A Quadruplet Loss for Enforcing Semantically Coherent Embeddings in Multi-output Classification Problems

This paper describes one objective function for learning semantically\ncoherent feature embeddings in multi-output classification problems, i.e., when\nthe response variables have dimension higher than one. In particular, we\nconsider the problems of identity retrieval and soft biometrics labelling in\nvisual surveillance environments, which have been attracting growing interests.\nInspired by the triplet loss [34] function, we propose a generalization that:\n1) defines a metric that considers the number of agreeing labels between pairs\nof elements; and 2) disregards the notion of anchor, replacing d(A1, A2) <\nd(A1, B) by d(A, B) < d(C, D), for A, B, C, D distance constraints, according\nto the number of agreeing labels between pairs. As the triplet loss\nformulation, our proposal also privileges small distances between positive\npairs, but at the same time explicitly enforces that the distance between other\npairs corresponds directly to their similarity in terms of agreeing labels.\nThis yields feature embeddings with a strong correspondence between the classes\ncentroids and their semantic descriptions, i.e., where elements are closer to\nothers that share some of their labels than to elements with fully disjoint\nlabels membership. As practical effect, the proposed loss can be seen as\nparticularly suitable for performing joint coarse (soft label) + fine (ID)\ninference, based on simple rules as k-neighbours, which is a novelty with\nrespect to previous related loss functions. Also, in opposition to its triplet\ncounterpart, the proposed loss is agnostic with regard to any demanding\ncriteria for mining learning instances (such as the semi-hard pairs). Our\nexperiments were carried out in five different datasets (BIODI, LFW, IJB-A,\nMegaface and PETA) and validate our assumptions, showing highly promising\nresults.\n