Free Component Analysis

We describe a method for unmixing mixtures of 'freely' independent random variables in a manner analogous to the indepedent component analysis (ICA) based method for unmixing independent random variables from their additive mixture. Random matrices play the role of free random variables in this context so the method we develop, which we call Free component analysis (FCA), unmixes matrices from an additive mixture of matrices. We describe the theory — the various 'contrast functions', computational methods and compare FCA to ICA on data derived from real-world experiments.

This is joint work with Hao Wu.

Since Fall 2009, I am an associate professor in the Department of Electrical Engineering and Computer Science at the University of Michigan. Prior to that I was at MIT where I received my Masters and PhD in Electrical Engineering and Computer Science as part of the MIT/WHOI Joint Program in Ocean Science and Engineering. I work at the interface of statistical signal processing and random matrix theory with applications such as sonar, radar, wireless communications and machine learning in mind. I particularly enjoy using random matrix theory to address problems that arise in statistical signal processing. An important component of my work is applying it in real-world settings to tease out low-level signals from sensor, oceanographic, financial and econometric time/frequency measurements/time series. In addition to the satisfaction derived from transforming the theory into practice, real-world settings give us insight into how the underlying techniques can be refined and/or made more robust.