Efficient and Scalable Information Geometry Metric Learning

Abstract—Information Geometry Metric Learning (IGML) is shown to be an effective algorithm for distance metric learning. In this paper, we attempt to alleviate two limitations of IGML: (A) the time complexity of IGML increases rapidly for high-dimensional data; (B) IGML has to transform the input low-rank kernel into a full-rank one since it is undefined for singular matrices. To this end, two novel algorithms, referred to as Efficient Information Geometry Metric Learning (EIGML) and Scalable Information Geometry Metric Learning (SIGML), are proposed. EIGML scales linearly with the dimensionality, resulting in significantly reduced computational complexity. As for SIGML, it is proven to have a range-space preserving property. Following this property, SIGML is found to be capable of handling both full-rank and low-rank kernels. Additionally, the geometric information from data is further exploited in SIGML. In contrast to most existing metric learning methods, both EIGML and SIGML have closed-form solutions and can be efficiently optimized. Experimental results on various data sets demonstrate that the proposed methods outperform the state-of-the-art metric learning algorithms. Keywords—Mahalanobis distance learning, Information Geom-etry Metric Learning, closed-form solution, range-space preservin