Hierarchical loss for classification
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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.
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