# Mapping Phonation Types by Clustering of Multiple Metrics
### Basis for Clustering  
To explain our rationale for clustering, we first visualize how one of the metrics varies with SPL only. In the example of Figure 1, the ubiquitous upward trend with increasing \(f_{\mathrm{o}}\) happens to be close to linear (although this is not always the case). To simplify the visualization, we now factor out this dependency, so as to consider only the variation with SPL, or rather, with the new \({}^{\prime}f_{\mathrm{o}}\)-detrended' SPL.Figure 2 shows this operation for the \(Q_{\Delta}\) metric (the normalized peak dEGG). It can be seen that in soft phonation (<65 dB adjusted SPL), the \(Q_{\Delta}\) metric is close to its minimum value of 1 (green), and as vocal fold collision sets in, it increases abruptly. If we were to map other metrics, they too are aligned intrinsically with the \(f_{\mathrm{o}}\) and SPL, but each metric varies differently in different regions of the voice map. We now create a graph similar to the black curve in Figure 2 but of all the six metrics that are objects of the present study (Figure 3). Here, the six metrics have been brought to a suitable ratio scale or log scale and scaled to 0%... 100% of their maximum expected range of variation in anticipation of statistical clustering. The metrics \(Q_{\mathrm{ci}}\) and \(\log_{10}\) (\(Q_{\Delta}\)) are already in the range 0... 1 and thus need no pre-scaling. For the following example, each metric has also been smoothed, with a 5 dB running average on the SPL axis. In Figure 3, five subranges can be qualitatively discerned on the axis of adjusted SPL, following a rationale that we will now discuss in detail. Consider first range A (50... 60 dB), of very soft and breathy phonation. Here, the EGG cycle-rate sample entropy (CSE) is high, meaning that the EGG wave shape is unstable. The quotient of contact by integration  
Figure 3: Variation of six metrics over the SPL range shown in Figure 2. The broken lines refer to acoustic metrics and the solid lines to EGG metrics. The adjusted SPL axis can be visually divided into five subranges based on the metric values. Range A: soft phonation without vocal fold contact; B: transition zone where vocal fold contact sets in; C: ‘loose’ phonation but not entirely stable; D: ‘firm’ phonation with high stability; E: ‘hard’ phonation, approaching saturation in most metrics. Figure 2: **(a)** A map of an exemplary metric \(Q_{\Delta}\) (the per-cycle-normalized peak derivative of the EGG signal), typically skewed with increasing \(f_{\rm o}\). The black line shows the average of \(Q_{\Delta}\) taken horizontally over all semitones. Its abscissa is the vertical SPL axis; its ordinate is on the horizontal color bar. **(b)** The same map with the dependency on \(f_{\rm o}\) was removed by adjusting the SPLs so as to make the dashed trend line horizontal. The increase in \(Q_{\Delta}\) is now more sharply focused, on the scale of adjusted SPL. (\(Q_{\rm ci}\)) is 0.5 (50%) because there is no vocal fold contact; therefore, the EGG signal is of very low amplitude and the average EGG wave shape is sinusoidal, and thus the area under the normalized wave shape is 0.5. The spectrum balance (SB) is relatively high but descending, as the low-frequency band energy rises above some noise floor (which could be due to aspiration noise, low-level system noise, or both). The cepstral peak prominence smoothed (CPPs) is low, due to irregular vibration, noise, or both, but rises as the periodicity of the acoustic waveform gradually increases. The crest factor is low, indicating a lack of transients in the acoustic waveform. The normalized peak EGG derivative (\(Q_{\Delta}\)) is at its minimum because there is no vocal fold contact. Range B (60... 70 dB) is a transition zone where vocal fold contact is setting in. This is most evident from the sharp rise in \(Q_{\Delta}\) and a fairly steep drop in CSE. \(Q_{\rm ci}\) now drops from its uncontacted 50% state into a range with just a little contact in each cycle, about 30%.