  A weakly supervised learning based clustering framework is proposed in this
paper. As the core of this framework, we introduce a novel multiple instance
learning task based on a bag level label called unique class count ($ucc$),
which is the number of unique classes among all instances inside the bag. In
this task, no annotations on individual instances inside the bag are needed
during training of the models. We mathematically prove that with a perfect
$ucc$ classifier, perfect clustering of individual instances inside the bags is
possible even when no annotations on individual instances are given during
training. We have constructed a neural network based $ucc$ classifier and
experimentally shown that the clustering performance of our framework with our
weakly supervised $ucc$ classifier is comparable to that of fully supervised
learning models where labels for all instances are known. Furthermore, we have
tested the applicability of our framework to a real world task of semantic
segmentation of breast cancer metastases in histological lymph node sections
and shown that the performance of our weakly supervised framework is comparable
to the performance of a fully supervised Unet model.
