  This paper describes one objective function for learning semantically
coherent feature embeddings in multi-output classification problems, i.e., when
the response variables have dimension higher than one. In particular, we
consider the problems of identity retrieval and soft biometrics labelling in
visual surveillance environments, which have been attracting growing interests.
Inspired by the triplet loss [34] function, we propose a generalization that:
1) defines a metric that considers the number of agreeing labels between pairs
of elements; and 2) disregards the notion of anchor, replacing d(A1, A2) <
d(A1, B) by d(A, B) < d(C, D), for A, B, C, D distance constraints, according
to the number of agreeing labels between pairs. As the triplet loss
formulation, our proposal also privileges small distances between positive
pairs, but at the same time explicitly enforces that the distance between other
pairs corresponds directly to their similarity in terms of agreeing labels.
This yields feature embeddings with a strong correspondence between the classes
centroids and their semantic descriptions, i.e., where elements are closer to
others that share some of their labels than to elements with fully disjoint
labels membership. As practical effect, the proposed loss can be seen as
particularly suitable for performing joint coarse (soft label) + fine (ID)
inference, based on simple rules as k-neighbours, which is a novelty with
respect to previous related loss functions. Also, in opposition to its triplet
counterpart, the proposed loss is agnostic with regard to any demanding
criteria for mining learning instances (such as the semi-hard pairs). Our
experiments were carried out in five different datasets (BIODI, LFW, IJB-A,
Megaface and PETA) and validate our assumptions, showing highly promising
results.
