Multi-dimensional data representation using linear tensor coding

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.