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Entropy
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Complex and Fractional Dynamics II
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Complex and Fractional Dynamics II

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: closed (31 March 2022) | Viewed by 11245

Special Issue Editor

Dr. António Lopes

E-Mail Website
Guest Editor
Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200–465 Porto, Portugal
Interests: complex systems modelling; automation and robotics; fractional order systems modelling and control; data analysis and visualization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Team sports can be seen in the framework of complex systems (CS), where multiple agents interact at different scales in time and space. For example, at the match time scale, we observe interactions between players, coaches, referees, supporters, and environment, among others, which lead to a certain team performance during the match. On the other hand, at the season time scale, we verify interactions between teams in several matches, while teams’ behaviour evolves as a result of transfers of players and coaches, injuries, suspensions, physical and mental stress, administrative decisions, and other factors. Therefore, a plethora of elements gives rise to the emergence of a collective dynamics, with time–space patterns that can be analyzed by the mathematical and computational tools adopted for tackling dynamical systems.

Entropy-based techniques have been successfully applied to the study of many CS in science and engineering. Divergence measures are tightly connected to entropy and assume a key role in theoretical and applied statistical inference and data processing problems, namely, estimation, classification, detection, recognition, compression, indexation, diagnosis, and others.

This Special Issue focuses on original and new research results on entropy-based techniques for modelling and analyzing team sports dynamics. Manuscripts addressing novel theoretical issues, as well as those on more specific applications, are welcome.

Contributions should fit the scope of the journal Entropy; topics of interest include (but are not limited to):

- Entropy and Information Theory

- Complex dynamics

- Complex networks

- Evolutionary computing

- Image and signal processing

- Big data

- Machine learning

- Fractional calculus

- Fractals and chaos

- Nonlinear dynamical systems

Prof. Dr. António M. Lopes
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Entropy
  • Complex systems
  • Sports dynamics
  • Big data
  • Machine learning
  • Image and signal processing
  • Simulation
  • Modelling

Published Papers (3 papers)

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Research

11 pages, 1152 KiB  
Article
Mathematical Models to Measure the Variability of Nodes and Networks in Team Sports
by Fernando Martins, Ricardo Gomes, Vasco Lopes, Frutuoso Silva and Rui Mendes
Entropy 2021, 23(8), 1072; https://0-doi-org.brum.beds.ac.uk/10.3390/e23081072 - 19 Aug 2021
Cited by 3 | Viewed by 2274
Abstract
Pattern analysis is a widely researched topic in team sports performance analysis, using information theory as a conceptual framework. Bayesian methods are also used in this research field, but the association between these two is being developed. The aim of this paper is [...] Read more.
Pattern analysis is a widely researched topic in team sports performance analysis, using information theory as a conceptual framework. Bayesian methods are also used in this research field, but the association between these two is being developed. The aim of this paper is to present new mathematical concepts that are based on information and probability theory and can be applied to network analysis in Team Sports. These results are based on the transition matrices of the Markov chain, associated with the adjacency matrices of a network with n nodes and allowing for a more robust analysis of the variability of interactions in team sports. The proposed models refer to individual and collective rates and indexes of total variability between players and teams as well as the overall passing capacity of a network, all of which are demonstrated in the UEFA 2020/2021 Champions League Final. Full article
(This article belongs to the Special Issue Complex and Fractional Dynamics II)
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19 pages, 37930 KiB  
Article
Uniform Manifold Approximation and Projection Analysis of Soccer Players
by António M. Lopes and José A. Tenreiro Machado
Entropy 2021, 23(7), 793; https://0-doi-org.brum.beds.ac.uk/10.3390/e23070793 - 23 Jun 2021
Cited by 6 | Viewed by 2579
Abstract
In professional soccer, the choices made in forming a team lineup are crucial for achieving good results. Players are characterized by different skills and their relevance depends on the position that they occupy on the pitch. Experts can recognize similarities between players and [...] Read more.
In professional soccer, the choices made in forming a team lineup are crucial for achieving good results. Players are characterized by different skills and their relevance depends on the position that they occupy on the pitch. Experts can recognize similarities between players and their styles, but the procedures adopted are often subjective and prone to misclassification. The automatic recognition of players’ styles based on their diversity of skills can help coaches and technical directors to prepare a team for a competition, to substitute injured players during a season, or to hire players to fill gaps created by teammates that leave. The paper adopts dimensionality reduction, clustering and computer visualization tools to compare soccer players based on a set of attributes. The players are characterized by numerical vectors embedding their particular skills and these objects are then compared by means of suitable distances. The intermediate data is processed to generate meaningful representations of the original dataset according to the (dis)similarities between the objects. The results show that the adoption of dimensionality reduction, clustering and visualization tools for processing complex datasets is a key modeling option with current computational resources. Full article
(This article belongs to the Special Issue Complex and Fractional Dynamics II)
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14 pages, 1292 KiB  
Article
Hybrid Basketball Game Outcome Prediction Model by Integrating Data Mining Methods for the National Basketball Association
by Wei-Jen Chen, Mao-Jhen Jhou, Tian-Shyug Lee and Chi-Jie Lu
Entropy 2021, 23(4), 477; https://0-doi-org.brum.beds.ac.uk/10.3390/e23040477 - 17 Apr 2021
Cited by 16 | Viewed by 5315
Abstract
The sports market has grown rapidly over the last several decades. Sports outcomes prediction is an attractive sports analytic challenge as it provides useful information for operations in the sports market. In this study, a hybrid basketball game outcomes prediction scheme is developed [...] Read more.
The sports market has grown rapidly over the last several decades. Sports outcomes prediction is an attractive sports analytic challenge as it provides useful information for operations in the sports market. In this study, a hybrid basketball game outcomes prediction scheme is developed for predicting the final score of the National Basketball Association (NBA) games by integrating five data mining techniques, including extreme learning machine, multivariate adaptive regression splines, k-nearest neighbors, eXtreme gradient boosting (XGBoost), and stochastic gradient boosting. Designed features are generated by merging different game-lags information from fundamental basketball statistics and used in the proposed scheme. This study collected data from all the games of the NBA 2018–2019 seasons. There are 30 teams in the NBA and each team play 82 games per season. A total of 2460 NBA game data points were collected. Empirical results illustrated that the proposed hybrid basketball game prediction scheme achieves high prediction performance and identifies suitable game-lag information and relevant game features (statistics). Our findings suggested that a two-stage XGBoost model using four pieces of game-lags information achieves the best prediction performance among all competing models. The six designed features, including averaged defensive rebounds, averaged two-point field goal percentage, averaged free throw percentage, averaged offensive rebounds, averaged assists, and averaged three-point field goal attempts, from four game-lags have a greater effect on the prediction of final scores of NBA games than other game-lags. The findings of this study provide relevant insights and guidance for other team or individual sports outcomes prediction research. Full article
(This article belongs to the Special Issue Complex and Fractional Dynamics II)
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