Many modern datasets contain a large number of variables, that is they are high-dimensional. Such high-dimensional datasets are often however characterised by an underlying low dimensional structure. Recovering this low dimensional structure can enable exploratory analysis, visualisation and feature construction.
This short course takes a journey through the development of dimensionality reduction techniques. These will range from linear methods such as Principal Components Analysis and Classical Multidimensional Scaling through to modern Manifold Learning techniques including Isomap, Laplacian Eigenmaps and Local Linear Embedding. Also covered will be the evaluation of different dimension reduction techniques compared to one another, both with respect to computational considerations and with respect to the fidelity with which they capture the structure of high dimensional data. Applications of dimensionality data to real data problems will also be covered.
Basic knowledge of matrix algebra, statistics and R
Anastasios Panagiotelis is an Associate Professor of Business Analytics at the University of Sydney Business School. He is also a Director of the International Institute of Forecasters. His work lies in the intersection of business analytics, statistics and econometrics. He conducts research on the development of novel statistical methodology and its application to large scale datasets in energy, macroeconomics and online retail. He led the Australian Research Council Discovery Project “Macroeconomic Forecasting in a Big Data World”. This project saw the launch of www.ausmacrodata.org, a website that enables researchers to easily search for and download data on over 40,000 Australian macroeconomic variables. He has published in a diverse range of top-tier journals including the Journal of the American Statistical Association, Journal of Econometrics, European Journal of Operational Research, Journal of Business and Economic Statistics, Journal of Computational and Graphical Statistics and Insurance: Mathematics and Economics. Anastasios received his PhD from the University of Sydney and was previously a member of Faculty at the Department of Econometrics and Business Statistics at Monash University and an Alexander von Humboldt Postdoctoral Researcher at the Chair of Mathematical Statistics at the Technical University of Munich.