General tensor decomposition, moment matrices and applications
نویسندگان
چکیده
منابع مشابه
General tensor decomposition, moment matrices and applications
The tensor decomposition addressed in this paper may be seen as a generalisation of Singular Value Decomposition of matrices. We consider general multilinear and multihomogeneous tensors. We show how to reduce the problem to a truncated moment matrix problem and give a new criterion for flat extension of Quasi-Hankel matrices. We connect this criterion to the commutation characterisation of bor...
متن کاملGuaranteed Tensor Decomposition: A Moment Approach
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 u...
متن کامل4 - 1 Moment Tensor – Applications 4 - 1 - 1 Damage Mechanics
where Mkk represents the trace components of the moment tensor, and are Lame constants. These results imply that the damage evolution and the accumulation of relative crack volume are also estimated from the moment tensor analysis. From moment tensors determined in bending tests of concrete specimens with a notch [Ohtsu & Ohtsuka 1998], the damage and the accumulation of crack volume were e...
متن کاملFast and robust tensor decomposition with applications to dictionary learning
We develop fast spectral algorithms for tensor decomposition that match the robustness guarantees of the best known polynomial-time algorithms for this problem based on the sum-of-squares (SOS) semidefinite programming hierarchy. Our algorithms can decompose a 4-tensor with n-dimensional orthonormal components in the presence of error with constant spectral norm (when viewed as an n2-by-n2 matr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2013
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2012.05.012