# Comparison of Multivariate Analysis Methods as Applied to English Speech
###### Abstract  
A newly developed factor analysis, origin-shifted factor analysis, was compared with a normal factor analysis to analyze the spectral changes of English speech. Our first aim was to investigate whether these analyses would cause differences in the factor loadings and the extracted spectral-factor scores. The methods mainly differed in whether to use cepstral filtering and an origin shift. The results showed that three spectral factors were obtained in four main frequency bands, but neither the cepstral filtering nor the origin shift distorted the essential characteristics of the factors. This confirms that the origin-shifted factor analysis is more recommendable for future speech analyses, since it would reduce the generation of noise in resynthesized speech. Our second aim was to further identify acoustic correlates of English phonemes. Our data show for the first time that the distribution of obstruents in English speech constitutes an L-shape related to two spectral factors on the three-dimensional configuration. One factor had center loadings around 4100 Hz, while the other was bimodal with peaks around 300 Hz and 2300 Hz. This new finding validates the use of multivariate analyses to connect English phonology and speech acoustics. speech perception; English phoneme; factor analysis; spectral change; sonority +
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express 70% of the phonological features of 15 Dutch vowels [4]. Moreover, the first and the second principal component of these vowels were found to be distinctly related to the formants of the vowels [5]. In a later study with principal component analysis, it was found that 3-5 components might convey enough clues to represent continuous speech [6]. In one of the most recent comparative studies using factor analysis with eight different languages/dialects, [PERSON] and [PERSON] (2017) showed that three spectral factors of 20-critical-band-filtered speech universally appeared in all speech samples they used [7]. Interestingly, [PERSON] et al. (2017) further found that one of the three common spectral factors extracted from English speech, which appeared in a frequency range around 1100 Hz, was highly related to sonority or aperture, terms used in phonology [8]. Sonority has been a hot topic for more than a century in speech research. It has played an important role in understanding syllable formation; many linguists believe that the structure of a syllable is driven by the principle of sonority [9]. Sonority is a concept used to classify phonemes, in the following order from the highest to the lowest on the sonority scale: vowels, glides, liquids, nasals, fricatives/affricates, and plosives [10]. The highest sonority is attributed to the phoneme that constitutes the closest clue to the core in English syllables [11]. [PERSON] et al. (2017) divided all English phonemes observed in a speech database into three major categories from high to low sonority, i.e., vowels, sonorant consonants (glides, liquids, nasals), and obstruents (fricatives/affricates, plosives). Their factor analysis showed that a factor related to the frequency range around 1100 Hz was specifically associated with vowels and sonorant consonants. By contrast, another spectral factor with a frequency range above 3300 Hz was strongly related to obstruents. Based on this, it was suggested that the extraction of spectral factors can be a powerful tool to connect phonology and acoustic aspects of English speech [8]. It was problematic that the subspace selected in the factor analysis of [PERSON] et al. (2017) did not include the acoustically silent point of the original spectral space. In this case, if speech were to be resynthesized, it would contain positive power at any temporal point (in most cases). This would make it unsuitable for listening experiments, because the listeners would perceive a steady background noise in the resynthesized speech, which then would not contain any silent part. To avoid this problem, [PERSON] et al.