scholarly journals Image Completion in Embedded Space Using Multistage Tensor Ring Decomposition

2021 ◽  
Vol 4 ◽  
Author(s):  
Farnaz Sedighin ◽  
Andrzej Cichocki
Keyword(s):  
Data Processing ◽  
Incomplete Data ◽  
State Of The Art ◽  
Sampling Rate ◽  
Higher Order ◽  
Image Completion ◽  
Tensor Completion ◽  
Order Tensor ◽  
Efficient Data ◽  
Very High

Tensor Completion is an important problem in big data processing. Usually, data acquired from different aspects of a multimodal phenomenon or different sensors are incomplete due to different reasons such as noise, low sampling rate or human mistake. In this situation, recovering the missing or uncertain elements of the incomplete dataset is an important step for efficient data processing. In this paper, a new completion approach using Tensor Ring (TR) decomposition in the embedded space has been proposed. In the proposed approach, the incomplete data tensor is first transformed into a higher order tensor using the block Hankelization method. Then the higher order tensor is completed using TR decomposition with rank incremental and multistage strategy. Simulation results show the effectiveness of the proposed approach compared to the state of the art completion algorithms, especially for very high missing ratios and noisy cases.

scholarly journals Tensor Decomposition with Missing Indices

2017 ◽  
Author(s):  
Yuto Yamaguchi ◽  
Kohei Hayashi
Keyword(s):  
Incomplete Data ◽  
Tensor Decomposition ◽  
Variational Inference ◽  
Tensor Completion ◽  
Order Tensor ◽  
Decomposition Problem ◽  
Decomposition Model ◽  
Stochastic Variational Inference ◽  
Completion Task

How can we decompose a data tensor if the indices are partially missing?Tensor decomposition is a fundamental tool to analyze the tensor data.Suppose, for example, we have a 3rd-order tensor X where each element Xijk takes 1 if user i posts word j at location k on Twitter.Standard tensor decomposition expects all the indices are observed but, in some tweets, location k can be missing.In this paper, we study a tensor decomposition problem where the indices (i, j, or k) of some observed elements are partially missing.Towards the problem, we propose a probabilistic tensor decomposition model that handles missing indices as latent variables.To infer them, we derive an algorithm based on stochastic variational inference, which enables to leverage the information from the incomplete data scalably. The experiments on both synthetic and real datasets show that the proposed method achieves higher accuracy in the tensor completion task than baselines that cannot handle missing indices.

A Novel Regularized Model for Third-Order Tensor Completion

2021 ◽  
pp. 1-1
Author(s):  
Yi Yang ◽  
Lixin Han ◽  
Yuanzhen Liu ◽  
Jun Zhu ◽  
Hong Yan
Keyword(s):  
Tensor Completion ◽  
Third Order ◽  
Order Tensor ◽  
Regularized Model

Suffix array for multi-pattern matching with variable length wildcards

2021 ◽  
Vol 25 (2) ◽  
pp. 283-303
Author(s):  
Na Liu ◽  
Fei Xie ◽  
Xindong Wu
Keyword(s):  
Dynamic Programming ◽  
Data Structure ◽  
Pattern Matching ◽  
Edit Distance ◽  
State Of The Art ◽  
Suffix Array ◽  
Variable Length ◽  
Distance Method ◽  
Efficient Data ◽  
Comparison Algorithms

Approximate multi-pattern matching is an important issue that is widely and frequently utilized, when the pattern contains variable-length wildcards. In this paper, two suffix array-based algorithms have been proposed to solve this problem. Suffix array is an efficient data structure for exact string matching in existing studies, as well as for approximate pattern matching and multi-pattern matching. An algorithm called MMSA-S is for the short exact characters in a pattern by dynamic programming, while another algorithm called MMSA-L deals with the long exact characters by the edit distance method. Experimental results of Pizza & Chili corpus demonstrate that these two newly proposed algorithms, in most cases, are more time-efficient than the state-of-the-art comparison algorithms.

VERY HIGH-ORDER SPATIALLY IMPLICIT SCHEMES FOR COMPUTATIONAL ACOUSTICS ON CURVILINEAR MESHES

2001 ◽  
Vol 09 (04) ◽  
pp. 1259-1286 ◽  
Author(s):  
MIGUEL R. VISBAL ◽  
DATTA V. GAITONDE
Keyword(s):  
Three Dimensional ◽  
Radiation Condition ◽  
Higher Order ◽  
High Order ◽  
High Frequencies ◽  
Decomposition Strategies ◽  
The Impact ◽  
Spurious Modes ◽  
Very High ◽  
Computational Strategy

A high-order compact-differencing and filtering algorithm, coupled with the classical fourth-order Runge–Kutta scheme, is developed and implemented to simulate aeroacoustic phenomena on curvilinear geometries. Several issues pertinent to the use of such schemes are addressed. The impact of mesh stretching in the generation of high-frequency spurious modes is examined and the need for a discriminating higher-order filter procedure is established and resolved. The incorporation of these filtering techniques also permits a robust treatment of outflow radiation condition by taking advantage of energy transfer to high-frequencies caused by rapid mesh stretching. For conditions on the scatterer, higher-order one-sided filter treatments are shown to be superior in terms of accuracy and stability compared to standard explicit variations. Computations demonstrate that these algorithmic components are also crucial to the success of interface treatments created in multi-domain and domain-decomposition strategies. For three-dimensional computations, special metric relations are employed to assure the fidelity of the scheme in highly curvilinear meshes. A variety of problems, including several benchmark computations, demonstrate the success of the overall computational strategy.

Sign in / Sign up

Export Citation Format

Share Document