Unifying Cosine and PLDA Back-ends for Speaker Verification

State-of-art speaker verification (SV) systems use a backend model to score the similarity of speaker embeddings extracted from a neural network. The commonly used back-ends 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 to the simple cosine scoring in terms of verification performance. This paper presents an investigation on the relation between the two back-ends, 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 speaker 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, the dimensional independence assumption does not hold and the PLDA would perform better than the cosine for domain adaptation.