Unifying Cosine and PLDA Back-ends for Speaker Verification

Abstract

State-of-art speaker verification (SV) systems use a backend model to score the similarity of speaker embeddings extracted from a neural network model. The commonly used back-end models are the cosine scoring and the probabilistic linear discriminant analysis (PLDA) scoring. With the recently developed neural embeddings, the theoretically more appealing PLDA approach is found to have no advantage against or even be inferior the simple cosine scoring in terms of SV system performance. This paper presents an investigation on the relation between the two scoring approaches, aiming to explain the above counter-intuitive observation. It is shown that the cosine scoring is essentially a special case of PLDA scoring. In other words, by properly setting the parameters of PLDA, the two back-ends become equivalent. As a consequence, the cosine scoring not only inherits the basic assumptions for the PLDA but also introduces additional assumptions on the properties of input embeddings. Experiments show that the dimensional independence assumption required by the cosine scoring contributes most to the performance gap between the two methods under the domain-matched condition. When there is severe domain mismatch and the dimensional independence assumption does not hold, the PLDA would perform better than the cosine for domain adaptation.

Probabilistic Back-ends for Online Speaker Recognition and Clustering

“…PLDA with spherical covariances. Despite being a gold standard for previously popular i-vectors [17], one could recently observe a gradual shift towards replacing PLDA with a simpler parameter-less cosine scoring back-end [18]. As discussed in [14], the high intra-speaker compactness of the large-margin embedding makes the conventional full-rank PLDA model superfluous.…”

“…Relationship with cosine scoring. As was shown in [18], for length-normalized and centered embeddings, the verification likelihood ratio of the spherical PLDA can be written as a scaled and shifted cosine similarity measure. Since an affine transformation of scores is order-preserving, the two scoring rules are equivalent.…”