Correlation mining in high dimension with limited samples

Alfred Hero (University of Michigan, Ann Arbor, MI, USA)
January 30, 2015 — 10:30 — Location: None


Correlation mining arises in many areas of engineering, social sciences, and natural sciences. Correlation mining discovers columns of a random matrix that are highly correlated with other columns of the matrix and can be used to construct a dependency network over columns. However, when the number n of samples is finite and the number p of columns increases such exploration becomes futile due to a phase transition phenomenon: spurious discoveries will eventually dominate. In this presentation I will present theory for predicting these phase transitions and present Poisson limit theorems that can be used to determine finite sample behavior of correlation structure. The theory has application to areas including gene expression analysis, network security, remote sensing, and portfolio selection.


Alfred O. Hero III received the B.S. (summa cum laude) from Boston University (1980) and the Ph.D from Princeton University (1984), both in Electrical Engineering. Since 1984 he has been with the University of Michigan, Ann Arbor, where he is the R. Jamison and Betty Williams Professor of Engineering. His primary appointment is in the Department of Electrical Engineering and Computer Science and he also has appointments, by courtesy, in the Department of Biomedical Engineering and the Department of Statistics. From 2008-2013 he was held the Digiteo Chaire d’Excellence at the Ecole Superieure d’Electricite, Gif-sur-Yvette, France. He is a Fellow of the Institute of Electrical and Electronics Engineers (IEEE) and several of his research articles have recieved best paper awards. Alfred Hero was awarded the University of Michigan Distinguished Faculty Achievement Award (2011). He received the IEEE Signal Processing Society Meritorious Service Award (1998), the IEEE Third Millenium Medal (2000), and the IEEE Signal Processing Society Technical Achievement Award (2014). Alfred Hero was President of the IEEE Signal Processing Society (2006-2008) and was on the Board of Directors of the IEEE (2009-2011) where he served as Director of Division IX (Signals and Applications). Alfred Hero’s recent research interests are in statistical signal processing, machine learning and the analysis of high dimensional spatio-temporal data. Of particular interest are applications to networks, including social networks, multi-modal sensing and tracking, database indexing and retrieval, imaging, and genomic signal processing.