Linear reconstruction measure steered nearest neighbor classification framework

• Introduce and provide a theoretical justification for linear reconstruction measure (LRM).
• Analyze the role of regularization items in regularized LRM.
• Analyze the advantages of LRM over the conventional point-to-point measure (C-PtP).
• Present the LRM steered nearest neighbor classification framework (LRM_NNCF).

The linear reconstruction measure (LRM), which determines the nearest neighbors of the query sample in all known training samples by sorting the minimum L2-norm error linear reconstruction coefficients, is introduced in this paper. The intuitive interpretation and mathematical proofs are presented to reveal the efficient working mechanism of LRM. Through analyzing the physical meaning of coefficients and regularization items, we find that LRM provides more useful information and advantages than the conventional similarity measure model which calculates the distance between two entities (i.e. conventional point-to-point, C-PtP). Inspired by the advantages of LRM, the linear reconstruction measure steered nearest neighbor classification framework (LRM-NNCF) is designed with eight classifiers according to different decision rules and models of LRM. Evaluation on several face databases and the experimental results demonstrate that these proposed classifiers can achieve greater performance than the C-PtP based 1-NNs and competitive recognition accuracy and robustness compared with the state-of-the-art classifiers.