# Generalized Replay Spoofing Countermeasure Based on Combining Local Subclassification Models
## 3 Related Works
### Combination of Unsupervised and Supervised Learning  
Recently, a spoofing countermeasure based on mining hidden partitions of genuine and spoofed utterances using fuzzy clustering was proposed in [72]. This countermeasure partitions each class (genuine/spoofing) into subgroups such that each subgroup shared the same characteristics and thus exhibited low variance. The classification of unknown utterances was than performed by assigning them to the closest subgroup.  
Figure 1 depicts the spoofing countermeasure reported in [72]. First, audio features are extracted from all utterances. Then, the instances of each category (genuine/spoofing) are clustered using the fuzzy clustering approach. As such, the representatives of the genuine sub-categories and those of the spoofing one are learned. In particular, fuzzy clustering techniques are employed. The experimental results showed that two genuine clusters and two spoofing clusters dramatically increased the performance. It yielded a testing EER of 1.07% on the ASVspoof 2017 replay benchmark dataset.  
An illustrative example of the countermeasure reported in [72] is depicted in Figure 2. In this example, six clusters {\(S_{1}\), \(S_{2}\), \(S_{3}\), \(S_{4}\), \(S_{5}\), \(S_{6}\)} are learned for the spoofing class, and four clusters {\(G_{1}\), \(G_{2}\), \(G_{3}\), \(G_{4}\)} are learned for the genuine class. Then, an unknown utterance is compared to the 10 cluster centers. Since the closest cluster is \(G_{1}\), one of the genuine clusters, the unknown utterance is classified as genuine.  
Figure 1: Architecture of the spoofing countermeasure based on mining hidden partitions of genuine and spoofed utterances [72].  
Tables 1 and 2 report the performance of the state-of-the-art approaches for 2017 and the 2019 ASVspoof replay benchmark datasets, respectively. The study in [72] achieved the best performance, with a testing error rate of 1.07% on the ASVspoof 2017 replay benchmark dataset. For the ASVspoof 2019 replay benchmark dataset, the countermeasure proposed in [50] obtained the best performance, with a testing error rate of 0.59%.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Reference** & **Input** & **Model** & **Training Error Rate (\%)** & **Testing Error Rate (\%)** \\ \hline
[4] & CQCCs & GMM & 10.35 & 24.77 \\ \hline
[46] & Signal Logspec via FFT & ResNet & 6.09 & 8.54 \\ \hline
[48] & CQCC and MFCC & GMM, ResNet & 2.58 & 13.30 \\ \hline
[49] & Fusion of HFCC and CQCC & DNN, SVM & 7.6 & 11.5 \\ \hline
[54] & MFCC, Fbank & LSTM and GRU RNN & 6.32 & 9.81 \\ \hline
[60] & CQT and FFT & LCNN, SVM, CNN + RNN & 3.95 & 6.73 \\ \hline
[66] & Spectrogram features & LC-GRNN + PLDA & 3.26 & 6.08 \\ \hline
[69] & CQCC & C-VAE & 18.1 & 28.1 \\ \hline
[69] & Spectrogram & C-VAE & 22.81 & 29.52 \\ \hline
[73] & CQCC & LCNN & 21.73 & 8.20 \\ \hline
[72] & MFCC, CQCC & SCAD, KNN & 0.13 & **1.07** \\ \hline \hline \end{tabular}
\end{table}
Table 1: State-of-the-art training and testing error rates when using the ASVspoof 2017 replay benchmark dataset.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Reference** & **Input** & **Model** & **Training Error Rate (\%)** & **Testing Error Rate (\%)** \\ \hline
[50] & CQCC, spectrogram &
\begin{tabular}{c} Fusion of SENet, Mean-Std ResNet, \\ and Dilated ResNet \\ \end{tabular} & 0.129 & **0.59** \\ \hline
[64] & Spectrogram features &
\begin{tabular}{c} Ensemble Weights for Bayesian \\ NN, LCNN \\ \end{tabular} & 0.78 & 0.88 \\ \hline
[66] & Spectrogram features & LC-GRNN + PLDA & 0.73 & 2.23 \\ \hline
[69] & CQCC & AC-VAE2 & 34.06 & 36.66 \\ \hline
[71] & spectrogram, CQT & VGG, SincNet, LCNN & 0.66 & 1.51 \\ \hline \hline \end{tabular}
\end{table}
Table 2: State-of-the-art training and testing error rates when using the ASVspoof 2019 replay benchmark dataset.  
Figure 2: Illustrative example of the spoofing countermeasure based on mining hidden partitions of genuine and spoofed utterances [72].