Image classification using Binary Cross Entropy but with only training examples for one of the classes e.g. class 1 VS anything else I am training a 'specialist network' to reconstruct images of an object using a Variational Autoencoder (VAE). The training set (~15000 images) is of a single object in multiple poses.
I also want this network to classify the object identity as being either the object it was trained on (class 1) VS anything else (class 0).
Is this possible using Binary Cross Entropy (BCE) loss and ONLY images of class 1? Or will it need negative examples (class 0)? If it does need negative examples, will these need to be exhaustive to ensure accuracy of classifying class 0? e.g. previously unseen images could yield class 1 if not included as class 0 in training.
Is there another method to achieve this other than BCE?

Because you only have data about 1 class, standard classification approaches are not applicable. Ideally, you could just collect data for the other classes, and then employ a standard approach, but that's not always feasible.
The term of art for this task is "one-class classification." Here's a review article from a few years back -- there have been a number of different options proposed.
Khan, S., & Madden, M. (2014). One-class classification: Taxonomy of study and review of techniques. The Knowledge Engineering Review, 29(3), 345-374. doi:10.1017/S026988891300043X

One-class classification (OCC) algorithms aim to build classification models when the negative class is either absent, poorly sampled or not well defined. This unique situation constrains the learning of efficient classifiers by defining class boundary just with the knowledge of positive class. The OCC problem has been considered and applied under many research themes, such as outlier/novelty detection and concept learning. In this paper, we present a unified view of the general problem of OCC by presenting a taxonomy of study for OCC problems, which is based on the availability of training data, algorithms used and the application domains applied. We further delve into each of the categories of the proposed taxonomy and present a comprehensive literature review of the OCC algorithms, techniques and methodologies with a focus on their significance, limitations and applications. We conclude our paper by discussing some open research problems in the field of OCC and present our vision for future research.

