Hierarchical loss for classification

Failing to distinguish between a sheepdog and a skyscraper should be worse and penalized more than failing to distinguish between a sheepdog and a poodle; after all, sheepdogs and poodles are both breeds of dogs. However, existing metrics of failure (so-called “loss” or “win”) used in textual or visual classification/recognition via neural networks seldom view a sheepdog as more similar to a poodle than to a skyscraper. We define a metric that, inter alia, can penalize failure to distinguish between a sheepdog and a skyscraper more than failure to distinguish between a sheepdog and a poodle. Unlike previously employed possibilities, this metric is based on an ultrametric tree associated with any given tree organization into a semantically meaningful hierarchy of a classifier’s classes. MSC 2010 subject classifications: Primary 62H30; secondary 68T05, 65K10.