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Suppose we have a database with 10 classes, and we do classification test on it by Deep Belief Network or Convolutional Neural Network. The question is that how we can understand which neurons in the last layer are related to which object? In one of the post, a person wrote " to understand which neurons are for an object like shoes and which ones are not you will put that all units in the last layer to another supervised classifier(this can be anything like multi-class-SVM or a soft-max-layer). I do not know how it should be done? I do need more expansion.

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If you have 10 classes, make your last layer have 10 neurons and use the softmax activation function. This will make sure that they all lie between 0 and 1 and add up to 1. Then, simply use the index of the neuron with the largest value as your output class.

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You can look into class activation maps which does something similar to what you are asking for. Here is an insightful blog post explaining CAMs