Department of Phonetics and Linguistics



In this paper a general framework for research on phonetic perception is presented in which a pattern classifier plays a central role. The framework is intended as a comprehensive and formal representation of the widely adopted cue-based approach to phonetic perception. The framework consists of several interconnected information-processing modules and storage facilities. Explicit distinctions are made between various levels of information: acoustic, general auditory, specific auditory, and phonological.

First the functionality of the various modules is formally defined and discussed. Next, a number of long-standing issues related to variability with phonetic context are discussed from the perspective of the framework. In this discussion a number of fresh insights are gained into problems such as acoustic variability versus perceptual constancy, acoustic constancy versus perceptual variability, the segmentation issue and cue-trading relations. It is argued that viewing the phonetic categorisation problem as multidimensional pattern classification unifies these issues and may inspire a reformulation of some research questions.

1. Introduction
The work presented in this paper is based on the viewpoint that it is extremely useful to treat the issue of perception of consonants and vowels as a pattern-recognition problem. A pattern recognition-based framework is proposed which can serve as a starting point from which research questions can be formulated and human classification of speech sounds can be modelled and interpreted.

2. Background
Throughout the history of speech-perception research the issues of segmentation and variability have consistently been put forward as the most basic problems for theories of phonetic perception (e.g. Cooper et al., 1952; Liberman et al., 1967; Pisoni and Sawusch, 1975; Lindblom, 1986; Sawusch, 1986; Klatt, 1989; Nygaard and Pisoni, 1995). The segmentation issue can be summarised as follows. When listening to speech, one has the impression of receiving a series of discrete linguistic units (e.g. phonemes or syllables). The acoustic signal, however, cannot be segmented into discrete chunks corresponding to these linguistic units. Instead, the acoustic consequences of the articulatory realisation of a particular linguistic unit generally strongly overlap with those of the neighbouring units. The variability issue refers to the finding that there does not seem to exist a set of acoustic properties that uniquely identifies any given linguistic unit. Any such set will show considerable variability depending on factors such as phonetic context, speaker identity, speaking rate and transmission conditions.

As far as the factor of phonetic context is concerned (i.e. the influence of surrounding linguistic units on the acoustic realisation of a particular linguistic unit), the issues of segmentation and invariance are intimately linked. Both can be considered to be acoustical consequences of a phenomenon known as coarticulation. Coarticulation can be defined as the temporal overlap of articulatory movements associated with different linguistic units.

In the vast majority of theoretical as well as experimental studies addressing the issues of segmentation and variability in phonetic perception the concept of the cue or acoustic cue has played a central role. Although the precise interpretation of this concept is rather hazy in most of these studies, some definitions are available. Repp's definition seems to correspond with the generally accepted interpretation:

"A cue ... is a portion of the signal that can be isolated visually, that can be manipulated independently in a speech synthesizer constructed for that purpose, and that can be shown to have some perceptual effect" (Repp, 1982).

In the history of phonetics, large numbers of acoustic cues for various phonetic distinctions have been found and their perceptual effects documented. It is generally assumed that in the process of classifying a speech sound, the listener extracts a certain number of acoustic cues from the speech signal and bases the labelling of the

speech sound on these cues. In the framework proposed here, the cue concept will also play an important role. I will, however, propose a slightly altered definition of the acoustic cue which closely corresponds to the "feature" in pattern-recognition theory.

In this paper it will be argued that, although the notion of a cue is very useful and has indeed generated a large body of knowledge, a number of aspects of this approach need to be better formalised and integrated into a whole. In the light of a more formal framework it will emerge that basic issues, as well as the interpretations of certain experimental findings, need to be re-evaluated.

2.1 Purpose
In this paper I will propose a pattern recognition-based framework for research on the classification behaviour of listeners in a phonetic perception experiment. Within the framework I will try to formalise the most important aspects of the cue-based account of phonetic perception that underlies the major part of phonetic research. This framework can serve as a starting point from which research questions can be formulated and human classification of speech sounds can be modelled and interpreted.

The framework is formulated within the general information-processing approach and consists of various interconnected modules that process and exchange information. Although the functions of the various modules as well as relevant terminology will be defined as precisely as possible, the framework will remain qualitative and as such cannot deal with quantitative data without additional assumptions and parameter estimations. This is the reason why I use the term framework rather than model, reserving the latter term for instantiations of the framework that can actually simulate or predict quantitative data.

The framework is restricted in two basic ways, dealing only with:

Other problems of variability such as speaker identity, speaking rate and transmission conditions will not be considered. Clearly, these restrictions considerably reduce the complexity of the problem at hand. It will be argued, however, that the framework can be extended in a consistent way to incorporate at least some of the additional sources of variability mentioned. Furthermore, the framework is kept as simple as possible, while at the same time being able to qualitatively account for several experimental findings reported in the literature. In particular, it will be argued that the removal of one or more of the information processing modules or connections between these modules will cause the framework to be inadequate in accounting for certain experimentally observed phenomena.

It is emphasised that it is not the purpose of this paper to formulate a novel speech perception theory that competes with existing ones such as the motor theory (Liberman et al., 1967; Liberman and Mattingly, 1985), the theory of acoustic invariance (Blumstein and Stevens, 1981; Stevens and Blumstein, 1981) or the direct-realist account of speech perception (Fowler, 1986). Instead, these theories can all be formulated as particular instances of the proposed framework, although strictly speaking the scope of the framework is narrower than that of these theories.

The structure of the paper is as follows. In the next section the general setup of the framework will be introduced. Next, in section 3, the functionality of the individual modules in the framework will be described. Section 4 is devoted exclusively to a discussion of principles and aspects of the pattern-classification module. In section 5, I will use the proposed framework to shed fresh light on a number of experimental findings and theoretical issues.

3. General structure of the framework
The proposed framework is intended as a comprehensive and formal representation of the widely adopted cue-based approach to phonetic perception. As indicated earlier, the framework specifically deals with the classification behaviour of listeners in a phonetic perception experiment, i.e., an experiment in which subjects are instructed to classify speech sounds. As is the case for the subjects, the input and output for the framework are speech waveforms and response labels, respectively. Although, after an experiment is completed, the waveforms and response labels are generally all you have as experimenter, several distinct intermediate processing steps are commonly assumed to take place in the subject (e.g. Massaro, 1987; Ashby, 1992). Each of these processing steps transforms information from one level of description to another. I assume that the following four levels of description must be distinguished, both in the subject as well as in the framework.

The terminology used above will be defined more precisely later. Repp (1981) has already convincingly argued that these distinctions are essential, but we will return to this issue later.

Figure 1 displays a graphical representation of the proposed framework. Note that the four levels of description are explicitly distinguished within the framework, as indicated on the left-hand side of Figure 1.

Figure 1. General processing framework. Ovals represent information, rectangles represent processing modules. Circles with "M" inside indicate memory. Arrows indicate information flow. "P", "SA", "GA", and "A" indicate the phonological, specific auditory, general auditory, and acoustic levels of description, respectively.

4. Description of modules
In this section the modules found in Figure 1 will be described, introducing a number of definitions along the way.

4.1 General auditory processing
The input to this module is the acoustic signal (pressure wave), the output is roughly equivalent to the representation found in the auditory nerve. It is assumed that the general auditory processor can be reasonably well modelled by converting the speech signal into some form of time-frequency representation like the spectrogram. It is noted, however, that such a model has the potentially significant drawback that it does not emphasise transients the way the auditory system does.

Definition: General auditory context
The general auditory context is defined as the information in the auditory time-frequency representation(s) which is available at a given point in time.

In accordance with Crowder and Morton (1969) we assume that the most recent incoming general auditory information is stored in some relatively unprocessed form in a "precategorical acoustic storage" (PAS), where it is available for further processing. Old information is assumed to be lost or to become progressively "blurred" or noisy with the passage of time. Hence, a time window can be associated with the general auditory context. The length of this window is assumed to be in the order of several hundreds of milliseconds. This corresponds to the "short auditory store", which is one of the two precategorical storages proposed by Cowan (1984).

The general auditory level is general in the sense that only peripheral auditory processing takes place indiscriminately with regard to the incoming signal. That is, it is assumed to be independent of higher-level processes. In later modules of the framework, several specialised (non-general) processing will take place, which is dependent on higher-level information.

4.2 Detection of landmarks
Definition: Landmark
A landmark is defined as a time instant in the speech signal which functions as a reference point for one or several cue-extraction mechanisms.

The input to this module is the general auditory context. The output is twofold: (1) the landmarks, i.e. the time instants, (2) a broad phonetic ("manner") classification of the landmark.

A form of landmark detection has been implicitly assumed in many cue-based phonetic studies. For example, if the listener is supposed to use the frequency of F2 at voicing onset in place-of-articulation perception, it is implicitly assumed that he or she knows where in the signal the F2 should be sampled. Hence, the instant of voicing onset has to be established first.

The concept of acoustic landmarks has been explicitly put forward by Stevens and co-workers (e.g. Stevens and Blumstein, 1981; Stevens, 1985; Stevens, 1995) in the context of the "lexical access from features" (LAFF) theory. In Stevens's approach an acoustic landmark is generated by a significant articulatory event such as establishing or releasing a (locally) maximum constriction in the vocal tract, reaching a (locally) maximum opening of the vocal tract, and onset or offset of voicing. Acoustically, landmarks are generally characterised by a maximum or minimum of spectral change. A computational model of an "abrupt-nonabrupt" landmark detector has recently been implemented by Liu (1995). In line with this work it is assumed here that the landmark detector module comprises several individual detectors which essentially continuously monitor the auditory representation(s) and trigger on a threshold-like basis. There may, for instance, be a detector for stop closure and release based on detection of a large enough spectral discontinuity or a voice-onset detector based on some form of periodicity detection.

4.3 Cue extraction
There are four types of input to this module: landmarks, the general auditory context, the specific auditory context (previously determined cue values) and phonological context (previously determined phonological labels). The landmarks specify where acoustic cues are to be measured, the phonological and specific auditory context specify which cues are to be measured. Cues are always measured on the general auditory context. Obviously, the output of the cue extractor are cue values.

Definition: Cue extraction
Cue extraction is defined as a mapping of the general auditory context onto a scalar variable.

The cue-extraction operation is in essence simply a measurement operation. Examples of cue-extraction operations are the (perceptual) measurement of the length of a stop release burst and of the frequency of F2 at voicing onset.

Definition: Acoustic cue
An acoustic cue is defined as the output of a cue-extraction operation.

Typical examples of acoustic cues are the length of the stop release burst and the frequency of F2 at voicing onset. Note that the release burst and the F2 themselves do not qualify as acoustic cues, as they are multidimensional acoustic structures. Also a "F2 frequency of 1800Hz at voicing onset" is not a cue, but a value of the cue "F2 frequency at voicing onset".

Let us compare my definition of acoustic cue to the one by Repp (1982). I have dropped the conditions that a cue:

Thus, the only meaningful element in Repp's definition that remains is that an acoustic cue is a "portion of the signal", and I have tried to sharpen up the definition of a "portion". The resulting definition of acoustic cue is similar to that of a "(pattern) feature" in the automatic speech recognition literature in the sense of being simply a measurement result. A major difference between the cue and the pattern feature is, however, that, while in statistically-based automatic speech recognition the same set of feature measurements is repeated at constant intervals throughout the speech signal, the details of the cue measurement are dependent on the type and position of the earlier detected landmark.

Definition: Specific auditory context
The specific auditory context is defined as the set of earlier extracted values of acoustic cues which is available at a given point in time.

As for the general auditory context, the most recent incoming specific auditory information is put in storage, where it is available for further processing. Old cue values are assumed to be lost or to become progressively blurred or noisy with the passage of time. The storage of cue values corresponds to Cowan's "long auditory store" (the second component of PAS), with a time constant of at least several seconds.

4.4. Classification
The specific auditory context and the phonological context constitute the input to the classifier. The output of the classifier is phonological labels.

Definition: Classification
Classification is defined as the mapping of a vector of cue values onto a phonological label.

Essential to the concept of classification is that the number of possible output elements is smaller than the number of possible input elements. Theoretically, the input vector to the classifier at hand consists of a vector of scalar cue values, each of which can assume any real value. Hence, the number of input elements is infinite, while the output can only assume one value out of a finite set of discrete values (phonological labels).

Definition: Phonological label
A phonological label is defined as an element of a finite set of phonologically meaningful elements.

Each phonological label is associated with at least one landmark.

Examples of phonological labels are distinctive features such as [+voice], articulatory movements such as "labial closure", segments such as [b], or syllables such as [ba].

Definition: Phonological context
Phonological context is defined as the set of earlier established phonological labels which is available at a given point in time.

Definition: Phonological cue
A phonological cue is defined as an element of the phonological context.

For example, if the value of the feature continuant has been labelled as [-continuant], this value may have an influence on the subsequent measurement of place of articulation of the same consonant. Or, the labelling of a preceding vowel as [i] may influence the classification of the following consonant.

As for the auditory contexts, the most recently generated phonological labels are put in storage. Old labels are assumed to be lost or to become progressively blurred or noisy with the passage of time. A time window is associated with the availability of phonological cues, which is assumed to be at least as long as the window associated with the specific auditory context.

The classifier will be discussed in more detail in section 4.

4.5. A note on information storage
In the framework it is assumed that three types of short-term memory are used. One memory is associated with each of the 3 levels of information that are assumed to be explicitly used by the listener: the general auditory level, the specific auditory level, and the linguistic level. The memories are necessary because before one of the modules can process information from level A to level B, a certain body of information has to be accumulated at level A. For instance, before a classification can be made, the values of all relevant cues have to be available.

The specific auditory storage would not be necessary if it is assumed that for each classification all cues are measured simultaneously on the general auditory storage. I have chosen, however, to associate the general auditory context with Cowan's short auditory store and the specific auditory context with his long auditory store (Cowan, 1984). Cowan estimated the maximum duration of the short store at 200 to 300ms. This implies that, if the specific auditory memory were to be dropped, only cues within a 200 to 300ms window would be able to contribute to a phonetic classification. Repp and other Haskins researchers have repeatedly demonstrated that listeners integrate acoustic information pertaining to a particular phonetic distinction over temporal windows with a length of up to 400ms (e.g. Repp et al., 1978; Repp, 1980; Mann and Repp, 1981; Repp, 1988). This is somewhat longer than Cowan's short auditory storage, but of the same order of magnitude.

Besides the respective time constants associated with the long and short auditory stores, there is an additional motivation to use both these stores in the present framework. Cowan claimed that the short store holds a relatively unanalysed auditory representation of the incoming signal, while the long store holds partially analysed information. Obviously these properties corresponds closely to the notions of the general and specific auditory information in the framework.

The memory associated with the linguistic context is not an auditory memory because it contains abstract linguistic units such as distinctive features or segments. I assume that this memory is therefore situated at some cognitive level of information processing.

4.6. Example
Let us clarify the time course of the framework by means of a discussion of a hypothetical example of the classification process in a phonetic experiment. Suppose it is the subject's task to classify the second consonant in a CVCV nonsense utterance, for example [bada]. For the moment, a number of additional assumptions will be made, the most important of which are (1) classification is made in terms of distinctive features; and (2) relevant acoustic cues are the frequencies of the first three formants and their first time derivatives plus some additional burst cues. Note that, although these choices reflect some of my preferences in the actual filling-out of the framework, they are by no means fundamental.

Figure 2. Example of the general auditory context (bottom), specific auditory context (middle) and phonological context (top) in the proposed framework at an arbitrary instant of a hypothetical classification of the utterance bada. The vertical lines in the general auditory context (represented by the spectrogram) indicated by the symbols LM3, LM4 and LM5 represent acoustic landmarks. The symbols in the bottom of the spectrogram indicate cues that are measured by the cue extractor, i.e. the frequencies of the first three formants at landmark 3 and 4, and the slopes of the first 3 formants at landmark 4.

Figure 2 displays the status of the listener at a particular instant in time, as it is represented in the framework. The "present" time instant is defined as t = 0 at the plosive release of [d]. The three rectangles in Figure 2 represent, from top to bottom, the present phonological context, the present specific auditory context, and the present general auditory context, respectively. The general auditory context contains a time-frequency representation of the most recent 300ms of the stimulus. Both the specific and the phonological contexts, having much longer time constants, contain information on the entire stimulus so far. All information in the latter two contexts is associated with landmarks. As indicated in the top two boxes, five landmarks have been detected in the stimulus so far: a stop release landmark at t = -361ms, a voice onset landmark at t = -349ms, a vowel nucleus landmark at t = -244ms, a stop closure landmark at t = -138ms, and a stop release landmark at t = -18ms. Note that the specific auditory context contains psychophysical information in terms of e.g. times and frequencies. The phonological context, on the other hand, contains none of these, and the time dimension is represented simply as an ordering of the landmarks and their associated distinctive features.

Although the "target" consonant has not yet been classified, a number of classifications have already been made. First of all, landmark 1 was classified as a stop release landmark, based on the sudden energy increase across frequencies detected by the landmark detector. Next, landmark 2 was classified as a voicing onset landmark based on the onset of periodicity.

After these classifications some acoustic cues were measured. The overall level of the burst (log-energy) was established to be 30 dB below the overall level of the first few voicing periods, and the voice-onset time (VOT), defined as the interval between landmark 1 and 2, was found to be 12ms. In addition the frequencies of F1, F2 and F3 were measured at the first voicing pulse, as well as their change in frequency over the first few voicing pulses. Now a new classification was made. The initial stop consonant was classified as voiced based on the acoustic cue values of the relative burst level, VOT, the F1 frequency at voicing onset and its initial change, and the phonological cue that the consonant is a stop.

At t = -244ms a new landmark (L3) was placed (this landmark is visible in the present general auditory context). Landmark 3 was classified as a vowel nucleus based on the detection of a local minimum in spectral change. The frequencies of the first 3 formants were measured at this landmark. Based on these 3 acoustic cues, the previous acoustic cues measured at landmarks 1 and 2, and the phonological cue that the consonant is a voiced stop, the consonant was classified as labial, which fully specifies the initial consonant as [b].

Due to a sudden decrease of energy across frequencies, landmark 4 was placed at t = -138ms and classified as a stop closure. The frequencies of the first 3 formants, as well as their initial change, are measured just before the closure landmark. Based on the available acoustical cue values for landmark 2, 3 and 4, as well as the phonological cue of the initial consonant being labial, the vowel is classified as low, back and unrounded, or [a].

Most recently, a stop release landmark has been positioned at t = -18ms due to a sudden energy increase across frequencies. No acoustic cues have been measured here yet and the place and voicing features of the consonant associated with landmark 4 and 5 (and 6, the upcoming voice onset landmark) have yet to be classified before the actual response can be given. These classifications are postponed until more cues are available. If the hypothetical experiment would involve gating (e.g., Cotton and Grosjean, 1984) and the sound presented so far actually was the complete gated stimulus, the listener would have to base the classification of the consonant on the information currently available. Based on the cue values associated with landmark 3 and 4, an educated guess could be made on the consonant's place of articulation. The classification of the voicing feature would however be very difficult, as no information on VOT or F1 at voice onset are available.

5. Aspects of the classifier
This section is devoted to a discussion of the classification module. In the history of research on phonetic perception relatively little attention has been given to this topic. In my opinion, however, some basic knowledge of pattern-recognition theory greatly helps in the formulation of research questions as well as the interpretation of classification data generated in a phonetic perception experiment. In this section I will introduce and discuss a number of basic issues relevant to the classifier in the framework. I will concentrate on (1) the classification strategy, (2) the input representation, and (3) the output representation.

5.1. Classification strategies
Before a number of classification strategies are discussed, first some extra definitions are given.

Definition: Cue space
The cue space is defined as a vector space which is spanned by acoustic cues. The cue extractor effectively maps individual utterances onto points in the cue space.

In pattern-recognition literature the cue space is usually termed feature space. Figures representing cue spaces abound in the phonetic literature, see Liberman et al. (1957), Figure 2, Cooper et al. (1952), Figure 3, and Hoffman (1958), Figure 4, for some well-known early examples of 1-, 2-, and 3-dimensional cue spaces for stop consonants, respectively.

Definition: Response region
A response region is defined as the subspace of the cue space either which is assigned to one phonological label, or where the probability of selecting a particular phonological label is larger than the probability of selecting any one of the other labels.

Definition: Class boundaries
A class boundary is defined as the subspace of a cue space which separates two response regions. At a class boundary the labels associated with the two adjacent response regions are equally likely.

Definition: Convex response region
A response region is convex if a line segment connecting any pair of points with the same label lies completely within the response region associated with that class.

On a conceptual level one could say that a convex response region has a highly regular shape without any dents or protrusions. For examples of convex response regions in the phonetic literature see all "territorial maps" for the classification of the four fricative-vowel syllables in Nearey (1990) and (1992). For an example of non-convex response regions see Jongman and Miller (1991), Figure 2. Note that the response region for /t/ consists of two subregions - which in itself makes the /t/-region non-convex - each of which is also non-convex.

Definition: Classifier complexity
The classifier complexity is defined as the number of free parameters in the classifier that are to be estimated.

This definition only holds for truly automatic classifiers. Non-automatic classifiers are often used in phonetic research. For example, Blumstein and Stevens (1979) used carefully hand-prepared templates which were designed to optimally classify a training set of tokens, and to which during testing individual tokens were matched visually. The complexity of such non-automatic classifiers can be roughly assessed by estimating roughly how many parameters would need to be fitted if a truly automatic classifier were to simulate the non-automatic one.

Both in the field of automatic pattern recognition and the field of human classification behaviour, a number of different classification strategies have been put forward (for an overview, see Medin and Barsalou, 1987; Ashby, 1992). Roughly, they can be divided into three classes.

Prototype models:
Each response class is represented by one prototype, which is a point in the cue space. Probabilities for choosing each of the possible response labels are calculated on the basis of distances of the stimulus to each of the prototypes. The similarity-choice model (Shepard, 1958; Luce, 1963) and the fuzzy logical model of perception (Oden and Massaro, 1978) are well-known prototype models.

Exemplar models:
Each response class is represented by a number of exemplars, which may be conceptionalized as a cloud of labelled points in the cue space. Probabilities for choosing each of the possible response labels are calculated on the basis of average distances of the utterance to all exemplars of each class (Nosofsky, 1986).

Boundary models:
The cue space is divided up into response regions by a number of class boundaries. The position of a stimulus in the cue space is established through an evaluation of its position relative to all class boundaries. The stimulus receives the label of the response region it finds itself in. Detection theory (Macmillan and Creelman, 1991) and general recognition theory (Ashby and Perrin, 1988) use a boundary-based approach.

A few remarks are in order here. First of all, although the three classification strategies differ in their fundamental assumptions, their behaviour can be hard to distinguish purely on the basis of classification data. It has been shown, for example, that the similarity-choice model (which is a prototype model) is asymptotically equivalent to a boundary-model based on the single-layer perceptron (Smits and Ten Bosch, submitted). Other experimental tasks than straightforward classification may be needed to distinguish between the strategies. If it is assumed, for example, that a token is classified more rapidly with decreasing distance to the reference, the boundary-based approach would predict that subjects classify a stimulus near a class boundary most rapidly. In contrast, a prototype-based approach would predict that subjects classify a stimulus near a class prototype most rapidly. Hence, a categorisation response time experiment may discriminate between the two strategies (e.g. Ashby et al., 1994).

Secondly, it needs to be stressed that the finding that some stimuli are "better" or more prototypical instances of a category than others (e.g. Kuhl, 1991) does not imply that a prototype-based strategy is actually used in classification. The essential difference between the prototype-based and the boundary-based classification strategies is that the classification in based upon a comparison of the stimulus to the class prototypes or the class boundaries, respectively. Both strategies will however rate a stimulus far away from the class boundary as typical and one close to the class boundary as non-typical.

Which of the three general types of classification strategies most resembles human phonetic classification behaviour is unclear. Indeed, although each of these models have played a role in the history of research on phonetic perception, experiments explicitly addressing this issue are rare. Early phonetic research operated exclusively within the boundary approach (e.g. Liberman et al., 1957). Later, extensive work by Rosch on the use of prototypes in various kinds of human categorisation behaviour (see for example Rosch, 1973) inspired a prototype-based approach in the modelling of phonetic perception (e.g. Samuel, 1982; Kuhl, 1991). Recently, Pisoni and co-workers have argued against an account of phonetic perception in which incoming sounds are matched against idealised prototypes. Instead, an exemplar-based approach is advocated (e.g. Pisoni, 1992; Nygaard and Pisoni, 1995).

5.2. Input representation
The cues that span the cue space form the input representation of the classifier. Many different types of cues have been proposed over the years:

The assumption that a certain type of cues is used will have consequences for the resulting complexity of the classifier. If one assumes, for example, that formant frequencies are the relevant cues in place perception of stop consonants, and an experiment is set up in which formant-frequency continua are presented to listeners for classification, the resulting data may require a complex classification model. Conclusions in this vein were drawn on the basis of the early Haskins speech perception experiments, which inspired the formulation of the motor theory (Liberman et al., 1967). If, on the other hand, an input representation is chosen in terms of gross spectral shapes, the classification model may be much simpler, which was essentially advocated by Stevens and Blumstein (1981). Hence, the complexity of the phonetic classifier is intimately tied to its input representation.

5.3. Output representation
The output representation is determined by the set of labels used by the classifier. Note that the output representation can be different from the actual response set used in the phonetic experiment, which is usually segmental. For example, the subject may have to choose one of six consonants B, D, G, P, T, or K. Internally, however, the classifier may output distinctive-feature-sized labels. In such a case an additional mapping from the internal label to the response label has to take place. It is assumed here that this mapping is trivial.

The representation issue in speech perception is a long-standing one and it is by no means settled (e.g. theme issue on phonetic representation, J. Phonetics 18(3), 1990; Marslen-Wilson, 1989). Often used representations are articulatory gestures (e.g. Fowler, 1986), distinctive features (e.g. Stevens, 1995), and segments (e.g. Liberman et al., 1967), which all are valid candidates for the output representation in the present framework.

Obviously, as is the case for the input representation, assumptions on the nature of the output representation have far-reaching implications for the classifier. If the output representation is, for example, assumed to be in terms of binary features, the cue space for each individual feature classification is divided into 2 subspaces only, and it is reasonable to expect that the dimensionality of the cue space is relatively low. If, on the other hand, it is assumed that the classifier outputs segments, the number of response regions in the cue space is large and the dimensionality of the cue space is assumed to be proportionally large.

6. Discussion of some theoretical issues and experimental findings in the context of the framework
In this section a number of major theoretical issues as well as experimental findings will be discussed within the proposed framework. This discussion will hopefully show that the pattern-recognition-based framework indeed provides useful insight into a number of phonetic issues and findings. The issues and findings that will be discussed relate to:

6.1. The segmentation issue
Beside the variability versus invariance issue, one of the basic issues in speech perception is that, although, when listening to speech, one has the impression of receiving a string of discrete linguistic units (whatever their size), the acoustic signal cannot be cut up into discrete segments corresponding with these linguistic units. This issue is commonly known as the "segmentation issue". The segmentation issue and the variability and invariance issue are naturally related because both originate (at least partially) from coarticulation. How does the proposed framework deal with this issue?

As discussed earlier, the framework incorporates the "landmark detection" strategy proposed by Stevens and co-workers. A basic aspect of this approach is that the speech signal is not segmented at all. Instead of acoustic segments important instances, the acoustic landmarks, are identified (see Liu, 1995, for a more elaborate discussion). The landmarks are classified in a broad phonetic sense (e.g. manner features) and are subsequently used as reference points for cue measurements. Although each of the cues is associated with a single landmark (or for duration cues possibly two), in any subsequent classification cues associated with several different landmarks may be involved, as is the case in some of the examples discussed so far. Eventually, the classifications will result in a string of phonological labels as was illustrated in Figure 2. Thus we find that the specific auditory context for each classification that is made in the framework strongly overlaps with the specific auditory contexts of other classifications.

In conclusion, because the landmark-detection approach is adopted, the segmentation issue is hardly relevant in the context of the framework.

6.2. Variability and invariance
As discussed in the introductory section, among the most basic problems in research on phonetic perception is the variability and invariance issue. In this discussion I will restrict myself to variability and invariance related to phonetic context only. The variability and invariance issue has two components (e.g. Pisoni and Sawusch, 1975), namely acoustic variability versus perceptual constancy and acoustic constancy versus

perceptual variability. A well-known example concerns the role of the frequency of F2 at voicing onset (F20) in the perception of consonantal place of articulation. Numerous experimental studies has shown that F20 is a very important cue for consonantal place of articulation. However, the interpretation of this cue apparently strongly depends on the phonetic context. For example, a F20 of 1600Hz may cue a /b/ or /d/ depending on the following vowel (acoustic constancy versus perceptual variability). On the other hand, any F20 within the range of 900Hz to 1800Hz may cue a /b/, depending on the following vowel (acoustic variability versus perceptual constancy).

I will attempt to show here that this type of "problem" arises from an overly simplistic view of phonetic classification. First of all, the considerations presented above seem to be based on the assumption that a phonetic classification is based on the value of a single acoustic cue. Based on considerations of simplicity or parsimony this would undeniably be a desirable feature of a perception model. However, despite the large body of research devoted to finding the single acoustic cue that dominates the perception of a given phonetic contrast, there seems to be no fundamental reason whatsoever why the perceptual system would operate in such a fashion. Indeed, there seems to be convincing evidence that large numbers of acoustic cues play a significant role in the perception of any phonetic contrast (e.g. Lisker, 1978; Diehl and Kluender, 1987).

Furthermore, an implicit assumption that often seems to be made is that in order for two sounds to belong to the same phonetic class they need to be acoustically similar, or expressed in terms of cues, their representations in the cue space need to be close together. This is fundamentally untrue. Even in a very simple classifier, sounds that are mapped to points in the cue space that are far apart may receive the same label, while points that are close together may receive different labels.

It is useful to approach these issues from a pattern-recognition angle. Let us look at an example, based on a subset of the data of an acoustic and perceptual study of the voiced stops /b/ and /d/ in Dutch (Smits et al., submitted a, b). Figure 3 is a one-dimensional "scatterplot" of the values of F20 measured on 8 tokens of /bV/ and 8 tokens of /dV/, where V taken from /a, i, y, u/, spoken by a male Dutch talker.

Figure 3. One dimensional scatterplot representing measurements of F20 on 8 tokens of /b/ and 8 tokens of /d/ in CV context.

As can be seen in Figure 3, there is a large within-class variability, and the classes overlap to a great extent. If a boundary-based classification were to be made on the basis of this single cue, the class boundary would optimally be placed at approximately 1250Hz, as indicated by the tallest line segment in Figure 3. This would lead to a classification error rate of 25% (4 out of 16 misclassified).

Let us now measure another cue, the frequency of F2 at the vowel nucleus (F2n), in addition to F20. Figure 4 represents a two-dimensional cue space spanned by F2n and F20.

Figure 4. Two-dimensional scatterplot representing measurements of F20 and F2n on the same utterances as in Figure 3. The d symbols represent measurements for /d/ and the line with the short dashes represents the locus equation fitted through these points. The b symbols and the line with the long dashes represent the measurements and the locus equation for /b/. The solid line represents the class boundary.

The optimal classifier using the two cues has a rate of incorrect classification of 12.5% (2 out of 16), which is half the rate obtained for the single cue. The associated

class boundary is represented by the solid line in Figure 4. The two dashed lines in Figure 4 represent the locus equations associated with the two consonants (see also Sussman et al., 1991). Clearly, all points cluster closely around their associated locus-equation lines. Sussman hypothesised that the locus equations may function as perceptual class prototypes. Incoming stimuli would be mapped onto a point in the F20- F2n plane and the stimulus would be classified as the locus equation which is closest. This is equivalent to using the boundary depicted in Figure 4.

What can we learn from this simple example so far? First of all, theoretically speaking, the more stimulus measurements are used by the classifier, the higher the classifier's potential in terms of correct classification rate. In our example the 2-cue classifier clearly does a better job than the 1-cue one. Of course, in practice the classifier complexity rapidly increases with the dimensionality of the cue space, e.g. in terms of the number of parameters needed to defined a class separator. Therefore, a trade-off needs to be made in a classification model as well as in the perceptual system. It is stressed here, however, that from a pattern-recognition point of view, a large within-class variability on a single cue is only fundamentally problematic if the classifier is indeed restricted to using only this cue. Even when two classes strongly overlap on one acoustic dimension, using one or more additional cues may dramatically increase the correct classification rate, or even completely disambiguate the problem. This seems a rather trivial point to make, but it does steer phonetic problem formulations away from classical questions like "what is the best or most disambiguating cue" towards issues like "what is the cue space dimensionality" and "what set of cues leads to good or human-like classification".

Secondly, utterances that are acoustically very different on a number of important cues may receive the same label while utterances that are acoustically very similar may receive different labels. Consider for example three hypothetical utterances with (F2n , F20) pairs of (1kHz,1kHz), (2kHz,1.7kHz) and (2kHz,1.9kHz). The first two utterances, although being far apart in the cue space (Euclidean distance of approximately 1.2kHz), are both classified as /b/ by the classifier of Figure 4. The third utterance, on the other hand, though being close to the second one (Euclidean distance of 0.2kHz), is classified differently, namely as /d/.

Thirdly, from the viewpoint of the classifier, all cues are equal. In our example, F20 and F2n have exactly the same status. We, being phoneticians, know that F2n is almost completely determined by the vowel identity and we might be tempted to call it a "vowel cue" or a "context cue". However, from the classifier's perspective, a set of cues is measured and a classification is subsequently made. Thus, the status of F2n as an acoustic cue for stop place of articulation is exactly the same as that of F20.1

1Strictly speaking, the two cues are associated with different landmarks: F2n is associated with a vowel-nucleus landmark, while F20 is associated with a voice-onset landmark. Although the cues are different in this sense, the classifier treats them in a completely equivalent manner. Note that in the example the (phonological) vowel identity is not used in the classification.

Finally, the potential role of an acoustic cue in the perception of a phonetic distinction can only be established within the context of the total set of cues that is investigated. The value of a cue cannot be measured on the basis of its classification potential in isolation. For example, in the carefully pronounced CVs used for the example, F2n considered in isolation has no disambiguating value whatsoever. However, within the context of the two-cue set together with F20 , F2n does play an important role in the classification process.

Let us now use the example to further scrutinise the issues of acoustic variability versus perceptual constancy and acoustic constancy versus perceptual varibility. Figure 5 again depicts the F2n x F20 space with the /b/-/d/ class boundary. In addition four arrows are drawn in the Figure.

Figure 5. The two-dimensional cue-space of Figure 3 is shown again with the /b/-/d/ class boundary. In addition four arrows are drawn. Arrows 1 and 2 illustrate acoustic constancy versus perceptual variability, while arrows 3 and 4 illustrate acoustic variability versus perceptual constancy.

Arrow 1 shows that, although F20 is constant (1325Hz), the percept is shifted from /d/ to /b/ when the F2n is raised from 845Hz to 1400Hz. This is a classical case of perceptual variability versus acoustic constancy, where the perceived consonant changes although the "consonant property" F20 remains constant (e.g. Liberman et al., 1967; Lindblom, 1986; Nygaard and Pisoni, 1995). Arrow 2 shows that the percept is changed from /b/ to /d/ by shifting F20 from 1165Hz to 1490Hz, while keeping F2n constant. This case refers to classical experiments using F20 continua (e.g. Liberman et al., 1954), which have been used to emphasise the role of F20 (or the F2 transition) for the perception of consonantal place of articulation. I would like to argue that both are simply two sides of the same coin. (Here, the "coin" would the complete picture of the cue space plus perception model, where the model is represented by the class boundary). Both refer to a situation where one cue is held constant while another is changed, thus moving through the cue space parallel to one of the cue axes. Naturally, if the class boundary is not parallel to one of the axes, chances are that it will be crossed at some point and the percept will change. Referring back to a point made earlier, both cues have the same status within the classification process, so arrows 1 and 2 describe fundamentally equivalent situations. Moreover, formulated within a pattern-recognition context, the issue of acoustical constancy versus perceptual variability does not seem to be a particularly interesting one. It seems to arise only when one concentrates on a single cue, while the actual classification process is multidimensional.

Arrows 3 and 4 represent acoustical variability versus perceptual constancy. The arrows are placed on the locus equations of /b/ and /d/. While arrows 1 and 2 are parallel to a cue axis, arrows 3 and 4 are (more or less) parallel to the class boundary. This obviously results in perceptual constancy as the class boundary is not crossed. As argued earlier, if two stimuli have been given the same label, the points in the cue space associated with the two stimuli do not need to be close together, they only need to be in the same response region. Figure 5 clearly illustrates a situation in which both response regions are very large - indeed they are half-infinite. A word of caution is needed however. There is a bounded "natural region" in the cue space to which all stimuli will be mapped. Obviously, natural stimuli with an F20 of 15 kHz do not occur, and if synthesised, the perceptual system is unlikely to treat the resonance at 15 kHz as a second formant. Still, response regions may be acoustically quite extensive in practice.

6.3. Cue trading relations
As a definition of a cue trading relation I will use the one proposed by Repp (1982, p. 87):

Definition: Cue trading relation.
A trading relation between two cues occurs when "... a change in the setting of one cue (which, by itself, would have led to a change in the phonetic percept) can be offset by an opposed change in the setting of another cue so as to maintain the original phonetic percept."

Many examples of cue trading relations have been reported in the literature, (see Repp, 1982, for an overview). Perhaps the best known trading relation is the one between voice-onset time (VOT) and first formant onset frequency (e.g. Lisker, 1975). Lengthening VOT in a synthetic stop-vowel syllable which is ambiguous with respect to the voicing feature will increase the proportion of "voiceless" responses. However, this change can - to a certain extent - be repaired by creating an upward F1 transition by lowering F1 at voicing onset.

In this section I will argue that cue trading relations, such as the one described, naturally arise when a classification is multidimensional. Let us study an example. Ohde and Stevens (1983) have shown that a trading relation exists between F20 and the level Lb of the release burst in the perception of the labial-alveolar distinction in stop-vowel syllables. Both a high F20 and a high Lb cue an alveolar response, while the opposite holds for the labial response. The trading relation here refers to the finding that an increase in F20 can be offset by a decrease in Lb.

I have simulated this classification behaviour using a simple pattern classifier. On the same /b/-vowel and /d/-vowel utterances used for the earlier example I measured the level of the release burst Lb (for details on the measurement procedure see Smits et al., submitted b). Figure 6 is a scatterplot of the resulting values of Lb combined with the F20 values obtained earlier.

Figure 6. Scatterplot of measurements of Lb and F20 made on the same utterances used for Figures 4 and 5. The ellipses indicate the = 2 equi-probability lines of the two-dimensional (equal variance, zero covariance) Gaussian distributions fitted on the data. Again the x symbols and the short dashes refer to /d/ and the + symbols and the long dashes refer to /b/. The bell shapes on the top and right-hand side of the figure are the marginals of the two-dimensional distributions. The solid line indicates the /b/-/d/ class boundary.

Let us now analyse this situation using a well-known classification technique called linear discriminant analysis (LDA). Two-dimensional Gaussian probability-density functions (pdfs) can be calculated for the data of each class. As the actual number of data points is small, the assumption is used that the two classes have identical covariance matrices with covariances equal to zero. Equi-probability contours (corresponding with 2 standard deviations from the mean) of the resulting Gaussians are represented as dashed ellipses in Figure 6. Note that, as a result of the assumptions

of identical covariance matrices with zero covariance, the ellipses are simply shifted versions of each other, and their principle axes are parallel to the cue axes. The solid line represents the optimal class boundary in the Bayesian sense, meaning that the probability of misclassification is minimised. The marginal distributions of the two-dimensional Gaussians along with their respective optimal class boundaries are displayed at the top and right-hand side of the figure.

Figure 6 clearly shows that in the classifier thus defined, both a high F20 and a high Lb favour a /d/ response, as was found by Ohde and Stevens (1983). It is easy to demonstrate that this classifier will also produce a trading relation between F20 and Lb, like the listeners in Ohde and Stevens's experiments. Figure 7 again shows the F20 x Lb cue space with the /b/-/d/ boundary.

Figure 7. The F20 x Lb cue space of Figure 6, with the /b/-/d/ boundary (solid line). The arrows illustrate a cue trading relation.

The arrows in Figure 7 demonstrate the cue trading. Starting with a stimulus with a F20 of 1020 Hz and a Lb of 90.8 dB2, we increase F20 to 1800 Hz, thereby crossing the class boundary from /b/ to /d/. Next we move back into the /b/ region by lowering Lb to 84.8 dB. Thus, a trading relation is established, because the perceptual change induced by changing one cue is offset by a change in another. Note that in this example we have not moved outside the natural cue regions (indicated by the ellipses - see Figure 6).

2The level is calculated relative to an arbitrary but fixed amplitude.
More generally I make the claim that whenever more than one cue is involved in a classification trading relations will occur between all cues involved, except in very special circumstances. A cue will not take part in a trading relation only when the class boundary is parallel to the cue axis in question. In such a situation we are dealing with an "independent decisions classifier" (e.g. Ashby and Gott, 1988), or, in Nearey's terminology, a "primary cue model" (Nearey, 1990, 1991, 1992). This situation is only interesting when there are more than two classes involved, because when only two classes are involved and the class boundary is parallel to one of the cue axes, this axis is irrelevant and can be omitted altogether. When three or more classes are involved obviously two or more class boundaries are needed. Theoretically, this situation is equivalent to deciding for each cue separately on which side of the class boundary the stimulus is positioned and then combining the outcomes of these decisions into the final response (Ashby and Gott, 1988). Such a situation will occur if the decision process consists of a string of hierarchically ordered unidimensional processes.

Some evidence for such decision processes can be actually found in the phonetic literature. Blumstein and Stevens more or less assumed such a process in their classification of place of articulation based on gross spectral templates (Blumstein and Stevens, 1979). The decisions can be summarised as follows:

if (mid-frequency peak) then velar


if (rising spectrum) then alveolar

else labial

which is a hierarchical process of two separate decisions3.

3A problem here is that in Blumstein and Steven's specific semi-automatic implementation mid-frequency peak and rising spectrum do not qualify as cues in my definition. I will come back to this point later

This type of decision making in place perception for stops has later been more or less replicated using more formal classification models by Forrest et al. (1988) and Smits and Ten Bosch (submitted). Nearey (1990, 1991) has explicitly tested the goodness of fit of several models on the data of Whalen (1989) for the perception of fricative-vowel syllables. He demonstrated that the "primary cue model", in which it is assumed that all boundaries are parallel to the cue axes, provides a significantly worse fit than a model in which this assumption is dropped. An explicit test of a general hierarchical model in which the vowel identity influences the consonant classification was not included, however.

The phenomenon of cue trading relations has been put forward as evidence for the "speech is special" doctrine supported by a number of motor theorists (e.g. Repp, 1982). The considerations presented above do not support this view. Instead, it is argued that cue trading is a natural expression of the multidimensionality of a classification process. This holds for classification processes is any modality, so it is definitely not special to speech perception. If anything, it is the multidimensionality aspect that is special, not the speech aspect. Interestingly, at some point Repp (1983) did put forward an argument in a similar vein, although he did not explicitly specify how the cue trading mechanism comes about. Recently, Parker et al. (1986) and Sawusch and Gagnon (1995) have shown that it is indeed possible to train subjects to classify abstract auditory stimuli using two stimulus (cue) dimensions. The subjects produced cue-trading behaviour in their classification, which confirms the multi-dimensionality account of cue trading. Furthermore Sawusch and Gagnon (1995) showed that the subjects were able to generalise their categorisation to a new set of stimuli which were acoustically dissimilar to the training set. Essentially, these experiments show that listeners are able to set up a perceptual pattern recognition mechanism based on a number of training exemplars, and, when the classifier is sufficiently well-defined, subsequently classify new auditory patterns. It seems reasonable to assume that such perceptual mechanisms provide the basis for phonetic perception. Earlier failures to elicit cue-trading behaviour in listeners using abstract auditory stimuli (e.g. Best et al., 1981) may be caused the fact that the listeners had not been effectively trained in actually using more than one auditory cue in the categorisation task.

Massaro has been advocating a pattern-recognition approach to phonetic perception for a long time (e.g. Massaro and Oden, 1980; Massaro, 1987). As Massaro's fuzzy logical model of perception (FLMP) is in essence a multidimensional (fuzzy) pattern classifier, it reproduces cue trading relations. Unfortunately, the work of Massaro and colleagues is sometimes given the interpretation that the cue trading/integration phenomena essentially arise from the use of fuzzy logic and prototypes in the classification model (e.g. Pisoni and Luce, 1987). Neither of these properties are essential to cue trading, however. Only the multidimensionality of the classification process is a necessary condition, as was shown above.

6.4. The role of phonetic context in perception
As described earlier, three types of context are distinguished within the general framework presented in this paper: general auditory context, specific auditory context, and phonological context. From such a starting point the observation that an acoustic cue is "interpreted in a context-dependent manner" (for example, the effect of F20 depends on the vowel context) is ambiguous. At least two very different situations can apply. First of all, several cues may be used in the classification, some of which are "directly" related to the target (e.g. the consonant) while others are "directly" related to the context (e.g. the vowel). In a previous section we encountered such a situation, regarding the classification of stops as /b/ or /d/ using F20 and F2n. I was argued that a formal distinction between the cues is not valid. The total set of cues used in the classification constitute the specific auditory context, and the status of the various cues is identical, i.e. all cues are equally "direct".

In the second situation, a phonological label that was obtained earlier may influence the current classification. For example, it may be the case that the vowel is classified prior to the consonant and the details of the classifier (for example the exact boundary locations) depend on the earlier established vowel identity. In this situation the relevant context is phonological.

In many phonetic experiments reported in the literature the distinction between the role of auditory and phonological context is not made, and it is hard to establish to which of the two the observed "context effects" can be attributed (e.g. Cooper et al., 1952; Schatz, 1954; Summerfield and Haggard, 1974; Mann and Repp, 1980, 1981; Mann, 1980; Fowler, 1984; Whalen, 1989). A number of investigations have however explicitly focused on the distinction between the two types of context and have provided evidence that in a number of phonetic classification tasks phonological context is indeed used by listeners. Carden et al. (1981) showed that, assuming that phonetic perception produces distinctive feature labels, place perception is dependent on perceived manner. It was demonstrated by Massaro and Cohen (1983) that the perception of C2 in C1C2V and C0C1C2V syllables is influenced by the identity of C1 and C0C1, respectively. Finally, Ohala and Feder (1994) showed that perception of V1 in V1CV2 utterances depends on the identity of C. The evidence provided by these studies has led me to include the concept of phonological context in the framework, as well as the information flow from the phonological level to the classifier.

Repp (1982) made an explicit distinction between trading relations and context effects. His definition of a trading relation has been cited earlier. A context effect occurs, according to Repp, "...when the perception of a phonetic distinction is affected by a preceding or following context that is not part of the set of direct cues for the distinction ..." (Repp, 1982, p. 87). As argued earlier, the notions of "context" as well as "direct cues" are insufficiently precise from my viewpoint. However, Repp's examples following the definition strongly suggest that his distinction between trading relations and context effects is equivalent to my distinction between auditory and phonological context. For example, Repp speaks of a context effect when "... the perceived vowel quality modifies the perception or interpretation of the fricative cues ..." in the perception of a fricative-vowel syllable (Repp, 1982, p. 88). Assuming that Repp's perceived vowel quality is equivalent to our phonological vowel label the vowel quality is a "phonological cue" in my terminology.

At this point it does make sense to distinguish between a direct acoustic cue and an indirect acoustic cue for the perception of a phonetic distinction.

Definition: Direct acoustic cue
A direct acoustic cue to the perception of a phonetic distinction is the output of a cue extraction operation which is explicitly used in the classification procedure associated with the phonetic distinction.

Definition: Indirect acoustic cue
An indirect acoustic cue to the perception of a phonetic distinction is the output of a cue extraction operation which is not explicitly used in the classification procedure associated with the phonetic distinction at hand, but which instead is explicitly used in the classification procedure associated with another phonetic distinction, whose output is used as a phonological cue in the classification procedure associated with the phonetic distinction at hand.

An example concerning the perception of CV syllables will clarify the distinction. If F2n is, together with F20 , used in the classification of the consonant, as in one of the earlier examples, it is a direct cue to the perception of the consonant. If, on the other hand, F2n is not used in the classification of the consonant, but is used instead in the classification of the vowel, and the vowel label influences the classification of the consonant, F2n is an indirect cue to the perception of the consonant.

In practice the distinction between the two situations will be very hard to make experimentally. For example, if one would vary the value of an indirect cue to the perception of the consonant in synthetic CV syllables, this would affect the perception of the consonant, just like a direct cue would. Within our framework, however, the process responsible for this influence is different in the two situations.

Let us briefly address the issue how the use of phonological cues may be implemented within the proposed framework. First of all, the set of cues used in the classification process can be adjusted. For example, let us assume that the classifier's output labels are distinctive features, and already classified manner features influence the classification of place features. Then, depending on the value of the feature nasal, the cues used in the place classification may or may not include the cue Lb (burst level). Secondly, the details of the classification procedure may be adjusted. Depending on the basic classification strategy that is hypothesised, these adjustments may be implemented as, for example, shifts and rotations of linear class boundaries, or relocations of class prototypes.

6.5. The theory of acoustic invariance
The issue of acoustic invariance has received much attention throughout the history of research on phonetic perception. It is useful to consider this issue from the viewpoint of the framework. Blumstein and Stevens, the principle proponents of the theory of acoustic invariance, proposed that invariant acoustic properties corresponding to distinctive features are present in the signal, and that these properties are used by listeners in their categorisation of speech sounds. The invariant properties are sampled in a relatively short segment of the speech signal (e.g. 25 ms) and are stable across all major sources of variability such as phonetic context, speaker identity, language, etc. (e.g. Blumstein and Stevens, 1981; Stevens and Blumstein, 1981). Here we will again restrict ourselves to variability associated with phonetic context. In order to translate these claims in terms of our model, additional specifications are necessary on two points:

Concerning the first point, we are faced with the problem here that in Blumstein and Stevens's initial acoustic classification studies, the classification procedures were semi-automatic. In a well-known experiment (Blumstein and Stevens, 1979), stop-vowel utterances were classified according to stop place of articulation by visually matching their onset spectra to spectral templates. The spectral templates were devised such that they put several constraints on the LPC-smoothed onset spectrum of

a token. As the LPC-smoothed spectra were made using a 14-pole model, each token is essentially described by 14 numbers. Therefore, effectively a classification takes place in a 14-dimensional cue space. It is clear that Blumstein and Stevens's property was not intended to be a scalar quantity, and as such it does not qualify as a cue within our definition.

With respect to the term "invariant" the situation is more difficult. In terms of the classification theory I have discussed so far, "invariant" would at least suggest that all tokens with the same labels are mapped to the same response region. However, in the particular implementation of Blumstein and Stevens (1979) this is strictly speaking not the case. This somewhat paradoxical aspect of Blumstein and Stevens's approach has already been observed and criticised by Suomi (1985). The velar template used by Blumstein and Stevens (1979) actually consists of 7 subtemplates. Their classification procedure thus effectively distinguishes 9 classes, 7 of which are subsequently combined to form the velar class. It remains therefore somewhat uncertain what "invariant" actually means in terms of the framework.

The term "relational invariance" as opposed to "absolute invariance" has been used by several authors (e.g. Fant, 1986; Sussman et al, 1991). Where absolute invariance applies when a single property or cue is invariant, relational invariance refers to situations in which the relation between two or more acoustic properties or cues is invariant. As discussed earlier, Sussman et al. (1991) showed that a highly linear relation relationship exists between F2n and F20 measured on CVC syllables. This relation, called a locus equation, is an example of a relational invariant.

If we approach the invariance concept in a somewhat more graded fashion, we can distinguish four components within the framework that would influence the "level of invariance":

Obviously, maximum acoustic invariance would be associated with a one-dimensional cue space, a short auditory context window, no effects of phonological context, and convex response regions. Note that on points 1 and 4 the implementation by Blumstein and Stevens (1979) is far removed from this situation.

6.6. The perceptual relevance of an acoustic cue depends on the phonetic context
Several studies have indicated that the perceptual relevance of certain acoustic cues is variable with phonetic context, i.e. in context A cue 1 dominates perception and cue 2 is hardly relevant at all, while the reverse holds in context B. Fischer-Jorgensen (1972) presented "burst-spliced" stop-vowel stimuli to listeners for classification of place of articulation. These stimuli consisted of a release burst isolated from a stop with one place of articulation (e.g. /pa/) spliced onto the burst-less part taken from an utterance with a different place of articulation (e.g. /ta/). The results of the experiment showed that listeners corresponded mainly in accordance with the burst in /i/ context, while they responded mainly in accordance with the formant transitions in context /u/. These results have recently been replicated by Smits et al. (submitted a) for the Dutch language. Summerfield and Haggard (1974) measured the influence of VOT and extent of first formant transition on the perception of the /g/-/k/ contrast. A two-dimensional synthetic continuum was used using CVs with vowels /a/ and /i/. Their results showed that the VOT cue is much more important in the /i/ context than in the /a/ context.

Intuitively, phenomena such as those discussed above could be translated into a perceptual mechanism which "actively" adjusts the classifier depending on the phonetic context, as was indeed suggested by Fischer-Jorgensen (1972) and Summerfield and Haggard (1974). More specifically, Fischer-Jorgensen (1972) observed that in stop-/a/ syllables the second formant transitions for labial, alveolar and velar place of articulation are very different while the bursts are acoustically rather similar. The reverse was found for the stop-/i/ syllables. Fischer-Jorgensen (1972) suggested that the perceptual system tunes in on these differences by giving more weight to formant cues in /a/ context and to burst cues in /i/ context. In a similar vein, Summerfield and Haggard (1974) suggested that, as the first formant transition is more pronounced in /a/ context than in /i/ context it is perceptually more useful in /a/ context than in /i/ context, and thus is weighted more heavily.

In our framework the classifier can be adjusted in accordance with an earlier classified phonological label, through the concept of the phonological cue. Obviously, such a mechanism can implement the context-dependent "cue weighting" strategy. Nevertheless, I will demonstrate in this section that for a number of context-dependent cue weighting situations it is not necessary to postulate such a mechanism. It will be shown that the context-dependent cue weighting behaviour can be reproduced by a "fixed" classifier, i.e. a classifier which does not employ any phonological cues.

Smits et al. (submitted a) performed a burst-splicing experiment on Dutch stop-vowel utterances containing the stops /p, t, k/ and the vowels /a, i, y, u/. The burst-splicing procedure was similar to the one used by Fischer-Jorgensen (1972), and was only carried out within syllables having the same vowel. Subjects were required to classify the stimuli as P or T or K. Table 1 lists the proportion of stimuli that were identified in accordance with the burst or transitions, respectively, broken down for vowel contexts. Only the data for speaker 2 in Smits et al. (submitted a) were used. Note that the burst dominates perception in vowel contexts /i/ and /y/, while the transitions are dominant in vowel context /a/.

Table 1. Percentage of listeners' classifications of the burst-spliced stop-vowel stimuli in accordance with the burst, the transitions, or the remaining class. For example, if the stimulus consists of a /pa/ burst spliced onto the burst-less part of /ta/, then the response P would be in accordance with "burst", T with "trans", and K with "other".


vowel = /a/
vowel = /i/
vowel = /y/
vowel = /u/

In follow-up study a simulation of the listeners' classification behaviour was carried out (Smits et al., submitted b). A large number of acoustic cues for place of articulation suggested in the phonetic literature were measured on the stimuli. Next it was attempted to reproduce the listeners' classification behaviour from the acoustic data using a formal model of human classification behaviour. To this end, several simple connectionist classification models were trained and tested on the perceptual data. The models used multidimensional acoustic vectors as input and produced an output vector containing the probabilities of responding /p/, /t/ or /k/. No phonological cues were used in the model, and the model made no formal distinction between the various vowel contexts. Eventually, the model that gave the best account of the perceptual data on the basis of the acoustic cues was selected. This model used a 5-dimensional cue space spanned by the following acoustic cues: the length of the release burst lb, the formant frequencies at voice onset F20 and F3n , and the frequency F0mfp and level L0 of a broad mid-frequency peak just after consonantal release. The model's class boundaries were linear functions of these 5 cues.

Upon closely studying the model's output it was found that the "context-dependent cue weighting" found in the perceptual data emerged from the model's classifications as well. Table 2 lists the percentages of classifications of the burst-spliced stop-vowel stimuli in accordance with the burst, the transitions, or the remaining class as predicted by the classification model.

Table 2. Percentage of classifications of the burst-spliced stop-vowel stimuli in accordance with the burst, the transitions, or the remaining class as predicted by the classification model.


vowel = /a/
vowel = /i/
vowel = /y/
vowel = /u/

In the classifier the burst appeared to play a more important role in determining consonant place of articulation in the vowel contexts /i/ and /y/, than in the vowel context /a/, which we had already observed in the perceptual data. For a comparison see Table 1. Nevertheless the model was "fixed", i.e. no context-dependent reweighting of cues took place in the model, and all stimuli were treated in the same way.

An examination of the distributions of the acoustic cues in the different contexts suggested an explanation for this phenomenon. It appeared to be the case that the three classes /p/, /t/, and /k/ were separated mainly on burst cues in vowel contexts /i/ and /y/, while they were mainly separated on formant cues in /a/ context. Stated differently, the acoustic between-class variability was predominantly accounted for by burst cues in /i/ and /y/ context, and by formant cues in /a/ context. This is illustrated in Figure 8. I have concentrated on the distributions of the most important burst cue F0mfp and the most important formant cue F20 for the vowel contexts /y/ and /a/. Two 2-dimensional Gaussian pdfs (one for /a/ and one for /y/) were fitted to the acoustic vectors (F0mfp,F20) representing all burst-spliced stimuli with a particular vowel context. Note that this time the extra assumptions of equal variances and zero covariances were not used. The ellipses in Figure 8 represent the = 2 equi-probability lines of the two-dimensional Gaussian pdfs and the solid lines are the class boundaries. Some typical stimuli are plotted within the ellipses (the labels representing the most probable classification by the subject as well as the model).

Figure 8. Two-dimensional cross-section of the 5-dimensional cue space used in the simulation of the listeners' classification of the burst spliced stimuli. The burst cue F0mfp is plotted along the x-axis, the formant cue F20 is plotted along the y-axis. The "frequencies" are expressed in ERB, units of equivalent rectangular bandwidth, which correspond to constant distances along the basilar membrane, therefore being a psychoacoustically more plausible unit than Hz (see Glasberg and Moore, 1990). The ellipses represent the = 2 equi-probability lines of the two-dimensional Gaussian pdfs fitted on all the stimuli with /a/ context (short dashes) and all stimuli with /y/ context (long dashes). The solid lines indicate the class boundaries. The individual utterances plotted in the ellipses represent typical stimuli.

The Figure clearly demonstrates that /p/, /t/, and /k/ are mainly differentiated on the basis of the formant cue F20 in the /a/ context, because the principle axis of the Gaussian representing the stimuli with /a/ context is almost parallel to the F20 axis. Evidently, the values of F20 are very different for /pa/, /ta/, and /ka/, while their values for F0mfp are similar. The reverse holds for the Gaussian representing the stimuli in the /y/ context. Here the values of F0mfp are very different for /p/, /t/, and /k/, while the values for F20 are similar.

In conclusion, the experimental finding that the perceptual relevance of an acoustic cue appears to depends on the phonetic context can be reproduced by a fixed model if the between-class distribution of acoustic cues varies with vowel context. No "active"

reweighting of cues is necessary.

7. Summary and conclusions

In this paper I have proposed a general framework for research on phonetic perception in which a pattern classifier plays a central role. The framework is intended as a comprehensive and formal representation of the widely adopted cue-based approach to phonetic perception. Formulated within the information processing philosophy, the framework consists of several interconnected information-processing modules and storage facilities. Explicit distinctions are made between various levels of information: acoustic, general auditory, specific auditory, and phonological. A pattern-recognition module plays a central role in the framework.

After the functionality of the various modules had been defined and discussed, a number of long-standing issues rated to variability with phonetic context were discussed from the perspective of the framework. In this discussion a number of fresh insights and reformulations of old problems were developed.

First of all, concerning the segmentation problem, it was concluded that within the proposed framework this is a non-issue, because the adopted approach is based on identifying important time instants (acoustic landmarks) instead of acoustic segments.

Secondly, it was argued that the issues of acoustic variability versus perceptual constancy and acoustic constancy versus perceptual variability arise from concentrating on one-dimensional "cross-sections" or "projections" of the more complete multidimensional classification problem. It was argued that it is useful to formulate the problem of phonetic perception in terms of a "dimensionality" rather than a "variability" issue.

Next, it was argued that if phonetic categorization is viewed as a pattern-recognition problem, the cue-trading phenomenon is no more than a natural expression of the multidimensionality of the pattern recogniser.

The framework allowed a more formal definition of acoustic invariance than is so far available in the literature. It was concluded that within the context of the framework four factors are relevant for assessing the level of invariance associated with a particular phonetic categorization model: the dimension of the cue space, the length of the window associated with the specific auditory context, the length of the window associated with the phonological context, and the convexity of the response regions.

Finally, it was concluded that for at least some context-effects found in the literature, active reweighting of cues by the perceptual system is not necessary. Instead, it was argued that the observed behaviour can be generated by a fixed pattern-recogniser when the between-class variability changes with phonetic context.

This work was funded by a NATO-Science fellowship. Many thanks to Louis ten Bosch and Terry Nearey for inspiring discussions relevant to this paper.

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