关键词: 度量学习, 测地线凸, 几何平均, Universum学习

Abstract: Metric learning improves the accuracy of classification and clustering by reflecting the distance between samples more realistically. GMML（Geometric Mean Metric Learning） aims to learn metric matrix [A] to make the distance within the same class as small as possible and the distance between different classes as large as possible. The training samples used by GMML are target data, but for the large number of real-world non-target class data, which called Universum data are ignored, result in the waste of domain information hidden in Universum data. This paper proposes a new metric learning algorithm U-GMML based on Universum learning. U-GMML aims to learn a new metric matrix [A] to ensure the distance within the same class samples as small as possible, the distance between different class samples as large as possible, and the distance between the Universum data and the target class data as large as possible. The metric matrix [A] which learned by U-GMML is more efficiency for classification. The experimental results on the real dataset verify the effectiveness of the algorithm.

Key words: metric learning, geodesically convex, geometric mean, Universum learning