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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Wednesday, February 14, 2001}
\centerline{Sequoia Hall Rm. 200}

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\centerline{\sl Allan Aasbjerg Nielsen}
\centerline{\sl Informatics and Mathematical Modellin}
\centerline{\sl Technical University of Denmark, Building 321}
\centerline{\sl DK-2800 Kongens Lyngby, Denmark}
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\centerline{\bf Multi-Set Canonical Correlations Analysis}

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This talk deals with extensions of the established two-set canonical
correlations analysis.  In two-set analysis data naturally divides into two
multivariate groups.  Based on the original zero-mean variables orthogonal
linear combinations with maximal correlations, the so-called canonical
variates, are found.  In multi-set analysis the maximization of
correlation, which is a scalar, to find two sets of canonical variates is
replaced by optimization of different measures of the correlation matrix of
more sets of canonical variates.  This optimization may be maximization of
the sum of correlations, maximization of the sum of squared correlations,
maximization of the largest eigenvalue, minimization of the smallest
eigenvalue, or minimization of the generalized variance.

Maximization of the sum of correlations will be used to give two examples
of remote sensing applications, one terrestrial and one oceanic.  The
terrestrial case will use annual Landsat TM data from 1984 to 1989 to look
into change in a forested region in northern Sweden.  This case will also
give a brief comparison between the five optimizations mentioned above.
The oceanic case will use monthly means of global sea surface temperatures
from the NOAA/NASA AVHRR Oceans Pathfinder data covering 1987 to 1998 to
reveal patterns in global temperature variation including El Niņo and La Niņa. 

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