# A Polarity Capturing Sphere for Word to Vector Representation
## 5 Results and Discussion
### Word Similarity  
Table 2 contains a number of word pairs where the corresponding similarity scores are obtained by the proposed word embedding. The similarity score is computed as the dot product between unit vectors. We have compared our scores with the scores of other published pre-trained word vectors: word2 vec [17], GloVe [19], and fastText [20]. The number of dimensions of the vectors in word2 vec, GloVe, and fastText is 300, while the dimension of the vectors in our approach is 50. The reason for selecting a number of dimensions of 50 is that more dimensions lead to sparser space, and more overfitting. N/A means that one or both of the words in the given pair have no pre-trained vectors in the method considered. In the table we have included word pairs from different categories:  
* Synonyms that occur in the training vocabulary of the proposed method. * Synonyms that are not part of the training vocabulary of the proposed method (marked with the
* symbol in the table). * Antonyms that are part of the training vocabulary. * Antonyms that are not included as part of the training vocabulary (also marked with the
* Unrelated words that occur in the training vocabulary. * Unrelated words that are not part of the training vocabulary (marked with the
* Word pairs that belong to a certain category (e.g., countries). Note that the pairs that are not part of the training set constitute an unbiased out of sample test, since the algorithm has not seen them while training. From Table 2, we can observe several interesting facts:  
1. By human judgment, the proposed algorithm seems to be more successful in capturing the similarity between the different words. For example, the pairs \"happy-joyful\", \"amusing-happy\" and \"district-county\" are close synonyms, and our algorithm manages to assign a high similarity. Opposing algorithms give low similarity scores around 0.5 or so. 2. For the antonyms, our algorithm assigns rightly negative numbers. For example, the pairs \"modern-outdated\" and \"unlike-same\" are assigned similarities lower than \(-0.8\). The competing algorithms assign similarities in the range of about 0.3 to 0.68, not really signaling that these words are antonyms. 3. For unrelated words, the proposed embedding generally gives them similarities close to zero. For example, the pairs \"array-again\", \"useful-wash\" and \"decent-morning\" are given respectively 0.294, 0.195, and 0.027, which are reasonably close to zero. 4. The competing algorithms are not very successful in differentiating antonyms from unrelated pairs. They give them all comparable scores. For example, the antonyms \"modern-outdated\" and \"unlike-same\", and the unrelated pairs \"array-again\", \"useful-wash\" and \"decent-morning\" are given similarities in the same range. It is not clear from the scores whether the pair is an an antonym or an unrelated pair. Additionally the pair \"yes-no\" is the most basic antonym, and in spite of that, the competing algorithms do not give them a zero score. 5. An antonymous pair such as \"happy-unhappy\" is given a high similarity score in all the other three competing approaches. Thus it is treated the same as a synonymous pair while it is given a negative similarity score in our approach. 6. An antonymous pair such as \"decelerate-speed\" is given a low similarity score in all the other three approaches, and thus is treated the same as an unrelated pair while it is given a negative similarity score in our approach. In all the four approaches, the \"country-capital\" pairs have close similarities. * In all the four approaches, the \"country-nationality\" pairs have close similarities. * The pair \"Japan-Greece\" has a lower similarity score than the pair \"Japan-China\", although both pairs are country pairs. This is due to the fact that Japan and China have more properties in common (both are Asian countries, and are distance-wise close to each other). * A combination such as \"African-country\" is not found in any of the other three vocabularies.