Machine Learning and Dimension Reduction methods for Functional Data

In today's environment where computer processors are powerful and computer memory cheap, researchers are able to collect and store huge amounts of data. Analysing that data needs sophisticated statistical and computational methods as most classic statistical methodology was developed at an era where data collection was not as easy and datasets where a lot of orders of magnitude smaller. Sufficient dimension reduction (SDR) is a class of methods for feature extraction in regression and classification problems with the purpose of reducing the size of a multidimensional dataset to a few important features.
This has the potential of improving visualization of the most important relationships between the variables. This project will focus on the improvement of existing methodology for more accurate and computationally faster estimation algorithms to achieve SDR for functional data. Among the most interesting suggestions in the literature for vector data uses machine learning algorithms and more specifically Support Vector Machines (SVM). We will explore the possibilities of extending the use of this methodology to functional data using classifications algorithms for Functional data.