Looking for the proper cost function to produce a one-hot encoding, but with the ability to also output all zeros

Question

For a research project, I am modeling parts of the human visual system using a VGG16 conv-net. A prominent feature of the visual system is that there are parts that only detect/classify certain categories of images (e.g. faces, text) and stay relatively silent for images not belonging to this category (not-face, not-text).

I'd like to train the model in such a way that it will classify, using a standard one-hot encoding scheme, different faces belonging to celebrities, but output all zeros (or all small values) for non-faces. Which training criterion should I use? Normally, I'd use cross-entropy for classifying faces, but how to incorporate wanting all zeros for training examples that are not faces?

Answer 1

You can add an extra class for non-face, still using cross-entropy.

Let's say you have four different celebrities that you want to recognize. Then create your model with five outputs. Let's say the first one corresponds to non-face. Training labels should be

0-0-0-1-0 or 0-1-0-0-0 for one of the celebrities, and 1-0-0-0-0 for a non face. Now you train your network with cross-entropy (on five outputs). Then a prediction from the network will result in for example

0.21-.38-.12-.52-.11 , this is prediction for the third celebrity, and a prediction of 0.91-0.12-0.23-0.23-0.11 corresponds to a prediction of a non-face.

This seems to a straightforward implementation of what you are looking for, using tools you already know.