# Addressing Text-Dependent Speaker Verification Using Singing Speech
## 4 Speaker Verification Systems  
This section describes the features and three types of speaker verification systems developed for this study: the GMM-based, DTW-based and the state-of-the-art deep neural network based systems. **Features**: As shown in Section 3, we extracted 20-dimensional MFCC, then applied PCA to reduce them to two dimensions for a better visualization. However, to preserve more detail information in the features, we did not use the reduced two-dimensional feature to train our speaker verification systems. All of the features used for GMM-based, DTW-based and deep neural network based ASV systems were 61-dimensional: the 20-dimensional MFCCs, their delta and delta-delta dynamic features [26] and the one-dimensional NCCF feature. All of these features were extracted using a 25 ms hamming window with a 10 ms frame shift. An energy-based voice activity detection (VAD) was applied to remove the silence. **GMM-based system**: We used the conventional GMM to model the speaker identity for each enrollment speaker. Assuming a \(d\)-dimensional input feature for each speech segment, the GMM with \(M\) mixtures is:  
\[p(x|\lambda)=\sum_{i=1}^{M}w_{i}g(x|\mu_{i},\Sigma_{i}) \tag{1}\]  
where \(\lambda=\{w_{i},\mu_{i},\Sigma_{i}\}\) is the GMM model, and \(g(x|\mu_{i},\Sigma_{i})\) represents a \(d\)-variate Gaussian probability density function, with mean vector \(\mu_{i}\), covariance matrix \(\Sigma_{i}\) and mixture weights \(w_{i}\) with \(\Sigma_{i=1}^{M}w_{i}=1\). During the speaker enrollment, one GMM model was built for each speaker using her/his enrollment speech segment. In the experiments, we took the GMM-based system as our baseline for performance comparison. The GMM mixture number was set to 32 and only diagonal covariance was used. In fact, we tried many different mixtures in our experiments, from 8 to 1024, and the 32 mixtures GMM obtained the best and most stable results. Given a set of acoustic features of each target speaker, the parameters of the target speaker GMM model was estimated using the maximum likelihood (ML) criterion with the popular expectation-maximization algorithm. More details of the GMM model training can be found in [1]. Figure 3: MFCC PCA feature distribution of reading **(left)** and singing (right) speech between two females with the same text. During the testing, given the \(d\)-dimensional feature vectors \(X=(x_{1},x_{2},...,x_{T})\) of test utterance with \(T\) frames, we computed the log-likelihood score on each target speaker model as:  
\[\Lambda(X)=\frac{1}{T}logp(X|\lambda)=\frac{1}{T}\sum_{t=1}^{T}log\sum_{i=1}^{M }w_{i}g(x_{t}|\mu_{i},\Sigma_{i}) \tag{2}\]  
These log-likelihood scores were then used to compare with a threshold to give the final speaker verification decision. **DTW-based system**: DTW is a dynamic programming technique to compute the distance between two sequences. It has been taken as a sequence-matching algorithm and it has been widely used to tackle the text-dependent speaker verification [1; 27]. It attempts to match the enrollment and test templates of feature vectors. In [28], it has been shown that a DTW-based ASV system can outperform model-based systems (relevance MAP and i-vector) in content-mismatch condition. In this study, the DTW algorithm was investigated for short-duration ASV systems. **X-vector based system**: With the rapid development of deep neural network technology in speaker recognition, many types of DNN embeddings have been proposed, such as the DNN-Ivector [29], the D-vector [5], J-vector [30], C-vector [31], S-vector [32], etc. All of these vectors were derived from DNN models to map a variable-length speech utterance to a fixed-dimensional space for speaker modeling. Given these types of vectors, a simple cosine distance measure or a probabilistic linear discriminant analysis (PLDA) [33] was then normally applied to these vectors as the final decision function for speaker verification. In this work, the state-of-the-art deep neural network based ASV system was the X-vector based system.