|Cluster-linked Principal Curves|
Another research interest is to explore causality given two or more time series collected on the same system. The dependency is usually not easy to establish. In one of my research articles with Dr. Bruns, I suggested a new algorithm (CLPC algorithm) to reduce the dimensionality of data, and applied the algorithm to a three-dimensional embedding of the bubble column. The algorithm facilitated testing for stationarity and reversibility, as well as nonlinear process monitoring. This algorithm has only one hyperparameter that can be chosen based on information-theoretic criteria. The algorithm can also be used for multiple time series obtained on the same system and serve as a measure of predictability of one variable given another. I am working on applying this algorithm to batch data to identify undesirable batches and help control the batch reactors better.
I presented a paper titled Principal Curves and Chaos at the 7th experimental chaos conference held at San Diego from Aug 26-29. The proceedings have been published by the American Institute of Physics and are out. The most recent presentation we had on the algorithm and its applications was in paper 448g at the 2003 AIChE Annual meeting. You can download the paper here.