  In speaker recognition, where speech segments are mapped to embeddings on the
unit hypersphere, two scoring backends are commonly used, namely cosine scoring
or PLDA. Both have advantages and disadvantages, depending on the context.
Cosine scoring follows naturally from the spherical geometry, but for PLDA the
blessing is mixed -- length normalization Gaussianizes the between-speaker
distribution, but violates the assumption of a speaker-independent
within-speaker distribution. We propose PSDA, an analogue to PLDA that uses Von
Mises-Fisher distributions on the hypersphere for both within and between-class
distributions. We show how the self-conjugacy of this distribution gives
closed-form likelihood-ratio scores, making it a drop-in replacement for PLDA
at scoring time. All kinds of trials can be scored, including single-enroll and
multi-enroll verification, as well as more complex likelihood-ratios that could
be used in clustering and diarization. Learning is done via an EM-algorithm
with closed-form updates. We explain the model and present some first
experiments.
