# Comparison of Multivariate Analysis Methods as Applied to English Speech
## 4 Discussion and Conclusions  
Here we performed a comparative study between different factor analysis methods applied to English speech. Our first aim was to determine whether the use of normal factor analysis and a modified \"origin-shifted\" factor analysis caused differences in the extracted spectral factors when applied to English speech. The difference between these two methods was manifested in two processing aspects: (1) whether cepstral filtering was applied or not, (2) whether the origin shift was used or not. The present results showed that without cepstral filtering, the factor loadings of one factor were more pronounced (Figure 1), but neither cepstral filtering nor the origin shift had a large impact on the factor scores (Figures 2-5), whose distributions were similar. The merit of the origin-shifted analysis is the following. Utilizing normal factor analysis, it can be difficult to find any features around silent parts in speech. When the speech is resynthesized, noise is very likely generated also at the silent parts, resulting in a continuous noise sounding in the background. The biggest advantage of the origin shift is that it makes all silent parts in speech signals plotted onto the silent point in the factor space, and that the silent parts remain silent when the speech is resynthesized. If the quality of the resynthesized speech is better, it can very likely be related more closely to the real auditory signal, which makes it more useful for listening experiments. Given that the results of the normal factor analysis and the origin-shifted factor analysis were similar, the origin-shifted factor analysis is highly recommendable for future research on speech resynthesis and subsequent listening experiments. The second aim of our study was to determine the acoustic correlates of English phonemes by the four factor analyses. New insight was obtained with regard to obstruents. In an English syllable, an isolated obstruent always has a position as a syllable-onset or a syllable-end. If two or more obstruents are next to one another, one of them begins or ends the syllable. Analyzing obstruents acoustically as in the present study helped to understand this phonological phenomenon. Our analyses showed a factor with a frequency range around 1100 Hz. According to [PERSON] et al. (2017) [8], this factor was only related to vowels and sonorant consonants [8]; it seems to be closely related to syllable nuclei, most of which are vowels but a few are sonorant consonants. We provided evidence that obstruents were not only associated with the factor related to a frequency range above 3300 Hz (the \"high factor\"), as suggested by [PERSON] et al. [8], but also with the bimodal factor with frequencies around 300 Hz  
Figure 7: The L-shaped distributions of obstruents divided into fricatives/affricates (**a**) and plosives (**b**) in the two-dimensional space of the “low & mid-high factor” and the “high factor”. Factor scores of the three extracted spectral factors were obtained by origin-shifted factor analysis with cepstral filtering (cf. Figure 2) and the English speech samples were from three native speakers. and 2300 Hz (the \"low & mid-high factor\"). One likely cause for this is the difference in the initial analysis processing of the speech signal, but further investigation is required. Our present findings thus suggest that these two extracted factors of the acoustic natures of obstruents reflect strong cues as to the beginning or the end of a syllable. It is important to note that the distributions of subsets of obstruents (voiced and voiceless, Figure 6; fricatives/affricates and plosives, Figure 7) indeed occupied high positions on the \"low & mid-high factor\" and the \"high factor\", but not on the \"mid-low factor\". The obstruents were often far from the origin, the silent point in the origin-shifted factor analysis, but they never went into the positive direction of the \"mid-low factor\".