Tensor decomposition for dimension reduction

Abstract

Tensor data are data with multiway array structure. They are often very high dimensional and are routinely encountered in many scientific fields. Dimension reduction is the technique of reducing the number of underlying variables for compressed data representation and for model parsimony. Tensor dimension reduction aims for reducing the tensor data dimension while keeping data's tensor structure. This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Deep Learning Statistical and Graphical Methods of Data Analysis > Dimension Reduction Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data

Detecting and Locating Passive Video Forgery Based on Low Computational Complexity Third-Order Tensor Representation

“…In the proposed method, mode-3 fibers are used. Since tube fibers preserve the continuity of the spatial and temporal video scene together with its correlation characteristics, in addition, the tracing features extracted from third-order tensor representation achieve high dimensionality reduction and exact continuity measure [ 8 ].…”

“…It is used in many applications as in [ 27 , 28 , 29 ]. Cheng et al [ 8 ] discussed tensor data decomposition and its great influence on dimension reduction. Tensor data are routinely encountered in many fields such as genomics, image processing, finance and chemometrics.…”

“…These features limit passive approaches performance in terms of detection time and accuracy, especially in the case of large video sizes with a low content variation. Recently, tensor data representation has been considered a trend computational approach to deal with large videos, it provides greater model fitting stability, easier to read and saves time [ 8 ].…”