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The classes of ImagNet have a hierarchy. Did anybody try to build a hierarchy of classifiers to use this fact?

Searching for "multistage classification" leads to different results.

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Yes, multiple papers have used this. I've heard of multiple ways to exploit this hierarchial structure. This paper Hierarchical Deep Convolutional Neural Network for Large Scale Visual Recognition uses multiple levels by predicting the more coarse distribution and I think it then passes this as features to the more low level classification. YOLO9000 actually uses the ImageNet hierarchy for the problem of object detection. Hierarchial classification is the name of the problem you are describing.

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