Guaranteed Tensor Decomposition: A Moment Approach

author: Gongguo Tang, Department of Electrical Engineering & Computer Science, Colorado School of Mines
published: Sept. 27, 2015,   recorded: July 2015,   views: 2009

See Also:

Download slides icon Download slides: icml2015_tang_tensor_decomposition_01.pdf (983.8┬áKB)

Help icon Streaming Video Help

Related Open Educational Resources

Related content

Report a problem or upload files

If you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
Lecture popularity: You need to login to cast your vote.


We develop a theoretical and computational framework to perform guaranteed tensor decomposition, which also has the potential to accomplish other tensor tasks such as tensor completion and denoising. We formulate tensor decomposition as a problem of measure estimation from moments. By constructing a dual polynomial, we demonstrate that measure optimization returns the correct CP decomposition under an incoherence condition on the rank-one factors. To address the computational challenge, we present a hierarchy of semidefinite programs based on sums-of-squares relaxations of the measure optimization problem. By showing that the constructed dual polynomial is a sum-of-squares modulo the sphere, we prove that the smallest SDP in the relaxation hierarchy is exact and the decomposition can be extracted from the solution under the same incoherence condition. One implication is that the tensor nuclear norm can be computed exactly using the smallest SDP as long as the rank-one factors of the tensor are incoherent. Numerical experiments are conducted to test the performance of the moment approach.

Link this page

Would you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !

Write your own review or comment:

make sure you have javascript enabled or clear this field: