Singular value decomposition and data compression techniques

• Grant number: 18/07318-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2018
• End date: June 30, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Sandra Augusta Santos
• Grantee: Giovanna Castello de Andrade
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This project addresses computational methods for obtaining singular values and singular vectors of matrices, focusing on the large-scale setting. Strategies of image compression based on the statistical technique of principal components analysis are our main motivation. Based on the fundamentals acquired in basic disciplines, the student will expand her background by studying and implementing Lanczos methods, which are matrix-free strategies to determine a set of eigenpairs of symmetric matrices. Then, she will analyze the use of such methods to obtain a partial singular value decomposition of data matrices, in order to explore practical problems through the principal components analysis.