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Multidimensional scaling locus of memristor and fractional order elements
J A Tenreiro Machado1, António M Lopes2
1Institute of Engineering, Polytechnic of Porto, Dept. of Electrical Engineering, Porto, Portugal.
Journal of Advanced Research
|September 14, 2020
Summary
This study introduces a novel framework combining fractional calculus, memristors, and information visualization to organize fractional order elements (FOE). Multidimensional scaling visualizes these elements, generalizing the periodic table for advanced data representation.
Area of Science:
- Mathematics and Computational Science
- Electrical Engineering
- Data Visualization
Background:
- Classical calculus and electrical elements are extended by fractional calculus and memristors.
- Current data representation methods lack a comprehensive framework for complex elements.
Purpose of the Study:
- To develop a unified framework for organizing and describing fractional order elements (FOE).
- To generalize the concept of the periodic table for characterizing these elements.
Main Methods:
- Integration of fractional calculus, memristor concepts, and information visualization.
- Characterization of FOE behavior in time and frequency domains using distinct distance indices (e.g., Arccosine, Jaccard).
- Application of Multidimensional Scaling (MDS) for pattern visualization and clustering.
Main Results:
- A novel 3-dimensional representation of FOE based on their characteristics.
- Successful organization and visualization of both linear and nonlinear FOE.
- Demonstration of MDS's capability to reveal clusters and patterns in element behavior.
Conclusions:
- The proposed framework offers a generalized approach to understanding and visualizing complex mathematical and computational elements.
- This work extends classical scientific organization principles to new domains, enhancing data representation and analysis.
Keywords:
Fractional calculusInformation visualizationMemristorMultidimensional scalingProcrustes analysisMore Related Videos
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