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Learning outcomes |
This course focuses on reviewing and understanding current computational information geometry techniques and problems and their applications in science, engineering, and business.
The general objectives of the curricular unit are the following:
- Provide doctoral students with an in-depth view of computational information geometry.
- Provide doctoral students with strong skills in scientific research methodologies.
- Prepare doctoral candidates for a scientific and/or academic career.
With regard to learning objectives, at the end of the course, the doctoral student should be able to:
- Understand the basic concepts and implement the basic tools for computation in computational geometry, differential geometry and information geometry.
- Apply information theoretical approaches to machine learning and stochastic optimization in your own research.
- Have a broad knowledge of current applications of information geometry.
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Main Bibliography |
Principal/Main:
1) K. Arwini and C. Dodson, “Information geometry”, Springer-Verlag, 2008.?
2) F. Nielsen, “Geometric Structures of Information”, Springer-Verlag, 2019.?
Complementar/Complementary:
3) A. Pressley, “Elementary Differential Geometry”, Springer-Verlag, 2010.?
4) F. Preparata and M. Shamos, “Computational Geometry: An Introduction”, Springer-Verlag, 1985.?
5) A. Gomes, I. Voiculescu, J. Jorge, B. Wyvill, and C. Galbraith, “Implicit Curves and Surfaces: Mathematics, Data Structures, and Algorithms”, Springer-Verlag, 2009.
6) S. Biasotti, B. Falcidieno, D. Giorgi, and M. Spagnuolo, “Mathematical Tools for Shape Analysis and Description”, Synthesis Lectures on Computer Graphics and Animation, Morgan & Claypool Publishers, 2014.
7) S. Jia and J. Li, “3D Shape Analysis: Construction, Classification and Matching”, VDM Verlag, 2008.
8) R. Grant. Data Visualization: Charts, Maps, and Interactive Graphics, CRC Press, 2018.
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