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I know AlexNet does object classification in images [categories] and R-CNN does object localization [category and bounding box]. How does R-CNN and AlexNet compare?

Are they used for the same purpose or R-CNN does more? Does R-CNN use Alexnet as a sub-module?

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I think you got most of it from the way you wrote your question.

How does R-CNN and AlexNet compare?

Are they used for the same purpose or R-CNN does more?

They are different things. AlexNet is a CNN architecture, i.e a neural network with a specific set of layers. R-CNN is multistep method that does object localization and classification using a search algorithm with a CNN (of any architecture) and a SVM.

Does R-CNN use Alexnet as a sub-module?

R-CNN can use AlexNet, or other CNN architectures, as its' feature extractor.

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