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Tutorial TUT-10: Independent Component Analysis and multiway factor analysis


P. Comon; Research Director at CNRS, University of Nice, France

Time & Location

Saturday, March 19, 13:30 - 16:30, Location: TBA


The problem of identifying linear mixtures of independent random variables only from outputs can be traced back to 1953 with the works of Darmois or Skitovich. They pointed out that when data are non Gaussian, a lot more can be said about the mixture.

In practice, Blind Identification of linear mixtures is useful especially in Factor Analysis, in addition to many other application areas (including signal & image processing, digital communications, biomedical, or complexity theory). Harshman and Carroll provided independently numerical algorithms to decompose a data record stored in a 3-way array into elementary arrays, each representing the contribution of a single underlying factor. The main difference with the well known Principal Component Analysis is that the mixture is not imposed to be a unitary matrix. This is very relevant because the actual mixture often has no reason to have orthogonal columns. The Parafac algorithm, widely used since that time, theoretically does not converge for topological reasons, but yields very usable results after a finite number of iterations under mild conditions.

Independently, the problem of Blind Source Separation (BSS) arose around 1985 and was solved -explicitly or implicitly- with the help of High-Order Statistics (HOS), which are actually tensor objects. It gave rapidly birth to the more general problem of Independent Component Anlalysis (ICA) in 1991. ICA is a tool that can be used to extract factors when the physical diversity does not allow to store efficiently the data in tensor format, in other words when the Parafac algorithm cannot be used.

This tutorial provides a very accessible background on Statistical Independence, High-Order Statistics, and Tensors. Simple examples are given throughout the talk in order to illustrate various concepts and properties. It emphasizes both the usefulness and limitations of Parafac and ICA algorithms. Mathematically advanced topics are only tackled, but striking tensor properties that are not satisfied by matrices are still touched upon. Some reported results show how strange and attractive this research area can be.

Overview: The following topics will be addressed along with demos and numerous simple examples:

Target Audience and Prerequisites: This tutorial is proposed to researchers, graduate students, or engineers. Participants are expected to be familiar with basic statistics and linear algebra, although all necessary algebraic and statistical tools will be recalled.

Presenter Information

Pierre Comon received his graduation in 1982, and his Doctorate in 1985, both from the University of Grenoble, France. He later received the "Habilitation to lead Researches" in 1995, from the University of Nice Sophia-Antipolis UNSA. His teaching has been mainly in the area of signal processing. His research interests include High-Order statistics, Tensors, Blind Deconvolution and Equalization, Digital Communications, Statistical Signal and Array Processing, and Numerical analysis. He has been for nearly 13 years in industry, first with Crouzet/Sextant between 1982 and 1985, and then with Thomson Marconi between 1988 and 1997. In 1987, he spent a post-doc at Stanford University, in the ISL laboratory. He joined Eurecom from March, 1997 to September, 1998, as a Teaching & Research Associate under contract. He has also been Research Director Associated with CNRS from January, 1994 to September, 1998, in the TSASI group of laboratory I3S. He holds a position of permanent Research Director at CNRS since October, 1998, as leader of the ASTRE project. He has been Associate Editor of the IEEE Transactions on Signal Processing from September, 1995 to March, 1998, and a member of the National Committee of scientific research between September, 1995 and July, 2000. He has been the coordinator of the 6620 European Basic Research Working Group ATHOS, from 1992 to 1995. Between Jan 1992 and 1998, he has been a member of the Technical and Scientific Council of the Thomson Group (multinational Company employing 96,000 persons over 50 countries). Between July 2001 and January 2004, he acted as launching Associate Editor with the IEEE Transactions on Circuits and Systems I, in the area of Blind Techniques. He has about 120 publications to his name, and 5 patents. He is currently Senior Member of the IEEE and of the SEE. He has been IEEE distinguished lecturer over the period 2002-2003. Since 2000, he is heading the SiCom PhD program.