Block Tensor Unfoldings
نویسندگان
چکیده
Within the field of numerical multilinear algebra, block tensors are increasingly important. Accordingly, it is appropriate to develop an infrastructure that supports reasoning about block tensor computation. In this paper we establish concise notation that is suitable for the analysis and development of block tensor algorithms, prove several useful block tensor identities, and make precise the notion of a block tensor unfolding.
منابع مشابه
Computing the Gradient in Optimization Algorithms for the CP Decomposition in Constant Memory through Tensor Blocking
The construction of the gradient of the objective function in gradient-based optimization algorithms for computing an r-term CANDECOMP/PARAFAC (CP) decomposition of an unstructured dense tensor is a key computational kernel. The best technique for efficiently implementing this operation has a memory consumption that scales linearly with the number of terms r and sublinearly with the number of e...
متن کاملScaled Nuclear Norm Minimization for Low-Rank Tensor Completion
Minimizing the nuclear norm of a matrix has been shown to be very efficient in reconstructing a low-rank sampled matrix. Furthermore, minimizing the sum of nuclear norms of matricizations of a tensor has been shown to be very efficient in recovering a low-Tucker-rank sampled tensor. In this paper, we propose to recover a low-TT-rank sampled tensor by minimizing a weighted sum of nuclear norms o...
متن کاملMultilinear Singular Value Decomposition for Structured Tensors
The Higher-Order SVD (HOSVD) is a generalization of the Singular Value Decomposition (SVD) to higher-order tensors (i.e. arrays with more than two indices) and plays an important role in various domains. Unfortunately, this decomposition is computationally demanding. Indeed, the HOSVD of a third-order tensor involves the computation of the SVD of three matrices, which are referred to as "modes"...
متن کاملTensor Decompositions via Two-Mode Higher-Order SVD (HOSVD)
Tensor decompositions have rich applications in statistics and machine learning, and developing efficient, accurate algorithms for the problem has received much attention recently. Here, we present a new method built on Kruskal’s uniqueness theorem to decompose symmetric, nearly orthogonally decomposable tensors. Unlike the classical higher-order singular value decomposition which unfolds a ten...
متن کاملMoment tensor and stress inversion for an active fault system in west part of Lut-Block, Iran
Iran is one of the most tectonically active regions on the Alpine-Himalayan earthquake belt. Eastern Iran, nowadays, is one of the most active regions of the country. The occurrence of several destructive earthquakes during the past 50 years provides the evidence for the seismic activity in this region. The earthquakes are mostly concentrated around the Lut-block. There are strike-slip fault sy...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Matrix Analysis Applications
دوره 33 شماره
صفحات -
تاریخ انتشار 2012