  Increasingly large datasets are rapidly driving up the computational costs of
machine learning. Prototype generation methods aim to create a small set of
synthetic observations that accurately represent a training dataset but greatly
reduce the computational cost of learning from it. Assigning soft labels to
prototypes can allow increasingly small sets of prototypes to accurately
represent the original training dataset. Although foundational work on `less
than one'-shot learning has proven the theoretical plausibility of learning
with fewer than one observation per class, developing practical algorithms for
generating such prototypes remains an unexplored territory. We propose a novel,
modular method for generating soft-label prototypical lines that still
maintains representational accuracy even when there are fewer prototypes than
the number of classes in the data. In addition, we propose the Hierarchical
Soft-Label Prototype k-Nearest Neighbor classification algorithm based on these
prototypical lines. We show that our method maintains high classification
accuracy while greatly reducing the number of prototypes required to represent
a dataset, even when working with severely imbalanced and difficult data. Our
code is available at https://github.com/ilia10000/SLkNN.
