## 2 Background and Literature Survey
### Recommendation Systems
All three said measures lack some co-rated items problem in a sparse rating dataset. In such a scenario,Patra et al. have introduced a SeM using the Bhattacharyya coefficient when few or no items are co-rated [4]. Their proposed SeM has been utilized to attain the overall co-relations among users, and local and global rating data are used. In literature, there are many prominent SeMs and prediction methodologies applied in the CF-based RS. The following Tables 3 and 4 represent the vital references and computational equations of SeMs and prediction approaches. Here, BC, CS, ED, ACS, SC, and PC denote Bhattacharyya Coefficient, Cosine Similarity, Euclidean Distance, Adjusted Cosine Similarity, Spearman Correlation, and Pearson Correlation respectively. The similarity of users \(u\) and \(v\) is determined by Cor(\(u\),\(v\)). Jacc(\(u\),\(v\)) notify the similarity of users \(u\) and \(v\) by Jaccard Similarity. The Bhattacharyya coefficient is used by BC(\(i\),\(j\)) to determine how similar two items \(i\) and \(j\) are, whereas \(loc(r_{u},r_{v})\) identifies the local similarity between users \(u\) and \(v\) with regard to items \(i\) and \(j\). Users \(u\) and \(v\)'s ratings on item \(i\) are shown by \(R_{u,i}\) and \(R_{v,i}\) respectively, whereas, \(\bar{R}_{u}\) and \(\bar{R}_{v}\) indicate, accordingly, the average rating of users u and v. \(k_{u,i}\) and \(k_{v,i}\) indicate the order in which users \(u\) and \(v\) rated item \(i\), whereas, \(\bar{k}_{u}\) and \(\bar{k}_{v}\) represent accordingly, the average rank based on the ratings of users \(u\) and \(v\). Here, \(\hat{r_{ui}}\) represents the predicted value of item \(i\) for active user \(u\). \(\sigma_{i}\) and \(\sigma_{j}\) are the standard deviation of rating of item \(i\) & \(j\) respectively. In this paper, we use BC for the comparative analysis because similarity measure using BC provides a more accurate recommendation, as discussed earlier. Table 5 represents a list of notable literature that discusses modified SeM. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Prediction Approach and References** & **Equation** \\ \hline
**Mean Centering (MC)** & \(\hat{r_{ui}}=\hat{r_{u}}+\frac{\sum_{c\in N_{u}(u)}sim(u,v)(r_{ui}-\sigma_{v})}{ \sum_{c\in N_{u}(u)}sim(u,v)}\) \\ \hline
**Weighted Average (WA)** & \(\hat{r_{ui}}=\frac{\sum_{c\in N_{u}(u)}sim(u,v)r_{ui}}{\sum_{c\in N_{u}(u)}sim \left|sim(u,v)\right|}\) \\ \hline
**Z-Score (ZS)** & \(\hat{r_{ui}}=\hat{r_{u}}+\sigma_{u}\frac{\sum_{c\in N_{u}(u)}sim(u,v)(r_{ui}- \hat{r_{v}})/\sigma_{v}}{\sum_{c\in N_{u}(u)}sim(u,v)}\) \\ \hline
**\(\hat{r_{ui}}=\hat{r_{u}}+\sigma_{v}\frac{\sum_{c\in N_{u}(u)}sim(u,v)(r_{ui}- \hat{r_{v}})/\sigma_{v}}{\sum_{c\in N_{u}(u)}sim(u,v)}\)** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Prediction Approach. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Co-Relation Metric** & **Reference** & **Equation** \\ \hline (BC) & [4] & \(Cor(u,v)=\frac{\sum_{c\in N_{u}}\sum_{c\in N_{u}}BC(i,j)loc(r_{u},r_{v})}{ \sum_{c\in N_{u}(R_{u})}sim(R_{u},r_{v})\sum_{c\in N_{u}(R_{u})}}\) \\ \hline (CD) & [33] & \(Cor(u,v)=\frac{1}{\sqrt{\sum_{c\in N_{u}(R_{u}-R_{v