%0 Electronic Article %A Xu Qiao %+ Department of Biomedical Engineering, Shandong University, Shandong 250061, People's Republic of China %A Xiaoqing Liu %+ Department of Radiology, People's Hospital of Feicheng City, Shandong 271600, People's Republic of China %A Yen-wei Chen %+ College of Information Science and Engineering, Ritsumeikan University, Shiga 525-8577, Japan %A Zhi-Ping Liu %+ Department of Biomedical Engineering, Shandong University, Shandong 250061, People's Republic of China %K data expansion %K basis functions %K multidimensional data %K concrete physical meanings %K multidimensional data representation %K linear combination %K high-level features %K linear image coding %K linear tensor coding algorithm %K multilinear algebra %X Linear coding is widely used to concisely represent data sets by discovering basis functions of capturing high-level features. However, the efficient identification of linear codes for representing multi-dimensional data remains very challenging. In this study, the authors address the problem by proposing a linear tensor coding algorithm to represent multi-dimensional data succinctly via a linear combination of tensor-formed bases without data expansion. Motivated by the amalgamation of linear image coding and multi-linear algebra, each basis function in the authors’ algorithm captures some specific variabilities. The basis-associated coefficients can be used for data representation, compression and classification. When the authors apply the algorithm on both simulated phantom data and real facial data, the experimental results demonstrate their algorithm not only preserves the original information of input data, but also produces localised bases with concrete physical meanings. %@ 1751-9659 %T Multi-dimensional data representation using linear tensor coding %B IET Image Processing %D July 2017 %V 11 %N 7 %P 492-501 %I Institution of Engineering and Technology %U https://digital-library.theiet.org/;jsessionid=2pko70hr5qko8.x-iet-live-01content/journals/10.1049/iet-ipr.2016.0795 %G EN