# Generalized Replay Spoofing Countermeasure Based on Combining Local Subclassification Models
## 3 Related Works
### Discussion  
Neither conventional nor deep learning approaches have managed to overcome the challenge posed by the high variation of utterances. Indeed, these models suffer from generalization issues. In other words, while these countermeasures increase the prediction performance of trained utterances, they are unable to generalize utterances. Alternatively, the countermeasure proposed in [72] addressed the generalization problem by mining hidden partitions of the genuine and spoofed utterances separately. Nevertheless, while taking into account the intra-class variance by learning the underline structure of each class, this solution did not consider overlaps between genuine and spoofed categories. Indeed, this method did not learn the overall underlying structure of the data. Proposed Approach: Generalized Replay Spoofing Countermeasure Based on Combining Local Sub-Classification Models  
We propose an alternative approach that mines the hidden structure of the whole data. More specifically, the proposed countermeasure splits the classification problem into local subproblems. In other words, in order to avoid learning a complex classification model for the whole data, we intend to split the data into groups formed of congregated instances and build a simpler classification model from each group. These groups are heterogeneous and include spoofing and genuine utterances assigned to the same group due to their similarities. By classifying the utterances of each cluster into spoofing and genuine, a classification model is learned with respect to each cluster. This results in a set of local classification models. Using these models, the classification of an unknown instance is then achieved through an ensemble learning approach that combines the obtained local models. The proposed spoofing countermeasure is depicted in Figure 3. First, audio features are extracted from the recorded utterances. Then, the three clustering techniques of FCM [14], SCAD [15], and CA [13] are investigated to partition the data. FCM-based clustering approaches are explored because they learn the cluster centers while also learning a fuzzy partition of the data. Alternatively, SCAD has the advantage of learning relevant feature weights and their combinations while clustering the data, whereas CA learns the number of homogeneous partitions automatically. From each cluster containing both spoofed and genuine instances, a classification model is learned. We propose to employ GMM [6] and SVM [17] as classification techniques, since these models were effective in the prediction of spoofed utterances [4; 5; 37; 42; 48; 49; 60]. Lastly, an ensemble learning technique is adopted to classify unknown instances by combining the decisions of the learned models. More specifically, the pairwise distances between the unknown utterance and the cluster representatives are computed. The classification model corresponding to the closest sub-group is then used for classifying this utterance. To better illustrate the proposed spoofing countermeasure based on local classification subproblems, an example is presented in Figure 4. In this example, audio instances are clustered into six groups: {\(R_{1}\), \(R_{2}\), \(R_{3}\), \(R_{4}\), \(R_{5}\), \(R_{6}\)}. Although the training set was labeled into spoofing and genuine instances, these labels were not used for the clustering task. In fact, the whole data were considered without consideration of the ground truth. Therefore, each obtained cluster included both spoofing and genuine instances. Then, during the training phase, a classification model was learned from each cluster. This resulted in a set of six classification models, which were used to classify the unknown utterance through ensemble learning techniques. For example, since the unknown utterance is closest to cluster \(R_{1}\), the model learned for \(R_{1}\) will be employed for its classification. Moreover,