## 4 Experimental Performance Evaluation
### Experimental Setup  
The _LibriMix_ dataset is an open-source, single-channel, and multi-speaker speech dataset derived from _LibriSpeech_[36]. It is composed of mixtures involving two or three speakers, along with ambient noise samples from _WHAM!_[37]. This dataset is constructed by mixing single-speaker recordings from _LibriSpeech_ with partial overlap and integrated noise. The dataset is divided into two primary collections [13]: _Libri2 Mix_, which features two speakers; and _Libri3 Mix_, with three speakers. We carried out experiments on _Libri2 Mix_ only because two-speaker mixing is much more common in real environments. Each of these subsets include versions with and without _WHAM!_ noise, leading to 'clean' data free from noise and 'both' data containing noise. There are four versions of the dataset available, differentiated by two sampling rates (16 kHz and 8 kHz) and two modes (min and max). In min mode, the mixture concludes at the end of the shortest utterance, while in max mode, the shortest utterance is extended to match the length of the longest one. For our proposed model, which is designed for scenarios with two speakers, we utilize the _Libri2 Mix_ subset of _LibriMix_. We specifically chose the 'clean' dataset without noise at a 16 kHz sampling rate and in max mode to maximize the inclusion of speech data for training. Table 1 presents the statistics of the evaluation datasets. The training dataset consists of 64,700 utterances, amounting to approximately 270 h. The development dataset consists of 3000 utterances, totaling 11 h. Similarly, the test set includes 3000 utterances, also spanning 11 h, and is completely independent from the training and development sets. The dataset includes the following six different rates of speech overlap: 0%, 20%, 40%, 60%, 80%, and 100%. The maximum duration of each utterance is 15 s. The training data, development data, and test data consist of 1172, 40, and 40 independent speakers, respectively. In Section 4.3, the evaluation results from the three types of speaker embeddings, _i_-vector, _d_-vector, and _x_-vector, are shown. The intermediate vector (_i_-vector) extractor [12] was constructed using Gaussian mixture models (GMM) based on the universal background model (UBM). We extracted 400-dimensional speaker embeddings using the _Kaldi_ toolkit [38, 39]. The pretrained _i_-vector extractor was obtained from the _Kaldi_ official website [38]. The _x_-vector extractor [12], based on a deep neural network, was utilized to extract 512-dimensional speaker embedding vectors from the input utterances. We employed a pretrained _x_-vector extractor from the _Kaldi_ official website. Both of these models were trained on the augmented VoxCeleb 1 and 2 datasets [40]. The input features for both extractors were 30-dimensional mel-frequency cepstral coefficients (MFCCs), with a frame length of 25 milliseconds and a shift size of 10 milliseconds. The _x_-vectors were only extracted from voice frames, which were selected by an energy-based voice activity detector. \(L\)2-normalized speaker embeddings were then used as an additional input to the speech recognition decoder. The _d_-vector extractor [11] was based on a recurrent neural network implemented in _PyTorch_[41]. We extracted 256-dimensional speaker embedding vectors. The input features for the extractor were 40-dimensional mel-scale log spectrograms, with \begin{table}
\begin{tabular}{c|c|c|c} \hline
**Dataset** & **No. Utterances** & **No. Speakers** & **Hours** \\ \hline Train & 64,700 & 1172 & 270 \\ Dev & 3000 & 40 & 11 \\ Test & 3000 & 40 & 11 \\ \hline \end{tabular}
\end{table} 
Table 1: Statistics of the evaluation datasets. The number of utterances, number of speakers, and total duration of recordings in hours are provided for each set. The Train set was used for training the models, the Dev set was for hyperparameter tuning, and the Test set was for the final evaluation. There were no overlaps in the samples or the speakers within the dataset.