Nonlinear dimensionality reduction

• Grant number: 19/01691-3
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: July 01, 2019
• End date: June 30, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Antonio Castelo Filho
• Grantee: Lucas Moutinho Bueno
• Supervisor: Jose Claudio Teixeira e Silva Junior
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: New York University, United States
• Associated to the scholarship: 17/25631-4 - GEM data structure for triangulations, BP.PD

Abstract

This document is a proposal of a one year duration research project with the theme of nonlinear dimensionality reduction that will be executed by Dr. Lucas Moutinho Bueno. Dimensionality reduction consists of projecting high-dimensional data to a low-dimensional space using a specic method. When linear functions are used by a method to project the whole data to a low-dimensional space, we say that the method is linear. If nonlinear functions are used to project data or if multiple linear functions are used and each one applied to a diýerent subset of the data, then the method is nonlinear. The execution of the project will take place in Dailhousie University, in Halifax, Canada, and will be supervised by Professor Fernando Paulovich. This project is part of the post-doctoral research of Dr. Bueno in the eld of applied mathematics, supervised by Professor Antionio Castelo Filho, at University of SaÜo Paulo, in SaÜo Carlos, Brazil. The post-doctoral research is funded by Fapesp, process number 2017/25631-4 , and is linked to the thematic project of CEPID-CeMEAI.