# A Simple Unsupervised Knowledge-Free Domain Adaptation for Speaker Recognition
## 1 Introduction  
Speaker verification involves determining whether a given speech corresponds to a claimed speaker. In recent years, deep embedding-based speaker verification systems have achieved remarkable performance [1; 2; 3]. A typical verification process with such a system entails a deep embedding model that converts variable-length speech segments into fixed-dimensional dense vectors known as'speaker embeddings' or'speaker vectors', followed by a simple back-end scoring using cosine distance to assess the similarity of the vectors from the enrollment and test segments. The x-vector model [3] is among the most popular deep embedding models, and with the advancement of more comprehensive architectures, improved pooling methods, and training strategies, the x-vector model has demonstrated state-of-the-art performance in complex acoustic environments [4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15]. However, due to the complexity and variability of acoustic environments, and the limited data coverage during training, well-developed models often experience significant performance degradation when deployed in real-world domains that differ from the training domain, which is known as the domain mismatch issue [16; 17; 18]. To adapt a pre-trainedmodel to an unknown working condition, existing practices can be broadly categorized into two types of approaches: (1) **Front-end network adaptation**[19; 20; 21], which involves fine-tuning the speaker embedding network to align the embedding vectors with the target environment. (2) **Back-end scoring model adaptation**[22; 23; 24], which modifies the parameters of the scoring model while keeping the front-end network unchanged. Recent adaptation approaches mostly fall into the front-end category, partly due to the diminishing use of complex back-end models like probabilistic linear discriminant analysis (PLDA) [25]. Moreover, most research efforts have focused on unsupervised adaptation [26; 27; 28], addressing the challenge of speaker labeling for target-domain data collected from a deployed system, owing to labeling cost and privacy concerns. A drawback of existing methods is that they require knowledge of the system and/or the source data used to train the model. For example, front-end adaptation methods require the model to be accessible, allowing modification of its parameters. Similarly, PLDA adaptation methods require access to the between-speaker and within-speaker covariances of the original PLDA model [22]. Additionally, most distribution alignment approaches even mandate the replay of the source data [29; 30; 31]. Requiring knowledge of the system is often impractical in many situations, not to mention the challenges associated with accessing the source data. In this paper, we introduce a knowledge-free adaptation approach. This concept was inspired by an intriguing observation that speaker embeddings of unknown domains are still separable. As depicted in Figure 1, one can find that while the performance in equal error rate (EER) significantly decreases when the data is from an unknown domain, the discriminability of the embedding vectors remains relatively stable. This suggests that the primary issue of domain mismatch may not be the reduction in discriminability, but rather a systematic distortion of the distribution of the embedding vectors, including shifting, rotation, and scaling. If this hypothesis holds, it may be feasible to compensate for this distortion through a simple linear transform in the speaker embedding space. This leads to the development of our clustering-based unsupervised linear adaptation approach, which involves four steps: (1) Utilizing a pre-trained model from the source domain to extract speaker embedding vectors from unlabeled data in the target domain. (2) Generating pseudo labels for these vectors using a clustering algorithm. (3) Training a full-rank linear discriminant analysis (LDA) model [32] based on the pseudo-labels.