A new linear coding algorithm for efficient multi-dimensional data representation without data expansion

Linear coding is used for finding succinct representations of data sets. It also discover basis functions that capture higher-level features in the data. However, finding linear codes for multi-dimensional data remains a very difficult computational problem. Motivated by the work of linear image coding and multilinear algebra, we propose a linear tensor coding algorithm (LTC), which is applied to represent multi-dimensional data succinctly by a linear combination of tensor-formed bases without data expansion. Each basis captures some specific variability. The coefficients of data, which are associated with the bases, can be applied for representation, compression and classification. When we applied LTC algorithm on the phantom data, experimental results illustrate that our algorithm not only produces localized bases but also preserve the information of the input data.