  In recent years, we have witnessed a surge of interests in learning a
suitable distance metric from weakly supervised data. Most existing methods aim
to pull all the similar samples closer while push the dissimilar ones as far as
possible. However, when some classes of the dataset exhibit multimodal
distribution, these goals conflict and thus can hardly be concurrently
satisfied. Additionally, to ensure a valid metric, many methods require a
repeated eigenvalue decomposition process, which is expensive and numerically
unstable. Therefore, how to learn an appropriate distance metric from weakly
supervised data remains an open but challenging problem. To address this issue,
in this paper, we propose a novel weakly supervised metric learning algorithm,
named MultimoDal Aware weakly supervised Metric Learning (MDaML). MDaML
partitions the data space into several clusters and allocates the local cluster
centers and weight for each sample. Then, combining it with the weighted
triplet loss can further enhance the local separability, which encourages the
local dissimilar samples to keep a large distance from the local similar
samples. Meanwhile, MDaML casts the metric learning problem into an
unconstrained optimization on the SPD manifold, which can be efficiently solved
by Riemannian Conjugate Gradient Descent (RCGD). Extensive experiments
conducted on 13 datasets validate the superiority of the proposed MDaML.
