# Mapping Phonation Types by Clustering of Multiple Metrics
## 3 Results
### Description of the Classification Voice Maps
#### 3.2.1 Intra-Participant Distribution  
Now, in Table 2 we may examine the distribution of phonation types in greater detail. The change of the distribution is given with an increasing cluster number \(k\). The coordinates in the clustering space of the cluster centroids are given in polar plots in Appendix A. Even though the cross-age comparison does not control well for the age variable and the cross-age groups are divided into an adult (male and female) group and a child (before mutation) group, the current plots still show clearly the large differences and variability due to age (or, in some sense, the impact of voice mutation). We now consider how the distribution of detected phonation types over the voice field changes as the number \(k\) of clusters is varied. As the number of \(k\) increases, the phonation type map progressively splits into more regions. For the male participant, it goes from the opposition of 'loud' and'soft' for \(k=2\) to a third 'transition' zone in between for \(k=3\). Figure 6: Examples of using \(k=5\) clusters, on individual full voice range voice maps (VRPs) on /a:/ vowel (**a**) VRP of male participant M01; (**b**) VRP of female participant F02; (**c**) VRP of child (boy) participant B02. The color plotted in any given cell is that of the most frequently occurring phonation type in the cell, i.e., the dominant cluster. Each cell may contain cycles from other clusters as well, but such overlap is not visualized here. The \(x\)-axis is \(f_{\text{o}}\) in semitones (on the midi scale, \(48=110\) Hz), and the \(y\)-axis is SPL in dB(C) at 0.3 m. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Male M01** & **Female F06** & **Child B09** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Male participant M01, female participant F06, and child participant B09, with their voice maps by cluster numbers. Notice that the colors across \(k\) indicate only the relative position. The same color not necessarily denotes the same cluster. The last row represents the speech range profiles, marked as grids, overlapping on the density map, where the darker the region, the more VF cycles are contained. This enables a comparison of the whole voice range with the habitual speech range. The \(x\)-axis is \(f_{\rm o}\) in semitones (on the midi scale, 48 = 110 Hz), and the \(y\)-axis is SPL in dB(C) at 0.3 m.  
The breathy soft zone in the bottom is characterized by the maximal values of CSE and \(Q_{\rm ci}\) and very low CPPs. Together, the \(Q_{\Delta}\) and the Crest factor indicate great phonatory instability in this area, as the centroid polar plot shows in Table 11. The firm and loud regions at the top of the map are where the phonation is the most stable, described by the CPPs, SB, Crest factor, \(Q_{\rm ci}\), and \(Q_{\Delta}\) at their maximum, and a minimal CSE. Those regions are the loudest part of the voice map. Those metrics show a high-functioning phonation type. The transition zone starts with the lower left part of the voice map and ends in the upper right, with a slope of about +1.3 dB/semitone. The transition region is featured by its \(Q_{\rm ci}\) slightly below its uncontacted 50% state. However, the values of the other metrics stay in the range between the top and bottom regions. With the change from three to four clusters, an interesting split occurs on the left side of the loud region, in a cream color 2 next to the dark blue 4. It represents the low-pitch modal phonation type and forms the center of the habitual speech range (when the participant read the Rainbow passage thrice) that is denoted by the grids in the bottom row. Its centroid exhibits a very high \(Q_{\Delta}\) and Crest factor and a \(Q_{\rm ci}\) of about 60%, while the voice metrics CSE, CPPs, and SB keep the same level as in the transition zone. This split corresponds to the habitual speech range. When it comes to \(k=5\), the classifier picks up the breathiest regions as a new cluster, characterized by zero CPPs, high SB, CSE, and \(Q_{\rm ci}\), and a moderate Crest factor and \(Q_{\Delta}\).