How can a sparse representation be made applicable for very low-dimensional data?

We analyze the problem of sparse representation on low-dimensional data.We extend applicable scope of sparse representations via a novel perspective.An effective method to double the dimensionality is proposed for classification. The sparse representation has achieved notable performance in the field of pattern classification, and has been adopted in many expert and intelligent applications such as access control and surveillance. However, sparse representation does not work as well for low-dimensional data as it does for high-dimensional data. For data of very low dimensionality, sparse representation methods usually have severe drawbacks; consequently, wider applications of sparse representations are seriously restricted. In this paper, we focus on this challenging problem and propose a very effective method for using sparse representations with low-dimensional data. Compared with the conventional sparse representation method, the proposed method achieves considerable improvement of classification accuracy by increasing the dimensionality of the data. Moreover, the proposed method is mathematically tractable and quite computationally efficient.