Multiple Cayley-Klein metric learning

• Published in: PloS one Vol. 12; no. 9; p. e0184865
• Main Authors: Bi, Yanhong, Fan, Bin, Wu, Fuchao
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 21.09.2017; Public Library of Science (PLoS)
• Subjects: Automation; Benchmarks; Biology and Life Sciences; Classification; Computer and Information Sciences; Computer vision; Datasets as Topic; Euclidean geometry; Face; Geometry; Humans; Image Processing, Computer-Assisted - methods; Internet; Iterative methods; Laboratories; Linear Models; Machine Learning; Neighborhoods; Neural networks; Nonlinear Dynamics; Optimization; Pattern recognition; Pattern Recognition, Automated - methods; Physical Sciences; Research and Analysis Methods; Researchers; Social Sciences; Task complexity; Teaching methods; Technology application; Time Factors; China; Beijing China
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0184865

As a specific kind of non-Euclidean metric lies in projective space, Cayley-Klein metric has been recently introduced in metric learning to deal with the complex data distributions in computer vision tasks. In this paper, we extend the original Cayley-Klein metric to the multiple Cayley-Klein metric, which is defined as a linear combination of several Cayley-Klein metrics. Since Cayley-Klein is a kind of non-linear metric, its combination could model the data space better, thus lead to an improved performance. We show how to learn a multiple Cayley-Klein metric by iterative optimization over single Cayley-Klein metric and their combination coefficients under the objective to maximize the performance on separating inter-class instances and gathering intra-class instances. Our experiments on several benchmarks are quite encouraging.