Nearest Feature Line: A Tangent Approximation

Nearest feature line (NFL) (S.Z. Li and J. Lu, 1999) is an efficient yet simple classification method for pattern recognition. This paper presents a theoretical analysis and interpretation of NFL from the perspective of manifold analysis, and explains the geometric nature of NFL based similarity measures. It is illustrated that NFL, nearest feature plane (NFP) and nearest feature space (NFS) are special cases of tangent approximation. Under the assumption of manifold, we introduce localized NFL (LNFL) and nearest feature spline (NFB) to further enhance classification ability and reduce computational complexity. The LNFL extends NFL's Euclidean distance to a manifold distance. And for NFB, feature lines are constructed along with a manifold's variation which is defined on a tangent bundle. The proposed methods are validated on a synthetic dataset and two standard face recognition databases (FRGC version 2 and FERET). Experimental results illustrate its efficiency and effectiveness.