# Recognition of Eye-Written Characters Using Deep Neural Network
## 3 Results  
The proposed method achieved a 97.78% accuracy for 10 Arabic numbers in the writer-independent validation, showing 12 errors among 540 characters. Table 1 compares the results of the proposed method and the conventional methods in the literature. This indicates that the proposed method increased the accuracy by employing a deep neural network, reducing the error rates by approximately half, from 4.26% as reported in [23] to 2.22%. We can directly compare the results because the same dataset was used in [23] and in this study. It is difficult to compare the current results to those of previous studies other than [23] because of the different experimental conditions. Instead of a direct comparison, we indirectly compared the results using the accuracy differences between the DTW and deep neural network (DNN) with the dataset from [23] because DTW was also used in previous studies. Notably, the error rates dropped significantly from 7.59% to 2.22% after employing DNN by the proposed method. Although the number of patterns in [20,21] were larger compared to those in our datasets, the accuracy also increased when we employed DNN instead of DTW. It is remarkable that the proposed method achieved higher accuracies than the previous methods in a writer-independent manner. The network was trained from the data from 17 writers and tested with the data from an unknown writer, which means that a similar accuracy was expected when a new writer's data were tested with the pretrained model. This proves the results to be trustworthy because the training and test dataset were independent of each other. Deep neural networks are commonly trained with a large amount of training data, which implies that the accuracy could be improved with a bigger dataset. Figure 7 shows an entire list of misrecognized characters. Many of the misrecognized characters had additional eye movements (a, b, h, i, j, k) or long-term fixations (c, d, e, j, k) at certain points in the middle. Some characters were written differently to their references and had distorted shapes (d, i, k). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & **Character Set** & **Number of** & **Writer-Dependent/** & **Accuracies** \\  & **(Number of Patterns)** & **Participants** & **Independent** & **(Metrics)** \\ \hline Heuristic [22] & Arabic numbers, arithmetic symbols (14) & 11 & Independent & 75.5 (believability) \\ \hline DTW [21] & English alphabets (26) & 20 & Dependent & 87.38\% (F1 score) \\ \hline HMM [20] & & & & & 86.5\% (F1 score) \\ \hline DTW [20] & & & & & 77.6\% (F1 score) \\ \hline DNN-HMM [20] & & (12) & & & 93.8\% (accuracy) \\ \hline GMM-HMM [20] & & & & 93.5\% (accuracy) \\ \hline DTW [23] & & & & & 92.41\% (accuracy) \\ \hline DPW [23] & & & & & 94.07\% (accuracy) \\ \hline DTW-SVM [23] & & (10) & 18 & Independent & 94.08\% (accuracy) \\ \hline DPW-SVM [23] & & & & & 95.74\% (accuracy) \\ \hline DNN (proposed) & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Recognition accuracies of eye-written characters with different methods. Figure 6: Confusion matrix of the proposed method. Table 3 summarizes the recognition accuracies of the participants with different classifiers. Evidently, the proposed method improved the accuracy for most of the participants. There were two cases in which the accuracy decreased: participant #10 (Figure 7c-e) and #17 (Figure 7i,j). The errors were because of the long-term fixation of the eyes during eye writing, as shown in Figure 7.  
It is evident that the accuracy increased through the trials (Table 4). There were eight errors in the first trial for all participants but only two in the second and third trials. This shows that the participants were accustomed to the eye-writing process after a short practice, which is beneficial for an HCI tool. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Trials** & **1** & **2** & **3** \\ \hline Number of errors & 8 & 2 & 2 \\ \hline Accuracies & 95.56 & 98.89 & 98.89 \\ \hline \hline \end{tabular}
\end{table}