scholarly journals Higher-order principal component analysis for the approximation of tensors in tree-based low-rank formats

2019 ◽  
Vol 141 (3) ◽  
pp. 743-789 ◽  
Author(s):  
Anthony Nouy
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Component Analysis ◽  
Higher Order ◽  
Low Rank

scholarly journals Differentially Expressed Genes Extracted by the Tensor Robust Principal Component Analysis (TRPCA) Method

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Yue Hu ◽  
Jin-Xing Liu ◽  
Ying-Lian Gao ◽  
Sheng-Jun Li ◽  
Juan Wang
Keyword(s):  
Principal Component Analysis ◽  
Differentially Expressed Genes ◽  
Principal Component ◽  
Component Analysis ◽  
Differentially Expressed ◽  
Low Rank ◽  
Cancer Gene ◽  
Sequencing Data ◽  
Robust Principal Component Analysis ◽  
The Matrix

In the big data era, sequencing technology has produced a large number of biological sequencing data. Different views of the cancer genome data provide sufficient complementary information to explore genetic activity. The identification of differentially expressed genes from multiview cancer gene data is of great importance in cancer diagnosis and treatment. In this paper, we propose a novel method for identifying differentially expressed genes based on tensor robust principal component analysis (TRPCA), which extends the matrix method to the processing of multiway data. To identify differentially expressed genes, the plan is carried out as follows. First, multiview data containing cancer gene expression data from different sources are prepared. Second, the original tensor is decomposed into a sum of a low-rank tensor and a sparse tensor using TRPCA. Third, the differentially expressed genes are considered to be sparse perturbed signals and then identified based on the sparse tensor. Fourth, the differentially expressed genes are evaluated using Gene Ontology and Gene Cards tools. The validity of the TRPCA method was tested using two sets of multiview data. The experimental results showed that our method is superior to the representative methods in efficiency and accuracy aspects.

scholarly journals Dimensionality Reduction of Dynamic Mesh Animations Using HO-SVD

2013 ◽  
Vol 3 (4) ◽  
pp. 277-289 ◽  
Author(s):  
Michał Romaszewski ◽  
Piotr Gawron ◽  
Sebastian Opozda
Keyword(s):  
Principal Component Analysis ◽  
Singular Value Decomposition ◽  
Dimensionality Reduction ◽  
Principal Component ◽  
Component Analysis ◽  
Higher Order ◽  
Singular Value ◽  
3D Mesh ◽  
Reduction Of Dimensionality ◽  
Value Decomposition

Abstract This work presents an analysis of Higher Order Singular Value Decomposition (HOSVD) applied to reduction of dimensionality of 3D mesh animations. Compression error is measured using three metrics (MSE, Hausdorff, MSDM). Results are compared with a method based on Principal Component Analysis (PCA) and presented on a set of animations with typical mesh deformations.

Low-rank tensor train for tensor robust principal component analysis

2020 ◽  
Vol 367 ◽  
pp. 124783 ◽  
Author(s):  
Jing-Hua Yang ◽  
Xi-Le Zhao ◽  
Teng-Yu Ji ◽  
Tian-Hui Ma ◽  
Ting-Zhu Huang
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Component Analysis ◽  
Low Rank ◽  
Robust Principal Component Analysis ◽  
Rank Tensor
Sign in / Sign up

Export Citation Format

Share Document