svd_2006_usc
svd_2006_usc,
"Turning Data into Information with the SVD",
a talk on 25 October 2006, to the
local SIAM Student chapter at the
Mathematics Department of the University of South Carolina.
A plain text abstract of the talk is available as
svd_2006_usc.txt.
The problem of analyzing data from a fluid flow simulation
and then reusing it as a reduced model for further calculations
is presented in
John Burkardt, Max Gunzburger, Hyung Chun Lee,
Centroidal Voronoi Tessellation-Based Reduced-Order Modeling
of Complex Systems,
SIAM Journal on Scientific Computing,
Volume 28, Number 2, 2006, pages 459-484.
Please note that the "face" images are used for comparison
and illustration, and come from the work of an entirely
separate research group. That research is described in
Neil Muller, Lourenco Magaia, Ben Herbst,
Singular Value Decomposition, Eigenfaces, and 3D Reconstructions,
SIAM Review,
Volume 46, Number 3, 2004, pages 518-545.
More information about the Singular Value Decomposition (SVD)
is available in most textbooks on linear algebra:
Lloyd Trefethen, David Bau,,
Numerical Linear Algebra,
SIAM, 1997,
ISBN: 0-89871-361-7,
LC: QA184.T74.
The following files were used:
-
accelerator.png, an image of the aftermath of a collision
in a particle accelerator.
-
faces_data.png, an image of facial width versus
height data, from Muller, Magaia, and Herbst.
-
faces_eigen.png, the first eight "eigenfaces" extracted
from a dataset, from Muller, Magaia, and Herbst.
-
faces_energies.png, a plot of the 600 singular values
of a facial dataset, from Muller, Magaia, and Herbst.
-
faces_new.png, shows how a face not in the dataset
was approximated using eigenfaces, from Muller, Magaia, and Herbst.
-
faces_three.png, shows the kind of facial images
used in the dataset, and in its testing,
from Muller, Magaia, and Herbst.
-
fingerprint.png, an image of a fingerprint.
-
fsu_logo.pdf, a little FSU logo that appears on
each slide.
-
inout_flow_elements.png, shows the decomposition of
the flow region into elements.
-
inout_flow_energies.png, a plot of the first 16
singular values from the INOUT dataset.
-
inout_flow_hat.png, shows the forcing of the boundary
term by a hat function, when using the reduced model
to solve new problems. (This plot was not used)
-
inout_flow_pod001_dir.eps, the direction field for
the IN/OUT flow, for POD basis vector 1;
-
inout_flow_pod002_dir.eps, the direction field for
the IN/OUT flow, for POD basis vector 2;
-
inout_flow_pod003_dir.eps, the direction field for
the IN/OUT flow, for POD basis vector 3;
-
inout_flow_pod004_dir.eps, the direction field for
the IN/OUT flow, for POD basis vector 4;
-
inout_flow_region.png, shows the flow region.
-
inout_flow_sinusoid_error.png, plots of the error between
an IN/OUT simulation and a CVT approximation using 4, 8 and
16 basis vectors, with a sinusoidal inflow parameter ALPHA;
-
inout_flow_sinusoid.png, shows the forcing of the boundary
term by a sinusoid function, when using the reduced model
to solve new problems.
-
inout_flow_steady_dir.png, the velocity direction field for
the IN/OUT flow field at steady state;
-
inout_flow_step001_dir.png, the velocity direction field for
the IN/OUT flow field at time step 1;
-
inout_flow_step100_dir.png, the velocity direction field for
the IN/OUT flow field at time step 100;
-
satellite.png, an image of an earth-orbiting satellite.
-
svd.png, an illustration from Muller, Magaia, and Herbst
showing the back-rotation, dilation, and roation effects of the SVD.
-
thematrix2.png, an image of "data rain" from The Matrix.
Last revised on 03 February 2024.