# New Vector-Space Embeddings for Recommender Systems
## 4 Evaluation and Results
### Recommendation  
For the recommendation problem we used the \"Online Retail\" dataset [54] as a case study. This dataset includes customers' transactions for an online retailer that focuses on selling all-occasion gifts. These transactions occurred between 1 December 2010 and 9 December 2011. The dataset contains 541,909 instances where each instance has the following attributes:  
* InvoiceNo: invoice number, which is a unique number identifying each transaction. * StockCode: item/product code, which is a unique number identifying each product/item. * Description: item/product descriptive name. * Quantity: quantity of item/product per transaction. * InvoiceDate: day and time of transaction. * UnitPrice: price of item/product. * CustomerID: customer number, which is a unique number identifying each customer. * Country: country where customer resides. We parsed the data to obtain the unique customers, there was a total of 4372 customers. Next, we divided the data into training and test sets where 80% and 20% of the customers constituted the training and test sets, respectively. The training set was used to provide input to the proposed item embedding algorithm where the items' vectors of dimension 20 were learned. After obtaining vectors for items, we recommended items for customers. For testing, the most recent transaction(s) of each customer were excluded from any computations in order to be used for assessment. These transactions were not regarded as part of the customer's history but were regarded as the customer's future transactions to be compared against the recommended items by the system. The number of such transactions was taken as one (i.e., the most recent customer's transaction) in one experiment, and two (i.e., the most recent two customer's transactions) in another experiment. These numbers were chosen as indicated in this dataset. The number of transactions per customer had an average of seven and a median of four. Finally, to assess the performance, the items in the excluded transactions were compared with the recommended items to determine the hit rate, which is defined as:  
\[HitRate=\frac{\sum_{ecC}HitRate_{c}}{C}, \tag{9}\]  
where  
* \(HitRate_{c}\) equals 1 if there is a hit for customer \(c\) and 0 otherwise. A hit is determined when at least one item in the set of recommended items matches one of the items in the true most recent transaction(s) of customer \(c\). * \(C\) is the total number of customers in the test set. Moreover, we built another model that learns vectors (also of dimension 20) for items using the word2 vec embedding approach [16]. This model was trained such that the customer's transaction was regarded as the sentence while the item was regarded as the word. Therefore, the customers' transactions were fed to the model the same way sentences were fed during training word2 vec on text corpora. The aim of building such a model was to compare the performance of the two models: using our sphere embedding approach and using the word2 vec embedding approach. We performed a number of experiments changing \(k\), which represents the number of items to recommend. Table 3 shows the performance (hit rate) of both models (larger numbers mean better recommendation). From Table 3, the following observations can be stated:  
* As \(k\) increases, the \"HitRate\" increases, because there would be more chance that the user's purchase is included in the recommended basket of items. * Our approach outperforms word2 vec for all \(k\) values. A point that is worth mentioning is that, when using the word2 vec approach, the user's positive taste can be represented, but not the user's negative taste. This is because vectors are learned for items in the users' history transactions. The question here is how such model can represent the user's negative taste, that is, the items that the user marks as uninteresting or marks as a dislike. This negative taste also plays a great role in the items to be recommended.