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This article 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. Such coherent embeddings can be used simultaneously for different tasks, such as identity retrieval and soft biometrics labelling. We propose a generalization of the triplet loss that: 1) defines a metric that considers the number of agreeing labels between pairs of elements; 2) introduces the concept of similar classes, according to the values provided by the metric; and 3) disregards the notion of anchor, sampling four arbitrary elements at each time, from where two pairs are defined. The distances between elements in each pair are imposed according to their semantic similarity (i.e., the number of agreeing labels). Likewise the triplet loss, our proposal also privileges small distances between positive pairs. However, the key novelty is to additionally enforce that the distance between elements of any other pair corresponds inversely to their semantic similarity. The proposed loss yields embeddings with a strong correspondence between the classes centroids and their semantic descriptions. In practice, it is a natural choice to jointly infer coarse (soft biometrics) + fine (ID) labels, using simple rules such as k-neighbours. Also, in opposition to its triplet counterpart, the proposed loss appears to be agnostic with regard to 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 results that are comparable to the state-of-the-art in both the identity retrieval and soft biometrics labelling tasks.

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