  Novel Categories Discovery (NCD) aims to cluster novel data based on the
class semantics of known classes using the open-world partial class space
annotated dataset. As an alternative to the traditional pseudo-labeling-based
approaches, we leverage the connection between the data sampling and the
provided multinoulli (categorical) distribution of novel classes. We introduce
constraints on individual and collective statistics of predicted novel class
probabilities to implicitly achieve semantic-based clustering. More
specifically, we align the class neuron activation distributions under
Monte-Carlo sampling of novel classes in large batches by matching their
empirical first-order (mean) and second-order (covariance) statistics with the
multinoulli distribution of the labels while applying instance information
constraints and prediction consistency under label-preserving augmentations. We
then explore a directional statistics-based probability formation that learns
the mixture of Von Mises-Fisher distribution of class labels in a unit
hypersphere. We demonstrate the discriminative ability of our approach to
realize semantic clustering of novel samples in image, video, and time-series
modalities. We perform extensive ablation studies regarding data, networks, and
framework components to provide better insights. Our approach maintains 94%,
93%, 85%, and 93% (approx.) classification accuracy in labeled data while
achieving 90%, 84%, 72%, and 75% (approx.) clustering accuracy for novel
categories in Cifar10, UCF101, MPSC-ARL, and SHAR datasets that match
state-of-the-art approaches without any external clustering.
