  Hypersphere classification is a classical and foundational method that can
provide easy-to-process explanations for the classification of real-valued and
binary data. However, obtaining an (ideally concise) explanation via
hypersphere classification is much more difficult when dealing with binary data
than real-valued data. In this paper, we perform the first complexity-theoretic
study of the hypersphere classification problem for binary data. We use the
fine-grained parameterized complexity paradigm to analyze the impact of
structural properties that may be present in the input data as well as
potential conciseness constraints. Our results include stronger lower bounds
and new fixed-parameter algorithms for hypersphere classification of binary
data, which can find an exact and concise explanation when one exists.
