# Mapping Phonation Types by Clustering of Multiple Metrics
## 4 Discussion  
As we can see above, the unsupervised learning method gives interpretable results that are relatively consistent with our prior knowledge of phonation. Thus, it is acceptable to stay with the current K-means++ method because of its computational rapidity and efficiency. Our present choice of metrics was in part determined by the current availability of metrics in the bespoke software that we are using as an acquisition front-end for the clustering. There are of course several other candidates for metrics, especially if concurrent automatic inverse filtering proves to be possible. Of particular interest would be metrics that represent the power in the rest of the spectrum relative to that of the fundamental partial, such as the 'harmonic richness factor' (HRF) [28] for the inverse filtered glottal flow signal; \(L_{\text{rest/HI}}\)[29] for the radiated sound or the maximum flow declination rate (Mfdr). This measurement paradigm strongly depends on the assumption that there should exist distinct regions in the \(f_{\text{o}}\)/SPL voice map. We expect to see connected regions representing phonation types instead of a speckled field of scattered dots. This assumption, to some extent, serves as a validation criterion. Spatial coherence is what we expect the voice maps to show, since our experience tells us that different kinds of phonation tend to be used in different parts of the voice range. A further perceptual assessment performed by voice professionals and clinicians will be required to establish the classified phonation modes either physiologically or perceptually. This perceptual assessment would be purpose-oriented and empirical. Different investigators may have different criteria for categorization into phonation types. For example, a trained singer could require a more specialized set of phonation types than a singing amateur. A phonetician would call for more information on the vibratory status; thus, more information on the vocal folds is needed. For pathological voices, the complexity might increase further; the optimum number of clusters could be dependent on the type of voice disorder and the treatment involved. In this case, the ground truth must also be task-oriented and requires professional or non-professional knowledge to confirm the validity of the classification. To assist in such work, FonaDyn includes a built-in audio player, which allows users to interactively listen to or annotate what a region indicated in the voice map sounded like. Figure 8: A classification that uses (**a**) all six metrics combined, (**b**) acoustic metrics only, and (**c**) EGG metrics only. Here, the acoustic metrics are the crest factor, CPPs, and SB, and the EGG metrics are the \(Q_{\text{cl}}\), \(Q_{\text{$\Delta$}}\), and CSE. 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.  
Many readers will be familiar with MDVP in Figure 9 (multidimensional voice program). The MDVP displays several objective voice quality parameters in a polar 'radar' plot, including Base Frequency (\(f_{\text{o}}\)), Jitter, Shimmer, NHR (Noise to Harmonic Ratio), VTI (Voice Turbulence Index), and ATRI (Amplitude Tremor Intensity Index). MDVP is well established in clinical practice and may provide an objective yet non-invasive and comfortable alternative to assess voice quality--and to some extent, diagnose voice-related abnormalities. However, a limitation lies in that the MDVP is designed for use with individual sustained vowels, while most metrics are greatly affected by the \(f_{\text{o}}\) and SPL. With clustering, we can combine the advantage of applying multiple metrics with the conceptual and graphical convenience of a flat 2D voice map. Such a representation collates the systematic changes across the voice range, thus providing a more complete basis for classification. This could be helpful for the clinical diagnosis and valuation of vocal status, for example, before and after medical intervention.