Decompositions of a Higher-Order Tensor in Block Terms - Part I: Lemmas for Partitioned Matrices
نویسنده
چکیده
In this paper we study a generalization of Kruskal’s permutation lemma to partitioned matrices. We define the k’-rank of partitioned matrices as a generalization of the k-rank of matrices. We derive a lower-bound on the k’-rank of Khatri–Rao products of partitioned matrices. We prove that Khatri–Rao products of partitioned matrices are generically full column rank.
منابع مشابه
Decompositions of a Higher-Order Tensor in Block Terms - Part III: Alternating Least Squares Algorithms
In this paper we derive alternating least squares algorithms for the computation of the block term decompositions introduced in Part II. We show that degeneracy can also occur for block term decompositions.
متن کاملDecompositions of a Higher-Order Tensor in Block Terms - Part II: Definitions and Uniqueness
In this paper we introduce a new class of tensor decompositions. Intuitively, we decompose a given tensor block into blocks of smaller size, where the size is characterized by a set of mode-n ranks. We study different types of such decompositions. For each type we derive conditions under which essential uniqueness is guaranteed. The parallel factor decomposition and Tucker’s decomposition can b...
متن کاملEstimating a Few Extreme Singular Values and Vectors for Large-Scale Matrices in Tensor Train Format
We propose new algorithms for singular value decomposition (SVD) of very large-scale matrices based on a low-rank tensor approximation technique called the tensor train (TT) format. The proposed algorithms can compute several dominant singular values and corresponding singular vectors for large-scale structured matrices given in a TT format. The computational complexity of the proposed methods ...
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 کاملTensor Networks for Latent Variable Analysis. Part I: Algorithms for Tensor Train Decomposition
Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of sub-tensors of order-2 or order-3 has, so far, not been widely considered in these fields, although this so-called tensor network decomposition has been long st...
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 30 شماره
صفحات -
تاریخ انتشار 2008