Multidimensional scaling locus of memristor and fractional order elements

Machado, J. A. Tenreiro; Lopes, António M.

doi:10.1016/j.jare.2020.01.004

Cited by 21 publications

(8 citation statements)

References 52 publications

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“…Therefore, to have a comparison of “real-world” data is virtually impossible, not only for researchers, but also for governments and for soccer associations. The experience gathered in other applications [ 69 , 70 ] allows us to consider whether a given algorithm is “better” or “worse” based on its clustering performance. Certainly, this is a subjective point of view, but the fact is that the assessment of the results provided by such kinds of techniques is based on the user experience and intuition.…”

Section: The Umap For Local Comparison and Visualization Of Soccer Playersmentioning

confidence: 99%

Uniform Manifold Approximation and Projection Analysis of Soccer Players

Lopes

Machado

2021

Entropy

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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.

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Section: The Umap For Local Comparison and Visualization Of Soccer Playersmentioning

confidence: 99%

Uniform Manifold Approximation and Projection Analysis of Soccer Players

Lopes

Machado

2021

Entropy

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“…Therefore, similar items lead to close points and, inversely, very different items produce points very far apart. Usually, the dimensions m MDS = 2 or m MDS = 3 are used, because they allow a straightforward visualization [32,33].…”

Section: The Transfer Functions Of the Sandhmentioning

confidence: 99%

A Review of Sample and Hold Systems and Design of a New Fractional Algorithm

Ortigueira

Machado

2020

Applied Sciences

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Digital systems require sample and hold (S&H) systems to perform the conversion from analog to digital and vice versa. Besides the standard zero and first order holds, we find in the literature other versions, namely the fractional and exponential order holds, involving parameters that can be tuned to produce a superior performance. This paper reviews the fundamental concepts associated with the S&H and proposes a new fractional version. The systems are modeled both in the time and Laplace domains. The new S&H stemming from fractional calculus generalizes these devices. The different S&H systems are compared in the frequency domain and their relationships visualized by means of hierarchical clustering and multidimensional scaling representations. The novel strategy allows a better understanding of the possibilities and limitations of S&H systems.

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“…(2) The memristor is used as a feedback term to couple into a neuron model such as the Hindmarsh-Rose (HR) neuron model [ 7 ], etc. Some recent research methods on memristors, such as Chua’s periodic table [ 16 , 25 , 26 ] and the multidimensional scaling [ 27 ], have not explained the causes of chaos from the perspective of Hamiltonian energy.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Analysis of a Three-Terminal-Memristor-Based Conservative Chaotic System

Wang

2021

Entropy

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In this paper, a three-terminal memristor is constructed and studied through changing dual-port output instead of one-port. A new conservative memristor-based chaotic system is built by embedding this three-terminal memristor into a newly proposed four-dimensional (4D) Euler equation. The generalized Hamiltonian energy function has been given, and it is composed of conservative and non-conservative parts of the Hamiltonian. The Hamiltonian of the Euler equation remains constant, while the three-terminal memristor’s Hamiltonian is mutative, causing non-conservation in energy. Through proof, only centers or saddles equilibria exist, which meets the definition of the conservative system. A non-Hamiltonian conservative chaotic system is proposed. The Hamiltonian of the conservative part determines whether the system can produce chaos or not. The non-conservative part affects the dynamic of the system based on the conservative part. The chaotic and quasiperiodic orbits are generated when the system has different Hamiltonian levels. Lyapunov exponent (LE), Poincaré map, bifurcation and Hamiltonian diagrams are used to analyze the dynamical behavior of the non-Hamiltonian conservative chaotic system. The frequency and initial values of the system have an extensive variable range. Through the mechanism adjustment, instead of trial-and-error, the maximum LE of the system can even reach an incredible value of 963. An analog circuit is implemented to verify the existence of the non-Hamiltonian conservative chaotic system, which overcomes the challenge that a little bias will lead to the disappearance of conservative chaos.

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Multidimensional scaling locus of memristor and fractional order elements

Abstract: Graphical abstract

Cited by 21 publications

References 52 publications

Uniform Manifold Approximation and Projection Analysis of Soccer Players

Uniform Manifold Approximation and Projection Analysis of Soccer Players

A Review of Sample and Hold Systems and Design of a New Fractional Algorithm

Modeling and Analysis of a Three-Terminal-Memristor-Based Conservative Chaotic System

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