Probabilistic Spherical Discriminant Analysis: An Alternative to PLDA for length-normalized embeddings

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 mixedlength 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 multienroll
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.