# Multi-Scale Recurrence Quantification Measurements for Voice Disorder Detection
###### Abstract  
Due to the complexity and non-stationarity of the voice generation system, the nonlinearity of speech signals cannot be accurately quantified. Recently, the recurrence quantification analysis method has been used for voice disorder detection. In this paper, multiscale recurrence quantification measures (MRQMs) are proposed. The signals are reconstructed in the high-dimensional phase space at the equivalent rectangular bandwidth scale. Recurrence plots (RPs) combining the characteristics of human auditory perception are drawn with an appropriate recurrence threshold. Based on the above, the nonlinear dynamic recurrence features of the speech signal are quantized from the recurrence plot of each frequency channel. Furthermore, this paper explores the recurrence quantification thresholds that are most suitable for pathological voices. Our results show that the proposed MRQMs with support vector machine (SVM), random forest (RF), Bayesian network (BN) and Local Weighted Learning (LWL) achieve an average accuracy of 99.45%, outperforming traditional features and other complex measurements. In addition, MRQMs also have the potential for multi-classification of voice disorder, achieving an accuracy of 89.05%. This study demonstrates that MRQMs can characterize the recurrence characteristic of pathological voices and effectively detect voice disorders. voice disorder; recurrence quantification analysis; speech signal +
Footnote †: journal: Applied Sciences  
cepstral coefficients (MFCC) [9]. MFCC is the coefficient of the linear transformation of the logarithmic energy spectrum based on the nonlinear mel scale of frequency. In the past, perturbation features and cepstral features are widely used in pathological voice detection. Both of them are based on the linear acoustic theory. Speech production with planar sound propagation is assumed in the linear source/filter model. With the development of nonlinear dynamics, [PERSON] et al. have pointed out that there are extensive nonlinear phenomena in the process of speech production. [PERSON] et al. used aerodynamic theory to study voice signals and found that voice production was not a deterministic linear process, nor a random process, but a non-linear process [10]. The research of [PERSON] et al. showed that the turbulence formed in the vocal tract during the speech production process is the reason for the chaotic characteristics of speech signals [11]. The physical model of the throat [12] and the fluid dynamics model [13] also proved that a sound description by nonlinear fluid dynamics was more realistic. Different from perturbation features, spectral and cepstral features, complexity measures tend to represent the speech signal's aperiodic, non-stationary and nonlinear characteristics [14]. Voice diseases directly affect the vibration of the vocal folds, and non-linear dynamic analysis can effectively capture this change. Complexity measures [15; 16] have been used in previous works, including the largest Lyapunov exponent (LLE), Hurst exponent (HE), sample entropy (SE), correlation dimension (CD), Shannon entropy, etc. These popular features tend to describe the signal's dynamics, periodicity and regularity [17; 18]. However, the non-stationary nature of speech causes significant fluctuations in the nonlinear representation obtained by calculation [19]. Short-term analysis is used in traditional speech signal processing methods to avoid the nonlinear and non-stationary problems of speech signals. [PERSON] [20] et al. proposed recurrence plots for nonlinear data analysis, representing the global state correlation of signals on the full-time scale. The most essential feature of a particular dynamic system is the recurrence phenomenon. Recurrence phenomenon refers to the fact that some states of the system have similar characteristics at a specific time. Recurrence characteristics exist in both nonlinear and chaotic systems. It can study high-dimensional phase space trajectory periodicity through a two-dimensional representation.