Google Scholar. Bahan, Benjamin. Baker-Shenk, Charlotte. Stokoe, Volterra V. Baker, Mark C. The Polysynthesis Parameter. Casey, Shannon. Huang, C. Lichtenberk, Frantisek. Liddell, Scott K. Mathur, Gaurav. Meir, Irit. Padden, Carol A. Moreover, this approach would not model sequences of events, e. ATL is a framework that allows us to analyze relative temporal information, such as event A happens before event B . Here, any two time events are related by a set of symmetric, mutually exclusive binary relations, called propositions.
In our modeling, we employ the following set of propositions: before , meets , overlaps , equals , starts , during and finishes. To show the use of the above defined propositions, consider the examples in Fig. In this figure, we have two events, A and B. A is said to be before B , when A happens disjointly before B , Fig.
For example, A could be head turns right and B head turns left. Here, we would write head turns right before head turns left. This could be the case when a subject is signing a negative statement with negation marked with a headshake. Note that the difference between before and meets is that before requires a non-empty time interval between both events. For example, when nodding, the head moves up and down without a visual pause, which could be written as, A meets B.
Obviously, in practice, two events involving different articulations would only perfectly follow one another by chance. To accommodate for small natural variabilities e. The value of will be estimated using cross-validation in learning. In cross-validation, we divide the training data into two or more sets; use all but one of those sets for training while using the left out set for testing values of , with small.
This is repeated multiple times to determine the value of the parameter yielding better generalizations. This is a common practice in pattern recognition where a learning algorithm uses a training set to come up with a representation that accurately represents some observations or discriminates between observations belonging to different categories classes.
A testing set is then used to determine whether the learned representation is capable of discriminating previously unseen examples into the correct class. In contrast, equals means that both events, A and B , share the same time interval, Fig. This proposition is useful to denote single featural events, e. Although this may seem redundant at first, this notation allows us to consider single actions without changing notation or the algorithm.
When both events start at the same time but A finishes before B , then A is said to start with B , Fig. Finally, during means that A 's time interval happens within B 's time interval, Fig. For clarity, here, we have listed the events and their time intervals in order of occurrence. The top row specifies the first event, with subsequent rows listing later occurring events.
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The bottom row summarizes the time interval of each signed concept. This visualization facilitates the coding of the events using the propositions in. For example, for the figure above, it is easy to see that head moves up occurs during event brows move up , which can be compactly expressed as head moves up, brows move up. The resulting coding using ATL relations is shown in Table 2. In summary, the Allen's Temporal Logic defined above is composed of a set of binary propositions.
The set operates over the time interval defined by the set of events. In this notation, any two events are related using one of the propositions in , e. The 17 feature categories Table 1 form a set of possible ATL first-order relations. We eliminated relations that cannot co-occur due to their mutually exclusive nature, e. It is also important to encode the number of consecutive occurrences for a given ATL relation. This might be important for some discriminant features, e. To correctly represent this information, we encode the relative frequency of each occurrence in a histogram, which displays the number of times that a given event happens.
Formally, we represent a sentence as , where is the number of times that the first-order relation repeats in a sentence. For instance, if a sentence includes four eye blinks, the feature vector will have a value of in the position ; where we have used to indicate that this is the feature used to code for blinks.
The dark blue color indicates a low number of occurrences for an event, while a dark orange color indicates a high number of repetitions. This figure is the histogram corresponding to the example in Fig. The feature vector entries are read from left to right. The histogram representation of the ALT described thus far provides a convenient numerical representation of the nonmanual events we wish to study. To determine the time relations that best discriminate a grammatical structure from the rest e. In pattern recognition, such approaches are called discriminant analysis . When the number of samples relative to the number of features is small, as is the case in the present study, Regularized Linear Discriminant Analysis RLDA is a possible algorithm to use .
RLDA adds a regularizing factor to the metrics being computed, preventing singularities even when the number of samples is small or when the underlying metric cannot be fully estimated . Also, RLDA has a single parameter to estimate, making it very efficient and easy to work with .
Formally, RLDA finds the projection vector that best separates in the least-square sense two classes by maximizing the ratio between the class means to the average variance of these classes. Consider the case where and represent class 1 and 2, respectively. And, let the sample sets be , where specifies the class and the number of samples belonging to it.
The discriminant hyperplane separating the samples of these two classes is defined by its normal vector,. This vector is given by, 1 where are the sample class means, is the sample within-class scatter matrix, is the regularizing parameter that is found using cross-validation, is the identity matrix and specifies the 2-norm euclidean measure. Recall that the regularizing parameter is used to ensure the above equation has a robust solution when the number of samples is small i.
Solving for 1 yields,. An ATL relation is hence defined as discriminative if its corresponding absolute magnitude in is larger than the others i. To rank their relative importance, each element of the vector is normalized with respect to its largest attained value, i. Our hypothesis is that nonmanual markers can be used to discriminate among the nine classes of sentences described above. More specifically, we hypothesize that first-order temporal relations of facial movements are sufficient to code for such grammatical structure.
To test this hypothesis, we use all the video sequences in our database except one to find the discriminant facial features as described in the Methods section and test whether the resulting model correctly classifies the left out sentence. Classification of the left out test sample is done using the nearest-mean classifier. The nearest-mean classifier assigns to the class label of the nearest class mean , i. If we have sample signed sentences, there are possible sentences we can leave out in the LOSO approach. In LOSO, we try all these possibilities and then compute the mean classification accuracy.
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We also estimate the expected by averaging the vectors generated from all LOSO iterations. Note that we only compute the classification accuracy for the features that provide the largest , since this value is correlated with discriminability. First, we wish to determine the nonmanuals that best discriminate each structure, i. To achieve this, we run a one-versus-all experiment.
This means that, for each class e.
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The resulting discriminant features need to distinguish between the grammatical structures under study. These features are those providing the highest classification accuracies in the LOSO test described above. They are in Tables 3 — 7. In Tables 3 — 7 we also specify the classification accuracy of each of the discriminant features found with the proposed approach.
To do this we use the following approach. Each discriminant feature defines a one-dimensional feature space with its corresponding basis vector. We project all vectors onto , i. We then use RLDA to learn the hyperplane that best separates the samples of our two classes. Note that Linear discriminant analysis and RLDA provide the Bayes optimal solution when we have only two classes with equal variances . Once this hyperplane has been determined, we compute the percentage of samples belonging to class 1 i.
These two numbers provide the percentage of classification accuracies listed in the last two columns in Tables 3 — 7. This refers to how discriminant the feature is.
Some discriminant features will of course be more common and, hence, will successfully discriminate more samples of than others, with. This makes it a very efficient, robust stand-alone nonmanual to indicate a sentence is not a Hypothetical conditional with classification accuracy at Thus, this second nonmanual is not as robust as the previous one.
This is because both methods of analysis assume the data is Normally distributed. Additionally, we tested for the statistical significance of our results. This was done by comparing our results with those given by a randomization of the class labels. That is, we compare the results obtained with the proposed approach to the results one observes when the class labels for each of the samples are assigned to a random class rather than their true class label.
The randomization was repeated times, yielding a total of classification results. These results specify the probability of obtaining the classification accuracies by chance.
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Let us now describe the results of this study in detail for each of the 5 classes under consideration. For example, a facial expression that could interfere with the marking of conditional might be that of surprise, which involves brows up, head back, and eyes wide open. Most notably, Table 3 provides novel and some unexpected results concerning the behavior of the head, and the mouth and teeth.
Thus, the frequent occurrence As reported in  , nouns in ASL and other sign languages are much more likely to be accompanied by mouthing of the surrounding spoken language word than other word categories e. This is diminished when the downward movement of the brows is preceded by the head turning right. This allows for very high classification rates of Wh-questions and other constructions even when they are using this single feature.
This placement of the Wh-word has the effect of allowing the main clause to be treated either as part of the question or as an Assertion followed by a question . When the signs preceding the postposed Wh-sign are treated as separate from the question at the end, we see very frequent One articulation in Wh-questions postposed that did not show up in other constructions is the occurrence of blinks.
Periodic blinks, the kind that are associated with eye-wetting, are well-known as a marker of the end of intonational phrases and syntactic constituents in ASL . But if these blinks were just periodic blinks, they would occur after the brows move down ends. The fact that we see blinks overlapping with brows move down implies that they are deliberate blinks — slower and longer in duration. Deliberate blinks are associated with prominence on a sign .
If the blink ended at the same time as the brows move down, we would also know that the blink occurred on the last sign in the clause. The fact that blinks overlap with brows down means that the blink is located on a sign inside the clause. However, head behavior can also function parallel to body lean behavior, with tilt forward suggesting inclusion of the addressee and tilt back indicating exclusion of the addressee .
This is a truly surprising result which undoubtedly suggests further investigations in this direction as, to our knowledge, no function for flat mouth in ASL has been assigned in the existing literature. Assertions have been traditionally viewed as not marked by specific nonmanuals, leaving the articulators free to reflect ones that accompany nonmanually marked lexical signs as well as to reflect the signer's emotional status. The cues identified as distinctive in Table 7 are notable for their relative absence in Assertions as compared to the other constructions.
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The study of polarity follows the same procedure described above. These are the results for each of the four classes with polarity, i. Here, we also performed the statistical significant analysis described in Experiment 1 section. All our results were again statistically significant with: for Hypothetical conditionals, for Wh-questions, for Wh-questions postposed and for Assertions. From Table 8 , we see that all notable features for polarity in Hypothetical conditionals are associated with head turns and are more frequent in negatives than in positives. This is an expected finding as negatives are generally marked by headshakes in ASL  ,  ,  and many other sign languages  — .go to link
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When we dig into the details of the temporal behavior of head turns, we identify linguistic interactions that have not been available to impressionistic analysis so far. We believe this is an improvement our algorithm has made possible for sign language research. In this sense, the findings with the ordering and the relation of head turns alert us to two previously unrealized findings about negative polarity in ASL. When we look at the combination of Hypothetical conditional and negation, we are no longer looking at the simplest situation.
Instead, the conditional contains the negation as part of its clause, and we expect the conditional marking to begin before the negation marking. Therefore, brief pauses between head turns highlights the separation of the fast paced negative headshake from the rest of the headshakes in negative conditionals.
There is no need for these pauses in positive conditionals as the only head turns present are related to conditionality. Beyond the results above, our results further highlight the role of the mouth in nonmanuals. Although the involvement of the mouth for negation in ASL had been detected in previous research  , given the technology of the time, back then it was only possible to report the timing relation between the headshake and the hand movement, but not the exact temporal relation between the two nonmanual markers headshake and mouth position.
The contrast in discriminant percentages indicates that the mouth is actively involved in the expression of negation in ASL.
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