## 6 Results and Discussion
### Normalized Representation of Sentence Vectors  
This experiment was performed in three phases. Initially, _Avg-SOW_ and Avg-DOW methods were used, which are based on word averaging. In the second phase, we used _L1-AvgSOW_, _L1-AvgDOW_, _L2-AvgDOW_ and _L2-AvgSOW_ methods based on normalized average word vectors. In the third phase, normalized sum and difference of word vectors were used to represent sentences that are, _L1-SOW_, _L1-DOW_, _L2-SOW_ and _L2-DOW_. Normalized representation of sentence vectors achieved highest F1 scores in the ACD problem as compared to the best systems. Experimentation results are shown in Tables 5 and 6 (proposed methods are in bold letters). Figure 4: Loss and training plots. ### Normalized Representation of Sentence Vectors  
In un-normalized representation of sentence vectors, we combined all word vectors of a sentence using two arithmetic operators (i.e., addition and subtraction). This is a simpler way of representing a sentence. Two types of analysis were performed under un-normalized methods. In the first experiment, two methods were used, \(SOW\) and \(DOW\) that are based on the sum and difference of word vectors, whereas in the second experiment, concatenation of \(SOW\oplus DOW\) was used. All methods in this category outperformed the previous results in the ACD task. Results are shown in Tables 7 and 8 (proposed methods are in bold letters). Our experimental studies showed some interesting results and many of our proposed methods outperformed the state-of-the-art approaches in the ACD task. Moreover, our results show that the \(L1\)-norm for obtaining a sentence vector performed better than the \(L2\)-norm. In our research, we also used the difference of the word vectors in parallel with the sum of the word vector methods. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Precision** & **Recall** & **F1 Scores** \\ \hline _Avg-SUM_ & 79.16 & 90.19 & 84.31 \\ _Avg-DOW_ & 74.65 & 89.67 & 81.47 \\ _L1-AvgSOW_ & - & - & - \\ _L2-AvgSOW_ & 79.81 & 90.32 & 84.74 \\ _L1-AvgDOW_ & 93.85 & 94.58 & 94.21 \\ _L2-AvgDOW_ & 75.55 & 92.12 & 83.02 \\ _L1-SOW_ & 95.80 & 94.19 & 94.99 \\ _L2-SOW_ & 80.33 & 93.80 & 86.54 \\ _L1-DOW_ & 95.25 & 93.29 & 94.26 \\ _L2-DOW_ & 75.26 & 90.70 & 82.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of normalized representation of sentence vectors on SemEval-2015 dataset. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Precision** & **Recall** & **F1 Scores** \\ \hline \(SOW\) & 77.04 & 75.90 & 76.40 \\ \(DOW\) & 76.26 & 74.83 & 75.54 \\ \(SOW\oplus DOW\) & 75.09 & 76.31 & 75.70 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results of un-normalized representation of sentence vectors on SemEval-2016 dataset. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Precision** & **Recall** & **F1 Scores** \\ \hline \(SOW\) & 90.27 & 89.80 & 90.03 \\ \(DOW\) & 93.14 & 92.90 & 93.02 \\ \(SOW\oplus DOW\) & 89.28 & 91.35 & 90.30 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Results of un-normalized representation of sentence vectors on SemEval-2015 dataset. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Precision** & **Recall** & **F1 Scores** \\ \hline _Avg-SUM_ & 66.66 & 77.79 & 71.80 \\ _Avg-DOW_ & 62.88 & 79.81 & 70.34 \\ \(L1\)-AvgSOW_ & 74.62 & 73.21 & 73.91 \\ \(L2\)-AvgSOW & 65.82 & 77.52 & 71.19 \\ \(L1\)-AvgDOW & 75.20 & 73.88 & 74.54 \\ \(L2\)-AvgDOW & 65.74 & 80.08 & 72.20 \\ \(L1\)-SOW & 77.41 & 72.40 & 74.82 \\ \(L2\)-SOW & 69.65 & 78.46 & 73.79 \\ \(L1\)-DOW & 77.46 & 73.08 & 75.20 \\ \(L2\)-DOW & 67.88 & 77.65 & 72.44 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of normalized representation of sentence vectors on SemEval-2016 dataset. The difference of word vectors has shown some promising results. Consequently, our investigation shows that the proposed vector representation methods for sentence representation are suitable for the aspect category classification task.