Josip Juraj Strossmayer University of Osijek
Trg Ljudevita Gaja 6
Osijek, HR-31000, Croatia¸

Google Scholar Profile

phone: +385-31-224-827
fax: +385-31-224-801
email:  ksabo @ mathos.hr
office:  18 (ground floor)

 


Research Interests

Applied and Numerical Mathematics (Curve Fitting, Parameter Estimation, Data Cluster Analysis) with applications in Agriculture, Economy, Chemistry, Politics, Electrical Engineering, Medicine, Food Industry, Mechanical Engineering.

Degrees

PhD in Numerical Mathematics, Department of Mathematics, University of Zagreb, 2007
MSc in Mathematics, Department of Mathematics, University of Zagreb, 2003
BSc in Mathematics and Computer Science, Department of Mathematics, University of Osijek,  Croatia, 1999
 

Publications

Journal Publications

  1. R. Scitovski, U. Radojičić, K. Sabo, A fast and efficient method for solving the multiple line detection problem, Rad HAZU, Matematičke znanosti. 23 (2019), 123-140
    In this paper, we consider the multiple line detection problem on the basis of a data points set coming from a number of lines not known in advance. A new and efficient method is proposed, which is based upon center-based clustering, and it solves this problem quickly and precisely. The method has been tested on $100$ randomly generated data sets. In comparison to the incremental algorithm, the method gives significantly better results. Also, in order to identify a partition with the most appropriate number of clusters, a new index has been proposed for the case of a cluster whose lines are cluster-centers. The index can also be generalized for other geometrical objects.
  2. R. Scitovski, K. Sabo, Application of the DIRECT algorithm to searching for an optimal k-partition of the set $AsubsetR^n$ and its application to the multiple circle detection problem, Journal of Global Optimization 74/1 (2019), 63-77
    In this paper, we propose an efficient method for searching for a globally optimal k-partition of the set A subseteq R^n. Due to the property of the DIRECT global optimization algorithm to usually quickly arrive close to a point of global minimum, after which it slowly attains the desired accuracy, the proposed method uses the well-known k-means algorithm with a initial approximation chosen on the basis of only a few iterations of the DIRECT algorithm. In case of searching for an optimal k-partition of spherical clusters, the method is not worse than other known methods, but in case of solving the multiple circle detection problem, the proposed method shows remarkable superiority.
  3. R. Scitovski, K. Sabo, Application of the DIRECT algorithm to solving the multiple ellipse detection problem, Applications of Mathematics (2019), prihvaćen za objavljivanje
    In this paper, we consider the multiple ellipses detection problem on the basis of a data points set coming from a number of ellipses in the plane not known in advance, whereby an ellipse E is considered as a Mahalanobis circle with center S, radius r, and some positive definite matrix Sigma. A very efficient method for solving this problem is proposed. The method uses a modification of the k-means algorithm for Mahalanobis- circle centers. The initial approximation consists of the set of circles whose centers are determined by means of a smaller number of iterations of the DIRECT global optimization algorithm. Unlike other methods known from the literature, our method recognizes well not only ellipses with clear edges, but also ellipses with noisy edges. CPU-time necessary for running the corresponding algorithm is very short and this raises hope that, with appropriate software optimization, the algorithm could be run in real time. The method is illustrated and tested on 100 randomly generated data sets.
  4. R. Scitovski, K. Sabo, DBSCAN-like clustering method for various data densities, Pattern Analysis and Applications (2019), prihvaćen za objavljivanje
    In this paper, we propose a modification of the well-known DBSCAN algorithm, which recognizes clusters with various data densities in a given set of data points $A = {a^i in R^n : i = 1, ldots , m}$. First, we define the parameter $MinPts = floor ln |A| floor$ and after that, by using a standard procedure from DBSCAN algorithm, for each $a in A$ we determine radius $epsilon_a$ of the circle containing $MinPts$ elements from the set $A$. We group the set of all these radii into the most appropriate number $(t)$ of clusters by using Least Square distance-like function applying {tt SymDIRECT} or {tt SepDIRECT} algorithm. In that way we obtain parameters $epsilon_1 > · · · > epsilon_t$. Furthermore, for parameters ${MinPts, epsilon_1} we construct a partition starting with one cluster and then add new clusters for as long as the isolated groups of at least $MinPts$ data points in some circle with radius $epsilon_1$ exist. We follow a similar procedure for other parameters $epsilon_2, ldots, , epsilon_t$. After the implementation of the algorithm, a larger number of clusters appear than can be expected in the optimal partition. Along with defined criteria, some of them are merged by applying a merging process for which a detailed algorithm has been written. Compared to the standard DBSCAN algorithm, we show an obvious advantage for the case of data with various densities.
  5. A. Barron, M. Benšić, K. Sabo, A Note on Weighted Least Square Distribution Fitting and Full Standardization of the Empirical Distribution Function, TEST 27/4 (2018), 946-967
    The relationship between the norm square of the standardized cumulative distribution and the chi-square statistic is examined using the form of the covariance matrix as well as the projection perspective. This investigation enables us to give uncorrelated components of the chi-square statistic and to provide interpretation of these components as innovations standardizing the cumulative distribution values. The norm square of the standardized difference between empirical and theoretical cumulative distributions is also examined as an objective function for parameter estimation. Its relationship to the chi-square distance enables us to discuss the large sample properties of these estimators and a difference in their properties in the cases that the distribution is evaluated at fixed and random points.





Projects

  • Scientifically branded Pork (Member of the scientific project entitled above. Project started on June 1, 2014. Principal investigator is professor Goran Kušec from Faculty of Agriculture in Osijek, University of Osijek. Project was supported by Croatian Science Foundation.)

 


Professional Activities

Editorial Board

Since 2012 member of the Editorial board of the Journal Osječki matematički list

2001-2012 Editor in Chief of the Journal Osječki matematički list

 


 

Committee Memberships
  •  Member of the Organize Committee of the 4th Croatian Congress of Mathematics, Osijek, 2008
  •  Member of the Organize Committee of the 15th International Conference on Operational Research, Croatian Operational Research Society, Osijek 2014

 

Refereeing/Reviewing
 

Journal of Computational and Applied Mathematics, Journal of Classification, Mathematical Communications,  International Journal of Applied and Mathematics and Computer Science, Croatian Operational Research Review, TEAM 2012 International Conference, Osječki matematički list


 

Service Activities

Since 2013 president of Osijek Mathematical Society

2001-2013 secretary of Osijek Mathematical Society

 

Selected Other Activities (in Croatian)
 

 

  • 2014., 2015.  Večer matematike – manifestacija popularizacije matematike u organizaciji Udruge matematičara Osijeku i Hrvatskog matematičkog društva -  Član Programskog i Organizacijskog odbora
  •  2013.-2016. Matematičke pripreme za učenike srednjih škola • Programski i Organizacijski koordinator
  • 2000.-2016. Zimska matematička škola za učenike srednjih škola  • Član Programskog i Organizacijskog odbora
  • 2000.-2016. Zimska matematička škola za učenike osnovnih škola  • Član Programskog i Organizacijskog odbora
  • 2006.-2016. Stručni kolokvij Udruge matematičara Osijek • Član Programskog i Organizacijskog odbora
  • travanj, 2014.  Geometrijska škola Stanko Bilinski, Našice:  Predavanje za nastavnike: „Funkcija udaljenosti i odgovarajuća geometrija“,  Radionica za učenike: “Neki optimizacijski problemi u geometriji“
  • travanj, 2014. Festival znanosti Sveučilišta Josipa Jurja Strossmayera u Osijeku  Predavanje: „Što su optimalne izborne (upravne) jedinice i kako ih odrediti“.  Član Programskog i Organizacijskog odbora
  • listopad, 2012. Stručni skup: Nastava matematike i izazovi moderne tehnologije u organizaciji Udruge Normala - Predavanje: „Zaglađivanje podataka: metode, pristupi i primjene“

 

 


Teaching (in Croatian)

Konzultacije: Srijeda  11:00 - 12:00

Teme zavšnih i diplomskih radova (pdf)

 

Zimski semestar 2017./2018.

 

Matematika I, Prehrambeno tehnološki fakultet

Primijenjena i Inženjerska matematika, Prehrambeno tehnološki fakultet

 

 

Ljetni semestar 2015./2016.

Grupiranje podataka: pristupi, metode i primjene,  ponedjeljak 13:00 - 17:00, RP2

Linearno programiranje, petak 8:00-12:00, RP1

Numerička analiza, srijeda 10:00-12:00, P24

 

Zimski semestar 2015./2016.

 Diferencijalni račun, utorak, 8:00 - 11:00, P 1

 Matematički praktikum, srijeda, 8:00-10:00

 

Ljetni semestar 2014./2015.

Grupiranje podataka: pristupi, metode i primjene,  ponedjeljak 13:00 - 17:00, RP2

Linearno programiranje, utorak 15:00-19:00, P3

Numerička analiza, srijeda 8:00-10:00, P24

Primjene diferencijalnog i integralnog računa II, srijeda 10:00-11:00, P2

 


Personal

 

  • Birthdate: November 23, 1975
  • Birthplace: Kula, Vojvodina, Serbia
  • Family: married with Marija, and have one daughter Paula

 

Udžbenik Linearno programiranje (pdf)

Pelud(rar)

Uvodni sat (pptx)

Izvjesce procelnika 2017/2018 (pdf)

Diplomski sveucilisni nastavnicki studij matematike i informatike (pdf)