Modeling uncertainty with interval-valued type-2 fuzzy sets: Application to anomalous sound event detection

Since a few years, audio signal processing has been focused on detecting audio events in general, and defining anomalous/outlier sounds in particular. The application of such an anomaly detection problem to audio surveillance systems is made possible thanks to the advances of anomaly detection techniques, in particular for highly unbalanced data. However, outdoor audio signals are characterized by a high degree of uncertainty, since there is no way to model each category of sound, whether normal or anomalous, in presence of background noise. Thus, this paper proposes a rare/anomalous sound event detection method for road traffic surveillance, which aims at detecting hazardous events, such as car accidents, in presence of traffic noise. To model uncertainty for anomaly detection, the suggested method combines deep reconstruction techniques, interval-valued type-2 fuzzy sets and interval comparison methods. First, the reconstruction error of the input audio segment is yielded by a deep variational autoencoder which is trained on normal data only. Based on this reconstruction error, a fuzzy membership function with pessimistic/lower and optimistic/upper components is calculated. Next, a probabilistic interval comparison method is used to compute the membership score, and thus to evaluate the interval-valued fuzzy sets. Finally, defuzzification is used to classify events as normal or anomalous. During this process, several types of linear or nonlinear membership functions are utilized to model uncertainty with respect to the input, i.e., the VAE reconstruction error, or to the output, i.e., the value of the primary membership. According to the results obtained, the proposed method outperforms the state-of-the-art one-class SVM for anomaly detection and the baseline VAE error thresholding method, when specific parameters are carefully set, such as the weights of the anomalous/normal subsets and the lower/upper bounds of the membership function's components. Furthermore, the proposed linear and nonlinear membership functions succeed to improve modeling uncertainty in audio signals by interval-valued type-2 fuzzy sets, with regard to: a) the input, i.e., the VAE reconstruction error, and b) the primary membership value, respectively.