<inline-formula> <tex-math notation="LaTeX">${L_{2,1}}$ </tex-math></inline-formula>-Norm Discriminant Manifold Learning

• Main Authors: Yang Liu, Quanxue Gao, Xinbo Gao, Ling Shao
• Format: Article
• Language: English
• Published: IEEE 2018-01-01
• Series: IEEE Access
• Subjects: <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">L</italic>₁-norm; <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">L</italic>₂, ₁-norm; manifold learning; dimensionality reduction
• Online Access: https://ieeexplore.ieee.org/document/8419246/

Recently, L₁-norm-based robust discriminant feature extraction technique has been attracted much attention in dimensionality reduction and pattern recognition. However, it does not relate to the scatter matrix which well characterizes the geometric structure of data. In this paper, we propose a robust formulation of graph embedding framework for dimensionality reduction. In this robust framework, we use L₂-norm to measure the distance along space dimension and L₁-norm to sum overall data points. The proposed robust graph embedding framework retains the traditional framework's desirable properties, such as rotational invariance and well geometric structure, and simultaneously suppresses outliers. Based on this framework, we develop a simple and robust feature extraction method, namely L_2,1-norm-based discriminant locality preserving projections (L_2,1-DLPP) and provide an effective iterative algorithm to solve L_2,1-DLPP. Extensive experiments in artificial data and three popular face databases illustrate the effectiveness of our proposed method.