# A Polarity Capturing Sphere for Word to Vector Representation
## 5 Results and Discussion
### Antonymy Detection  
We have applied our approach on answering the closest-opposite GRE questions, collected in [27; 30]. The GRE, or Graduate Record Examinations, is a worldwide exam needed for admission to graduate schools. The verbal part has a group of multiple choice questions that seek the closest-opposite. The 162 questions of the development set are used as a part of our training vocabulary; i.e., the words together with the correct answers are added to the training vocabulary as antonymous pairs. On the other hand, both the 950 questions and the 790 questions datasets are used as test sets (i.e., their pairs do not exist in our training set).  
We applied our word embedding method to compute the similarities between the word in question and all candidate answers, and selected the answer that is closest to \(-1\), signifying an  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Word1** & **Word2** & **Sphere (Our Approach)** & **Word2 vec**[17] & **GloVe**[19] & **FastText**[20] \\ \hline active & passive & \(-0.916\) & 0.436 & 0.577 & 0.678 \\ happy & unhappy & \(-0.912\) & 0.613 & 0.565 & 0.767 \\ young & old & \(-0.841\) & 0.417 & 0.573 & 0.583 \\ youth & old & \(\ast-0.357\) & 0.212 & 0.384 & 0.392 \\ youth & elderly & \(-0.674\) & 0.215 & 0.39 & 0.499 \\ valuable & valueless & \(\ast-0.912\) & 0.334 & 0.262 & 0.614 \\ recall & forget & \(\ast-0.907\) & 0.3 & 0.532 & 0.567 \\ education & ignorance & \(-0.854\) & 0.2 & 0.306 & 0.487 \\ complex & easy & \(\ast-0.769\) & 0.213 & 0.439 & 0.453 \\ beginning & deadline & \(-0.73\) & 0.22 & 0.447 & 0.348 \\ modern & outdated & \(\ast-0.933\) & 0.404 & 0.427 & 0.528 \\ unlike & same & \(\ast-0.957\) & 0.299 & 0.681 & 0.482 \\ grow & eradicate & \(\ast-0.858\) & 0.241 & 0.308 & 0.491 \\ certainty & uncertainty & \(-0.931\) & 0.492 & 0.617 & 0.706 \\ truth & lying & \(\ast-0.766\) & 0.237 & 0.468 & 0.479 \\ daring & coward & \(\ast-0.676\) & 0.196 & 0.233 & 0.432 \\ decelerate & speed & \(\ast-0.843\) & 0.212 & 0.22 & 0.385 \\ \hline \hline \end{tabular}
\end{table}
Table 2: _Cont._  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Approach** & \multicolumn{2}{c}{**MC30**} & \multicolumn{2}{c}{**RG**} \\ \hline  & **Sp** & **RMSE** & **Sp** & **RMSE** \\ \hline Sphere (our approach) & **0.91** & **0.18** & **0.9** & **0.15** \\ word2 vec & 0.8 & 0.3 & 0.76 & 0.29 \\ GloVe & 0.79 & 0.27 & 0.82 & 0.25 \\ fastText & 0.83 & 0.24 & 0.84 & 0.22 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Results of human-judged datasets.  
antonym. We have computed the precision, recall, and F-score as given in [27], so that we could make comparisons with the numbers given in the competing methods. They are given by  
\[Precision(P)=\frac{\text{Number of questions answered correctly}}{\text{Number of questions attempted}} \tag{14}\]  
\[Recall(R)=\frac{\text{Number of questions answered correctly}}{\text{Total number of questions}} \tag{15}\]  
\[F\text{-}score=\frac{2\times P\times R}{P+R} \tag{16}\]  
In our case we note that the precision = recall = F-score; this is because our approach attempted all the questions. All the words that exist in the questions and in the candidate answers have corresponding vectors in our word embedding method.  
Furthermore, we compared our results with the best results recorded in [27; 29; 30; 31; 32; 34] that use the same dataset. From Table 4, it is shown that we achieved the best precision, recall, and F-score for the development set. We achieved the second best scores in both test sets after [34]; however, the dimension of their vectors is 300 while the dimension of our vectors is only 50. As mentioned earlier, their model is trained such that there is no differentiation between antonymous pairs and unrelated pairs, as both will have low similarity scores. Moreover, we were able to compare our results with [34] only on antonymy detection as the authors did not include the performance of their vectors on synonyms or unrelated words.