# A Discriminative-Based Geometric Deep Learning Model for Cross Domain Recommender Systems
## 5 Conclusions and Recommendations for Future Work  
In this paper, a discriminative geometric deep learning (D-GDL) algorithm for cross-domain recommender systems is proposed. This research was conducted to handle efficiently user recommendations in both single and cross-domain settings, particularly for  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multicolumn{2}{c}{**Movies**} & \multicolumn{2}{c}{**Books**} & \multicolumn{2}{c}{**Games**} & \multicolumn{2}{c}{**Perfumes**} \\ \cline{2-7}  & **70\%** & **95\%** & **70\%** & **95\%** & **70\%** & **95\%** & **70\%** & **95\%** \\ \hline DMF & 0.5883 & 0.5354 & 0.9735 & 0.9612 & 0.5895 & 0.5456 & 0.5515 & 0.5425 \\ \hline DLMF & 0.5698 & 0.5215 & 0.9674 & 0.9554 & 0.5745 & 0.5318 & & 0.5342 \\ \hline DeepMusic & 0.5989 & 0.5673 & 0.9845 & 0.9786 & 0.5992 & 0.5693 & 0.5772 & 0.5682 \\ \hline GDL & 0.5982 & 0.5513 & 0.9834 & 0.9765 & 0.6024 & 0.5623 & 0.5579 & 0.5496 \\ \hline CDL & 0.5668 & 0.5198 & 0.9664 & 0.9478 & 0.5782 & 0.5298 &objects in the non-Euclidean domain. The proposed D-GDL method achieves optimal dictionary and further enhances the power of discriminability of recommended systems. This thus enables the realization of geometric DL representation of the 3D non-linear features in both sparse and dense settings to effectively deal with cold-start and sparsity issues. The D-GDL extracts visual and geometric features from recommended objects using LCNN and LDCBN models for an optimal and efficient recognition performance in both single and cross-domain recommender systems. The models are pre-trained by depth image generation and voxelization instead of using down-sampling techniques. This is achieved by passing the extracted features through an improved kernel density estimator. With the extraction of geometric features, the recommended objects are transformed into voxel-like forms from mesh similar to the original recommended object, which eliminates the need for down-sampling. The depth images are used as input features in the visual feature extraction process, which also undergoes down-sampling due to the multi-image representation of recommended objects by way of projection. It can be seen from the experimental results that incorporating kernel and geometric deep learning into the structure of representation solutions for recommender systems inherently improves the performance accuracy compared with other baseline deep learning approaches. Furthermore, the proposed method is more computationally effective as a result, which increases its stability. Thus, close-form solutions are derived from the learning network for both sparse and dense settings. We, however, propose to incorporate weighted K-nearness neighbor into the structure of the kernel discriminative sparse representation to enhance the power of classification and recognition accuracy of recommender systems. Conceptualization, J.K.A., C.Z. and E.A.M. ; methodology, J.K.A. and E.A.M. ; software, J.K.A. and Y.C. ; validation, J.K.A., C.Z., J.O.-K. and E.A.M. ; writing--original draft preparation, J.K.A. and E.A.M. ; writing--review and editing, J.K.A., J.O.-K., C.Z., E.A.M. and Y.C. ; supervision, C.Z. ; funding acquisition, C.Z. All authors have read and agreed to the published version of the manuscript. This paper was supported by the key research and development plan (social development) projects BE2016630 and BE2017628 of Jiangsu province, the scientific research project Z201603 of Wuxi health and family planning commission. Not applicable. The authors declare no conflict of interest. Figure A2: Performance of D-GDL against the comparative approaches based on Recall vs. M for CiteULike-t dataset in the sparse setting. Figure A3: Performance of D-GDL against the comparative approaches based on Recall vs. M for netflix dataset in the sparse setting. Figure A5: Performance of D-GDL against the comparative approaches based on recall vs. M for CiteULike-a dataset in the dense setting.