  Online metric learning has been widely applied in classification and
retrieval. It can automatically learn a suitable metric from data by
restricting similar instances to be separated from dissimilar instances with a
given margin. However, the existing online metric learning algorithms have
limited performance in real-world classifications, especially when data
distributions are complex. To this end, this paper proposes a multilayer
framework for online metric learning to capture the nonlinear similarities
among instances. Different from the traditional online metric learning, which
can only learn one metric space, the proposed Multi-Layer Online Metric
Learning (MLOML) takes an online metric learning algorithm as a metric layer
and learns multiple hierarchical metric spaces, where each metric layer follows
a nonlinear layers for the complicated data distribution. Moreover, the forward
propagation (FP) strategy and backward propagation (BP) strategy are employed
to train the hierarchical metric layers. To build a metric layer of the
proposed MLOML, a new Mahalanobis-based Online Metric Learning (MOML) algorithm
is presented based on the passive-aggressive strategy and one-pass triplet
construction strategy. Furthermore, in a progressively and nonlinearly learning
way, MLOML has a stronger learning ability than traditional online metric
learning in the case of limited available training data. To make the learning
process more explainable and theoretically guaranteed, theoretical analysis is
provided. The proposed MLOML enjoys several nice properties, indeed learns a
metric progressively, and performs better on the benchmark datasets. Extensive
experiments with different settings have been conducted to verify these
properties of the proposed MLOML.
