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5Detecting Handwriting Difficulty in

Relation to the Use of Graphic Rules: An Application of Model Free Estimators

in RehabilitationPuspa Inayat Khalid

Narges Tabatabaey-MashadiMokhtar Harun

Rubita Sudirman

5.1 INTRODUCTION

The term poor writer is commonly referred to children who have difficulty in developing and acquiring handwriting skills (Graham and Weintraub, 1996; Rosenblum et al., 2003). It is neither due to any obvious neurological problem nor to a lack of early education (Hamstra-Bletz and Blote, 1993; Rosenblum et al., 2003). Even though handwriting difficulty has nothing to do with the child’s academic performance such as learning, reading (dyslexia), or calculating (dyscalculia) disabilities (Bonoti et al., 2005; Graham and Weintraub, 1996), handwriting performance may be affected by extrinsic and intrinsic factors. Extrinsic factors are related to environmental issues such as sitting position, writing materials, and writing instruction (Feder and Majnemer, 2007). Intrinsic factors, on the other hand, stem from the child’s actual handwriting capabilities such as kinaesthesia, fine motor skill, and visual motor integration skill (Alston and Taylor, 1987; Gillespie, 2003).

Children’s life has been shown to be affected by the inability of the children to make a skilful use of handwriting as an ingredient for success in school. Research study has provided evidence that failure to attain handwriting competency during

2 Detecting Handwriting Difficulty in Relation to the Use of Graphic Rules

school age years can interfere child’s confidence (Zwicker, 2005) which may consequently prevent them from reaching their true potential, academically and socially. Therefore, when the child starts school, it is important for the teacher to observe each pupil individually to ascertain the child existing strengths and weaknesses. If the problem with handwriting proficiency arises, the teacher can refer the child to school-based occupational therapist or remedial teacher for further assessment and offer the intervention program that match the child’s need. With early intervention, the child could overcome his difficulty before it becomes entrenched. However, if the difficulty is not detected, it may lead to improper writing habits that have their implications throughout a child’s career.

Over the years, many tools have been developed to evaluate early writing skills in the primary grades. Two main outcomes have been used to assess and define poor handwriting: product legibility (readability of the written output) and performance time (writing speed). Product-oriented ways of assessment not only laborious and depend on the subjective judgment on the written product but the assessment also does not provide any insight into the strategies and dynamics of the hand movement. The drawbacks in qualitative analysis of handwritten product have shifted the researchers’ interest to handwriting process. Guest et al. (2003), Rosenblum et al. (2003), Rosenblum et al. (2006), and Gilboa et al. (2010) have given preliminary evidence favouring dynamic data from handwriting process (such as hesitancy, pen angular trajectory, in-air time, and the amount of variability in the movement profiles) over static data from written product (such as malformed letters, uneven spacing, and irregular letter sizes and shapes) to evaluate children’s handwriting skill.

While many studies have attempted to use writing process to assess handwriting ability, drawing strategy is believed to have more advantages in the study of the dynamic characteristics of poor writers. This is due to the fact that writing skill is basically a combination of individual drawing skill. In addition, both writing and drawing are rule-governed activities. Rule-governed activity

Advances in Biomedical Image and Signal processing: Series 1 3

means the activity is subjected to certain convention. The conventions which are known as graphic production rules (GPR) have been described as developmental rule based copying behaviour that reflect the tendencies of pupils to use pre-determined rules and procedures when drawing or producing letters (Goodnow and Levine, 1973). According to Simner (1981), starting rule reflects pupil’s preferences to initiate his drawing by selecting a certain location point. For example, right-handed children prefer to start at the top rather than at the bottom of the figure, or at the left rather than at the right. Progression rule on the other hand reflects pupils’ preferences to segments’ directions such as downward rather than upward.

With regard to the preliminary evidences that show young children use pictures and pre-writing graphic principles before true alphabet writing appears (Gillespie, 2003) and that there exist differences between children with and without handwriting difficulties in their drawing behaviour (Khalid et al., 2010 a, b), it is postulated that the dynamic attributes derived from drawing activities, particularly in relation to the GPR (drawing strategy), may provide insight on the drawing mechanisms that contribute to handwriting difficulty in young children. This paper highlights the feasibility of using the attributes that represent quantitative differences in drawing behaviour to assess handwriting ability. This paper also reports the classification accuracy of early writing screening assessment to validate the use of the drawing behavioural traits in seeking out at risk pupils for handwriting difficulty.

5.2 PREDICTIVE MODELS

Predictive models may be applied to validate the use of attributes in the construction of decision models for procedures such as assessment and intervention planning. The goal of predictive models in validating the attributes is to select, explore, and model the object specific information in order to discover unknown


pattern or relationships which provide a clear and useful result to the data analyst to predict the outcome of interest and to thereby support the decision making.

Predictive models can be developed using various techniques. Artificial Neural Network (ANN), Logistic Regression (LR), and Support Vector Machine (SVM) are the techniques that have the ability to model complex nonlinear relationship even without a predefined mathematical relationship between dependent and independent variables. Among the three techniques, LR is superior to ANN for identifying possible causal relationship. However, ANN has the ability to detect all possible interactions between predictor variables even though its solution is not unique (Tu, 1996). A global and unique solution is best achieved through SVM (Delen, 2009); this is a significant advantage of SVM over ANN.

Predictive models that use supervised learning rely on a priori knowledge to predict unseen behavior of a complex system. To assess the performance of the predictive models, the data is normally divided into two datasets: training and test. The training or learning dataset is used to build the predictive model (determine its parameters) while the test dataset is used to assess the model performance (holding the parameters constant) (Sharma et al., 2008).

Artificial Neural Networks (ANN). Multilayer feed-forward neural networks (MFFNN) are the preferred neural network topology by most researchers (Wilamowski, 2009) and are based on minimization of an error function (Fazayeli et al., 2008). Typically, the MFFNN consists of an input layer, an output layer, and at least one hidden layer between the input and output layers. Each layer contains a set of neurons. Each neuron is connected to every neuron in the adjacent forward layer. The strength of each connection link is represented by a weight (Duh et al., 1998). MFFNN adjusts the weights such that the discrepancies between the network outputs and the target values are minimized (Fazayeli et al., 2008).


Back-propagation (BP) algorithm is the learning method that is most commonly used by researchers to update the connection weights (Chang and Hsu, 2009). By using BP learning algorithm, the calculated error is propagated backwards through the network starting at the output layer and working back toward the input layer. As the error is propagated, the weights for the next iteration are adjusted so that the error in the network response will be less for the same inputs. Even though the algorithm is slow compared to other learning algorithms, the performance of a multilayer back-propagation neural network can be improved by including adaptive learning rate and momentum in the algorithm. The adaptive learning rate and momentum were used to improve the performance of the network and secure the network’s stability.

Logistic Regression (LR). Logistic regression is based on the model that the logarithm of the odds of belonging to one class is a linear function of the feature vector elements used for classification:

where p is the probability of the outcome of interest (dependent variable), p/(1-p) is the odds ratio, β0 is an intercept parameter (constant), β1, β2, and β3 are the regression coefficients for each attribute, and i1, i2, and i3 are the potential predictors (input vector). The coefficients represent unknown parameters that need to be estimated based on data obtained on the attributes and on the outcome for a group of subjects (Kleinbaum, 1994). The most widely used method to estimate these coefficients is the maximum likelihood (Bellazzi and Zupan, 2008).

Each of the regression coefficients describes the contribution and the influence of the risk factors (the predictors) (SAS, 1999). A positive regression coefficient means that the risk factor increases the probability of the outcome while a negative

(5.1)


regression coefficient means that the risk factor decreases the probability of that outcome (Choi and Lee, 2010). On the other hand, a small regression coefficient means that the risk factor has less influence on the probability of the outcome while a large regression coefficient means that the risk factor has great influences on the probability of that outcome (Campbell et al., 2007).

Support Vector Machine (SVM). SVM uses an optimum linear separating hyper-plane to separate two set of data. This optimum hyper-plane is produced by maximizing the minimum margin between the two sets (Burges, 1998). Therefore the resulting hyper-plane will only be depended on border training patterns called support vectors. Non-linear classification of SVM takes place by mapping all the data into a new feature space with higher dimension, using a nonlinear mapping function . Then it builds the optimum separating hyper-plane by maximizing the minimum margin in this feature space. Fortunately SVM computations are only dependent on the dot product of the mapped vectors in the new space . The kernel function represents the dot product of the mapped vectors in the new space based on the vectors in the input space.

The kernel function has an important effect on the functional efficiency of SVM. The commonly used kernel function is Gaussian radius basis:

(5.2)

where γ =1/σ2 and σ is positive Gaussian kernel width. When a Gaussian kernel SVM is trained, the two parameters C and σ2

should be prefixed; C is the value for considering the effect of errors when training the system. Greater values for C represent our desire to compensate more for errors. However, greater C value does not necessarily cause a more accurate classifier.


5.3 METHODOLOGY

ParticipantsAs described in our previous research, Khalid et al. (2010b), 170 Year-One children were investigated on their drawing behaviour. Prior to the drawing activities, the children were classified into average (42 boys and 63 girls) and below-average (45 boys and 20 girls) writers using Handwriting Proficiency Screening Questionnaire (HPSQ) (Rosenblum, 2008). The pupils’ classroom teachers were asked to complete the questionnaire. These children were those who had achieved a total HPSQ score either less than 8 (represent the average writers) or greater than 19 (represent the below-average writers). This was done to ascertain that the pupils were representing the two groups of writers.

Drawing TasksFrom the results presented in Khalid et al. (2010 a, b), copying and tracing tasks had been identified as the basic tasks that could provide reliable dynamic attributes (in relation to the use of GPR). These attributes have been able to show some quantitative differences in drawing behavior between average and below-average writers. Moreover, copying activity does not require memory retrieval. The child only needs the ability to imitate. On the other hand, tracing task gives physical guidance to the child by assisting him in limiting the occurrence of variations when drawing a particular shape.

In the copying task, the pupils were asked to copy 4 basic lines: vertical, horizontal, right-oblique and left-oblique. Each of the four basic lines was required to be copied in two opposite directions: vertical downward (VD), vertical upward (VU), horizontal rightward (HR), horizontal leftward (HL), right-oblique downward (RD), right-oblique upward (RU), left-oblique downward (LD), and left-oblique upward (LU). The pupils were


presented with an overlay containing the figure printed in the left column and the response frame in the right column. The overlay for the right-oblique line is shown in Figure 5.1.

Figure 5.1 The overlay for copying right-oblique line

Following the copying task, the pupils were required to trace a sequence of rotated semicircle. As reported in Khalid et al. (2010b), the pupils were instructed to start with the left-most pattern and proceed through the tracing sequences. However the pupil was allowed to trace the semicircle in either the clockwise (CW) or counter clockwise (CC) direction. The overlay for this task is shown in Figure 5.2.

Figure 5.2 Tracing task given to the participated Year-One pupils

InstrumentsThe drawing tasks were performed on A5 papers overlayed on the surface of a digitizing graphic tablet (Wacom intous3). The tablet with a wireless electronic ink pen (pressure sensitive tip) was used to register the participants’ hand movement. Displacement (the x-y coordinates of drawing movements) and pen pressure (1024


levels) were sampled at 100 Hz and stored in laptop computer for further off-line signal processing.

Attributes extraction and classification of below-average writers was implemented on a Pentium IV machine under Window XP Professional platform. The attributes extraction as well as the ANN and SVM training and testing were performed using MATLAB 7.0 software package. On the other hand, the logistic regression training was performed using StatView software package and the performance of the LR technique was evaluated using Microsoft Office Excel 2007.

DatasetIn order to have a consistent and reliable result from the predictive models, an equal number of samples from both groups of writers were employed. As there were only 65 pupils in the study group who involved in the copying and tracing activities, 60 pupils (42 boys and 18 girls) from the study group (below-average writers) and 60 pupils (25 boys and 35 girls) from the control group (average writers) were randomly selected for the classification process. Two data sets were used: the training set (seen data) to build the model and the testing set (unseen data) to measure the model performance.

To maximize the use of the data, 10-fold cross-validation procedure was applied. The data was randomly divided into 10 folds of equal size (12 samples in each fold). Each fold consisted of equal number of samples from the two groups of writers (6 average writers and 6 below-average writers). This was done as a preventative measure for a consistent and reliable result.

The classification models were trained and tested 10 times. Each time, the models were trained on 9 folds and tested on the remaining single fold. The process was repeated until all folds were used as the test dataset. By doing this, it is ensured that the samples were assigned in one of the 10 testing sets. The classification of the testing data indicates the ability of the model to classify the data which were not used during the training. The


overall accuracy of the modelling techniques was then determined by taking the average of the 10 individual predictive accuracies.

ClassificationTo validate the use of the selected attributes in early writing screening assessment, three commonly used classifiers; Artificial Neural Network (ANN), Logistic Regression (LR), and Support Vector Machine (SVM) were adopted. The important parameters for the three classifiers are as follows:

Artificial Neural Networks (ANN). The designing of neural network involved the decision in the number of hidden layers and number of neurons in each layer along with the neurons’ transfer functions. Since training iterations often slow down dramatically when more hidden layers are used (Yu, 2000), the ANN employed in this study was a single hidden layer feed-forward network trained using BP algorithm.

Through trial and error approach, three hidden neurons was found to be the optimal number for the model employed in this study. With a smaller number of neurons, the network should have better generalization abilities. However, it is noted that the network with small number of neurons cannot be trained to obtain very small errors, as highlighted in Wilamowski (2009).

The network was trained by the BP algorithm and the log-sigmoid function was used as the activation function in the hidden and output layers. For the final output value to be dichotomy, the threshold θ was set to 0.5. The training function used for the BP was gradient descent with adaptive learning rate and momentum of 0.2 and 0.95 respectively. The multiplying factor used to increase and decrease the learning rate was set to 1.05 and 0.7 respectively. These typical values are suggested by Negnevitsky (2005).

Because each training process starts with random initial weights, the network could give slightly different results. Therefore each algorithm was called on 10 trials to get the average performance of the network. A mean squared error (MSE) chosen


as an evaluation criterion for each trial was set to 0.04. The training process for each trial was stopped when 5000 epochs (iterations) were reached. In this case, the network was considered to complete its learning even though the MSE was not reached its predefined value.

Logistic Regression (LR). For the LR training process, the default choices (no partial correlations, 95% confidence interval, and at most 30 iterations) given in the software were used to get the logistic regression coefficients for each attribute. The output value from the logistic function was then changed to dichotomy by setting the threshold θ to 0.5.

Support Vector Machine (SVM). For this study, the parameter for σ was prefixed to 0.1250 and the parameter for C was prefixed to 32. The best above parameters were found through grid-search explained in Hsu et al. (2010).

Performance EvaluationIn a two-class prediction problem, true positive (TP) and true negative (TN) denote the number of samples correctly classified. True positive denotes the number of positive instances that are correctly classified and true negative denotes the number of correctly classified negative instances. On the other hand, false positive (FP) denotes the number of cases classified as true when they are false and false negative (FN) denotes the number of cases classified as false when they are true.

The predictive performances of the above described three classifiers were probed using the following measures (Karaolis et al., 2010):

Sensitivity or true positive rate (TPR):

Specificity or true negative rate (TNR):(5.3)


Accuracy (ACC):

5.4 RESULTS & DISCUSSION

AttributesThe authors had analysed 85 dynamic attributes (in relation to the GPR) that were derived from the 2 drawing activities (copying and tracing) and had selected 3 non-confounding attributes for assessing handwriting ability: the standard deviation of pen pressure when drawing right oblique line in upward direction, the ratio of time taken to draw horizontal line in rightward direction as compared to the leftward direction, and the use of progression rules when tracing a sequence of semicircles. These 3 attributes had exhibited different behavioural pattern between average and below-average writers.

As stated in Rosenblum et al. (2004), children with poor handwriting achieve higher absolute scores of ‘neuromotor noise’ (variability of the motor movement) in comparison with good writers, and demonstrate less ability to regulate muscle force. Our findings had supported the statement. When the 170 samples were asked to copy right-oblique line in two opposite directions, the below-average writers were found to be less successful in inhibiting pressure variability when drawing the right-oblique line in upward direction (paired t-test: p-value < 0.0001). The average writers on the other hand did not exhibit much variation in pen pressure while drawing the right-oblique line either in downward or upward direction (paired t-test: p-value = 0.0936). Figure 5.3 illustrates the distributions of the pen pressure variability within

(5.4)

(5.5)


writers between the two groups when members of the groups drew the right oblique lines.

Razian et al. (2004) had claimed that the time taken to draw horizontal line is one of the dominating features for clustering dyspraxia children (those with difficulty in planning and carrying out complex movement) from the controls. Similarly, obvious differences in time taken to copy the horizontal line in rightward and leftward directions were noticed in below-average writers. Significant difference between the two groups of writers was observed when the ratio of time taken to draw the horizontal line in rightward direction to the time taken to draw the horizontal line in leftward direction was taken into consideration (unpaired t-test: p-value = 0.0027).

Figure 5.3 The variability in pen pressure within writers for the two groups of writers when drawing the right oblique lines in downward

(RD) and upward (RU) directions

The tendency of the below-average writers to speed the drawing in leftward (non-preferential) direction may indicate the writers’ motor constraints rather than their drawing fluency. The below-average writers’ preference for a more rapid movement may imply that they might have difficulty in incorporating the motor

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production rules; thus tried to reduce the disruptions in drawing movements by completing the task in less time.

The tracing task was introduced in this study to perceive the order (described by the graphic production rules) in which the pupils have chosen to trace each of the semicircles. It was found that significant number of below-average writers initiates drawing by selecting a starting point that is deviated from the starting rule and progressing their drawing in a non-preferential direction. Based on the result presented in Figure 5.4, the performed chi square test confirmed that the predicted movement in the last three semicircles’ orientations was related to the handwriting proficiency (χ2 = 19.25 and φ = 0.337). In addition, the use of starting and progression rules between the two groups was also observed to be significantly different (z-value = 4.39) at 0.01 level. As a result, the authors had decided to extract one dichotomous attribute from this finding. Those who did not trace the last three orientations in expected directions (as discussed in Khalid et al. (2010b)) were labelled ‘1’ and others were labelled ‘0’. It is important to note that this type of data was nominal values; the values were used to show whether typical drawing behaviour is existed.

Figure 5.4 Percentage of participants constructing a sequence of semicircles in non-preferential direction.


As the 3 highlighted attributes had evidently offered high discriminatory information, their inclusion in the screening method is likely to contribute towards an effective identification of below-average writers.

Classification performanceThe classification rate of the testing data signifies how well the models generalize the classification for new data. The classification was considered correct if the output from the model was similar to the one that had been judged by the teachers (using Handwriting Proficiency Screening Questionnaire (HPSQ)). The classification performance was divided into 2 parts: control (TNR) and test (TPR). Control performance was based on the classification rate of the samples from the control group in the testing set while test performance was based on the classification rate of the samples from the test group in the testing set.

The classification rate for ANN, LR, and SVM were recorded in Table 5.1. The results indicated that the classification rate for the control group (TNR) was better than the study group (TPR). The correct classification for the control group ranged between 87 % and 93 %. For the study group, the correct classification rate was between 78 % and 80 %. These high percentages indicated that the children who were defined by their teachers as having handwriting difficulty were also shown atypical drawing behavior when performing the drawing task in non-preferential direction.

Table 5.1: The classification performance of ANN, LR, and SVMClassification PerformanceAccuracy (%) TPR (%) TNR (%)

ANN 83.5 78.8 88.2LR 83.3 80.0 86.7SVM 85.8 78.3 93.3

The distributions of the sensitivity (proportion of subjects that were correctly predicted to be at risk of handwriting difficulty) are


shown in Figure 5.5. The illustration indicates that the LR classifier (indicated by dotted line) slightly outperformed the other two classifiers. However, if the measure of performance was the percentage of control group correctly classified, the SVM classifier (indicated by dotted line in Figure 5.6) outperformed the ANN and LR. Nevertheless, the differences in the classification performance among the three classifiers were not statistically significant.

Figure 5.5 Distributions of sensitivity resulting from the 10-fold cross validation procedure.

Figure 5.6 Distributions of specificity resulting from the 10-fold cross validation procedure.


Generally, the three classification techniques produced comparable classification performance. With only three attributes, the classifiers had equally good ability (for the unseen input data) to identify children with handwriting difficulty with average screening accuracy of 84 %. This performance was much better than the experimental results presented in Kim (2010). With 100 samples and 3 simulated independent variables (including one categorical variable), Kim (2010) had reported misclassification errors of 0.4 and 0.433 for the ANN and LR respectively. The good classification performance of the three classifiers used in this study indicates that the selected attributes are of reliable ones.

About 79 % of the children who were defined by their teachers as having handwriting difficulty were also found to have atypical dynamic attributes in relation to the use of graphic production rules. As measurements on human subjects rarely give absolute certainty (Campbell et al., 2007), the sensitivity of 79 % was considered good enough to highlight the importance of graphic rules in handwriting instruction. However, it is important to note that a higher sensitivity is required for a more effective and accurate detection of pupils who are having low prevalence but are at risk of having handwriting difficulty. On the other hand, about 11% of the participated children were detected to exhibit atypical trait with regard to the use graphic rules but these children were not observed to have any handwriting difficulty by their teachers. These children may be at risk of handwriting difficulty and may also miss their chance to be in the intervention program because their handwriting difficulty was not noticed by their teachers or parents. Thus, the importance of including the children’ dynamic attributes to objectively identify below-average writers is apparent; especially those who do not show observable symptom that can be spotted by their teachers or parents.

5.5 CONCLUSIONS


It would not be practical to extract dynamic data on the entire population of grade one children, nor would it be sufficient to base the screening of those at high risk of writing difficulties on the data from the questionnaire alone. The handwriting proficiency screening questionnaire (HPSQ) could be used to screen the individual who is at risk of handwriting difficulty. However, when comes to the mild handwriting difficulty, where no obvious symptom is available, the use of objective measures is suggested for the screening process to be effective. The approach of using dynamic attributes is proposed as an auxiliary technique to the current procedure of using subjective evaluation on written product.

Since writing system varies among countries and individuals, the use of outcome measures from drawing activities to screen poor writers is essential. The results presented in this article, which are consistent with the report in Khalid et al. (2010a), have revealed that evaluating children’s drawing process may help identify those who need close monitoring or specific intervention (such as handwriting instruction) for handwriting competency. The outcome measures from drawing mechanisms, particularly in relation to the use of graphic production rules, had created a profile of behavioural traits that were able to highlight behavioral differences between average and below-average writers.

There are distinct outcome when using drawing strategy in assessing handwriting proficiency. The proper use of graphic production rules seems to influence the handwriting ability. This study has shown that the dynamic attributes such as pen pressure variability within-writer when drawing RU line, the time ratio of drawing HR and HL lines, and the use of progression rules when tracing the last three rotated semicircles can exhibit functional impairment in handwriting ability. Even from a simple drawing task, these three statistically significant attributes (p-value < 0.005), which are inherent in the execution process, has made it possible to draw information and make deduction about the two groups with high confidence. Although the attributes are


considered as the symptoms rather than the causes of writing disability, the classification accuracy from the three commonly used predictive models had put into evidence the possibility of using the three attributes in assessing handwriting proficiency among children. This is particularly useful for the assessment tool that could be employed for school screening of handwriting difficulty.

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