# Cross-Modal Manifold Propagation for Image Recommendation
## 4 Experimental Analysis
### Visual Manifold Construction  
Along with sparse user-image interactions, informative visual contents are involved in CMP to perform semantic-oriented recommendation. The visual distribution of images is more powerful due to their abundant amounts of information than due to the valuable but incomplete user-image correspondence. Similar to user interest manifold construction, [PERSON] et al. [45] evaluated the pairwise correlation between images according to commonly shared users. The more that common users like two images, the higher the correlation between the two images. The correlation of images measures the proportion of common users shared by the two images as follows:  
\[W_{ij}=\frac{\left|M_{i}\cap M_{j}\right|}{\sqrt{\left|M_{i}\right|\left|M_{j} \right|}} \tag{10}\]  
where \(M_{i}\) represents the set of users taking correspondence to image \(v_{i}\), \(\left|M_{i}\right|\) is the size of \(M_{i}\), \(\left|M_{i}\cap M_{j}\right|\) calculates the number of common users having a relationship with images \(v_{i}\) and \(v_{j}\) simultaneously, for \(i,j=1,2,...,n\). It is obvious that the manifold of images constructed on common shared users is extremely sparse due to the rare user-image correspondences. It might contain very limited information, which would not fit the large-scale visual recommendation problem. To verify the point, experiments compared image recommendation by VMP with two options of image manifold construction as follows.  
* Relationship-based manifold by commonly shared users between images over user-image relationships.
* Representation-based manifold on semantic visual correlations over AlexNet-based visual features.  
Figure 4 presents the _precision_ of top-N recommendation of visual manifold propagation with user-image relationship-based manifold and visual representation-based manifold. Figure 4 shows that VMP with representation-based manifold outperformed that  
Figure 3: _Precision_ of Top-N recommendation of user interest manifold propagation with user-image relationship-based graph and user representation-based graph.  
with a relationship-based manifold. Results verify that (1) visual features as representation-based performance are more powerful in capturing image distribution for users' visual records propagation, and (2) the sparse user-image relationship provides extremely limited information between images in front of the large-scale scope of images and their complicated contents. Because visual contents contain rich information, and AlexNet provides good representation in revealing images' semantic distribution, the representation-based visual manifold is able to offer a dense innate and detailed visual network. In addition, since semantic visual correlation produces a better construction of visual distribution, it enables the user preference propagation on the visual manifold to contain more detailed visual relationships in recommending images. It could intuitively play a role in compensating UMP module on local semantics. Therefore, the visual manifold propagation module employs dense visual distribution of high-level semantic features by AlexNet and different but better source data to build visual manifolds, as illustrated in Figure 2.