An investigation of locus equations as a source of relational invariance for stop place categorization

Abstract

Locus equations were investigated as a potential metric capable of illustrating relational invariance for place of articulation in voiced initial stop consonants independently of vowel context. Locus equations are straight line regression fits to data points formed by plotting onsets of F2 transitions along the y axis and their corresponding midvowel nuclei along the x axis. Twenty subjects, 10 male and 10 female, produced/b/v/t/,/d/v/t/, and/g/v/t/tokens for ten vowel contexts. Each CVC token was repeated in a carrier phrase five times yielding 50 tokens per stop place category. Formant measures were obtained using the MacSpeech Lab II speech analysis system. Extremely linear regression functions were found characterized by distinct slopes and y intercepts as a function of place of articulation. A discriminant analysis using F2onse t and vowel frequencies as predictors showed 82%, 78%, and 67% classification rates for labial, alveolar, and velar place. Using derived slope and y-intercept values as predictors led to 100% classification into stop place categories. A neurobiologically oriented perspective on the invariance issue is developed and a brain-based recognition algorithm for stop place integrating burst and F2 trajectory cues is offered. PACS numbers: 43.71.Es, 43.71.Pc, 43.71.An INTRODUCTIONThe nature of the linguistic entity known as the "phonetic segment" and its higher-order abstraction, the "phonemic category," has long resisted an explicit specification in terms ofinstantiation in the speech signal, and ultimately, its form as a mental representation in the brain. There is even controversy as to whether linguistic units are abstract constructs (Repp, 1981; Hammarberg, 1976), or acoustic-based physical constructs possessing neurobiological reality (Sussman, 1988(Sussman, , 1989. The theoretical difficulty in accounting for the phoneme is due to its lack of transparency in the signal. The differences between a "planned segment" and an "uttered segment," as described by MacNeilage and Ladefoged (1976), succinctly capture this dilemma. The former is envisioned as discrete, static, and context-free, while the latter is characterized as overlapped, dynamic, and contextsensitive. The pervasive coarticulatory nature of speech has contributed to this theoretical puzzle known as the "noninvariance problem"--i.e., perceptual constancy despite physical variation in the signal. The "litmus test" for invariance is place of articulation in stop consonant + vowel utterances as they typify the coarticulated nature of speech.The overall purpose of this research was to present a refocused conceptualization of a traditional, but elusive, candidate for acoustic invariance for place of articulation-the second formant transition as its onset and trajectory vary with the following vowel. The departure point was to seek invariant acoustic patterns related to place of articulation, not for each individual token, but rather for an entire phonemic category. A. Searching for invariance: formant transitionsPerhaps the earliest w...

On the relevance of locus equations for production and perception of stop consonants

“…Our findings thus generally concur with those ofthe synthetic speech experiments by Fruchter and Sussman (1997) and Eek and Meister (1995), who found that the regions in F2 space corresponding to high-proportion selections of each consonant only partially overlapped with their respective locus equation lines. Thus, in response to the research questions posed by Sussman et al (1991), we found that proximity to locus equation lines bears only a gross relationship to perceptual consonant classification.…”

“…However, given that the F2 transition is proposed as a primary cue, and one for which evolution shaped the auditory perceptual system, it might be expected to have more predictive strength than was found here. A different sort of account could be devised in which F2, F3, and burst information are not treated as independent cues (Dorman, Studdert-Kennedy, & Raphael, 1977), but rather are considered together; for example, a model could be based on prototypes defined in a three-dimensional space ofF2 ons' F2yowel' and F3 0ns (Lindblom, 1990;Sussman, 1991). We believe, however, that the OOC hypothesis cannot apply to such a model.…”

“…Sussman proposed a partial solution to the invariance problem that involves the derivation of locus equations based on second-formant transitions (e.g., Sussman, 1989;Sussman et al, 1991)\ To derive locus equations, secondformant (F2) values at the midpoints ofa variety of vowels (F2vowel) are plotted on the horizontal axis of a twodimensional space, andF2 at the onset ofvoicing (F2 ) I f a zi ons following the re ease 0 a grven consonant is plotted on the vertical axis (see also Klatt, 1987;Lindblom, 1963; Copyright 1998 Psychonomic Society, Inc. Nearey & Shammass, 1987). Regression line fits to these plots reveal a linear relationship between F2yowel and F2 ons ' The regression lines for different consonants, or the locus equations that represent them, may be characterized by their slopes and intercepts.…”

“…Acoustic measurements were made by the first author. They were taken onF2, following the procedure of Sussman et al (1991), at vowel onset and vowel midpoint. The onset measure (F2 ons ) was taken at the first discernible pitch pulse after the release ofthe consonant.…”

“…Another is to assume that perception is of invariant articulatory gestures, which are specified in the acoustic signal, and that either there is invariant information in the signal that has not yet been discovered, or the specification of the gesture in a signal differs in different contexts, but specifies nonetheless (Fowler, 1994). A third approach is to look for invariance not in the acoustic signals of individual utterances, but rather as a higher order property found when appropriate context-sensitive acoustic signals are related to one another (Sussman, 1989;Sussman, McCaffrey, & Matthews, 1991). This approach will be our main focus.…”