Higher-Order QR with Tournament Pivoting for Tensor Compression
نویسندگان
چکیده
We present in this paper a parallel algorithm that generates low-rank approximation of distributed tensor using QR decomposition with tournament pivoting (QRTP). The algorithm, which is variant the higher-order singular value decomposition, factor matrices for Tucker by applying QRTP to unfolding blockwise (by subtensor) on set processors. For each mode logically reorganizes (unfolds) processors so associated matrix has suitable logical distribution. also establish error bounds between and compressed version generated algorithm.
منابع مشابه
Householder QR Factorization With Randomization for Column Pivoting (HQRRP)
A fundamental problem when adding column pivoting to the Householder QR factorization is that only about half of the computation can be cast in terms of high performing matrixmatrix multiplications, which greatly limits the benefits that can be derived from so-called blocking of algorithms. This paper describes a technique for selecting groups of pivot vectors by means of randomized projections...
متن کاملA Higher-Order Structure Tensor
Structure tensors are a common tool for orientation estimation in image processing and computer vision. We present a generalization of the traditional second-order model to a higher-order structure tensor (HOST), which is able to model more than one significant orientation, as found in corners, junctions, and multi-channel images. We provide a theoretical analysis and a number of mathematical t...
متن کاملCommunication Avoiding Rank Revealing QR Factorization with Column Pivoting
In this paper we introduce CARRQR, a communication avoiding rank revealing QRfactorization with tournament pivoting. We show that CARRQR reveals the numerical rank of amatrix in an analogous way to QR factorization with column pivoting (QRCP). Although the upperbound of a quantity involved in the characterization of a rank revealing factorization is worse forCARRQR than for QRCP...
متن کاملHigher Order Prediction for Geometry Compression
A lot of techniques have been developed for the encoding of triangular meshes as this is a widely used representation for the description of surface models. Although methods for the encoding of the neighbor information, the connectivity, are near optimal, there is still room for better encodings of vertex locations, the geometry. Our geometry encoding strategy follows the predictive coding para...
متن کاملA Maximum Enhancing Higher-Order Tensor Glyph
Glyphs are a fundamental tool in tensor visualization, since they provide an intuitive geometric representation of the full tensor information. The Higher-Order Maximum Enhancing (HOME) glyph, a generalization of the second-order tensor ellipsoid, was recently shown to emphasize the orientational information in the tensor through a pointed shape around maxima. This paper states and formally pro...
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: SIAM Journal on Matrix Analysis and Applications
سال: 2023
ISSN: ['1095-7162', '0895-4798']
DOI: https://doi.org/10.1137/20m1387663