This paper presents a novel classifier based on collaborative representation (CR) and multiple one-dimensional (1D) embedding with applications to face recognition. To use multiple 1D embedding (1DME) framework in semi-supervised learning is first proposed by one of the authors, J. Wang, in 2014. The main idea of the multiple 1D embedding is the following: Given a high-dimensional dataset, we first map it onto several different 1D sequences on the line while keeping the proximity of data points in the original ambient high-dimensional space. By this means, a classification problem on high dimension reduces to the one in a 1D framework, which can be efficiently solved by any classical 1D regularization method, for instance, an interpolation scheme. The dissimilarity metric plays an important role in learning a decent 1DME of the original dataset. Our another contribution is to develop a collaborative representation based dissimilarity (CRD) metric. Compared to the conventional Euclidean distance based metric, the proposed method can lead to better results. The experimental results on real-world databases verify the efficacy of the proposed method.
On the One-Dimensional Space Allocation Problem
