# A Polarity Capturing Sphere for Word to Vector Representation
## 2 Literature Review  
One of the earliest word vector embeddings is the work by [PERSON] et al. (2017), who published the Google word2 vec representations of words. Their method relies on the continuous skip-gram model for learning the vectors introduced in ([PERSON] et al., 2015). Finding vector representations that predict the surrounding words is the training goal of the skip-gram model. For computational efficiency, the authors have replaced the full softmax with three alternative choices, and evaluated the results for each: hierarchical softmax, noise contrastive estimation, and negative sampling. Moreover, subsampling of frequent words was introduced to speed up the training and leverage the accuracy of word representations. [PERSON] et al. (2019) have published another approach (called GloVe) of word vector modeling using a method that combines the benefits of the techniques of global matrix factorization and local context window. The authors have suggested the idea of learning the word vector with the ratios of co-occurrence probabilities rather than the probabilities themselves. The result is a new global log-bilinear regression model, where the model directly captures global corpus statistics. [PERSON] et al. (2019) developed a model known as fastText that is based on continuous bag-of-words (cbow) used in word2 vec ([PERSON] et al., 2015). The authors used a combination of known improvements to learn high-quality word vector representations. To obtain higher accuracy, the authors added position-dependent weights and subword features to the cbow model architecture. [PERSON] et al. (2017) developed a technique that aligns word vector representations from different sources such as word2 vec ([PERSON] et al., 2017) and GloVe ([PERSON] et al., 2015). The authors extend absolute orientation approaches to work for arbitrary dimensions. It can be noted that word2 vec ([PERSON] et al., 2017; [PERSON] et al., 2015), GloVe ([PERSON] et al., 2015), and fastText ([PERSON] et al., 2015) are distributional models for learning word vector representations. Words are assigned similarity relations based on co-occurrence in text. The limitation of these models is a weakness in distinguishing antonyms from synonyms because antonymous words such as \"good\" and \"bad\" very often occur in similar contexts so their learned vectors will be close. This way it may be hard to figure out whether a pair of words is a pair of synonyms or antonyms. However, such information is crucial for some applications such as sentiment analysis. On the other hand, our approach is a simple relaxation algorithm that takes into account learning word vectors that are able to distinguish between word relations such as synonyms, antonyms, and unrelated words. It is based on embedding the vectors on the sphere. The sphere provides a natural setting for this task, because antonyms can be placed on opposite sides of the sphere. In contrast, most methods embed the vectors in the space \(R^{n}\), which does not provide a natural way of modeling opposites. The aforementioned models rely on corpus data of huge sizes to guarantee the effectiveness of the generated vectors. In our approach, we make use of the available experts' lexicons, dictionaries, and thesauruses, and so the similarity relations are fairly accurate, because of the expert knowledge used to construct these lexicons. Other works include [PERSON] et al. [22], who introduced density-based distributed embeddings by learning representations in the space of Gaussian distributions. [PERSON] et al. [23] focused on incorporating morphological, syntactic, and semantic knowledge with deep learning to obtain more efficient word embeddings. [PERSON] et al. [24] used the category information associated with the community question answering pages as metadata. These metadata are fed to the skip-gram model to learn continuous word embeddings, followed by applying Fisher kernel to obtain fixed length vectors.