## 3 Proposed Method
### Proposed Algorithm  
In multi-view score propagation, the criterion of FME becomes:  
\[g(\mathbf{F},\,\mathbf{Q},\,b)=\mathbf{F}^{T}\,\hat{\mathbf{L}}\,\mathbf{F}+( \mathbf{F}-\mathbf{Y})^{T}\,\mathbf{U}\,(\mathbf{F}-\mathbf{Y})+\mu\,(|| \mathbf{Q}||^{2}+\gamma\,||\mathbf{X}^{T}\mathbf{Q}+\mathbf{1}\,b-\mathbf{F}|| ^{2}) \tag{9}\]  
In the above equation, \(\hat{\mathbf{L}}\) is given by Equation (8), and the data matrix \(\mathbf{X}\) is simply the concatenation of the data matrices in all views. Thus, \(\mathbf{X}=[\mathbf{X}_{1};\ldots;\mathbf{X}_{M}]\)  
If \(\hat{\mathbf{L}}\) is known (i.e., \(\mathbf{L}_{corr}\) is known) then the closed-form solution of Equation (9) giving the optimal \(\mathbf{F},\mathbf{Q}\) and \(b\) is as follows. \[\mathbf{Q}=\gamma\,[\gamma\,\mathbf{X}\mathbf{H}_{c}\,\mathbf{X}^{T}+\mathbf{I }]^{-1}\mathbf{X}\mathbf{H}_{c}\mathbf{F} \tag{10}\]  
\[b=\frac{1}{n}[\mathbf{F}^{T}\mathbf{1}-\mathbf{Q}^{T}\mathbf{X}\mathbf{1}] \tag{11}\]  
\[\mathbf{F}=(\mathbf{U}+\hat{\mathbf{L}}+\mu\,\gamma\,\mathbf{H}_{c}-\mu\, \gamma^{2}\,\mathbf{N})^{-1}\mathbf{U}\,\mathbf{Y} \tag{12}\]  
where \(\mathbf{N}=\mathbf{X}_{c}^{T}\,\mathbf{X}_{c}\,(\gamma\,\mathbf{X}_{c}^{T}\, \mathbf{X}_{c}+\mathbf{I})^{-1}\). \(\mathbf{X}_{c}\) and \(\mathbf{H}_{c}=\mathbf{I}-\frac{1}{n}\mathbf{1}\mathbf{1}^{T}\) are the centred data matrix and the centring matrix, respectively. Finally, our proposed algorithm proceeds as follows. After initialization of the soft scores of all images \(\mathbf{F}\), Equations (7), (8) and (12) are iterated until the solution stops to change or the maximum number of iterations is reached. In each iteration, the correlation graph \(\mathbf{W}_{corr}\) changes with the predicted scores and the associated score similarities. After each iteration, the updated \(\hat{\mathbf{L}}\) is used in the cost function of the proposed multi-view FME of Equation (9). The final solution is the predicted scores as well as a linear mapping model that allow to recover the score of unseen images. The flowchart of our proposed approach is shown in Figure 2. In the specific case of this work, Figure 2 shows the pipeline of this algorithm considering two deep feature similarity graphs and one geometric feature similarity graph. In each iteration, the prediction matrix \(\mathbf{F}\) obtained from FME is used to update the correlation graph. The projection matrix \(\mathbf{Q}\) obtained after \(t\) iterations, and the bias vector \(\mathbf{b}\) can be used to estimate the beauty scores of the unseen samples using the following:  
\[f_{unseen}=\mathbf{x}_{unseen}^{T}\,\mathbf{Q}+b \tag{13}\]The proposed MSMFME algorithm is summarized in Algorithm 1. ```
Input: 1. Vgg-fc6 feature matrix \(\mathbf{X}_{fc6}=[\mathbf{x}_{fc6}^{1},\mathbf{x}_{fc6}^{2},\ldots,\mathbf{x}_{ fc6}^{n}]\)  2. Resnet-50 feature matrix \(\mathbf{X}_{resnet}=[\mathbf{x}_{resnet}^{1},\mathbf{x}_{resnet}^{2},\ldots, \mathbf{x}_{resnet}^{n}]\)  3. Geometric feature matrix \(\mathbf{X}_{geo}=[\mathbf{x}_{geo}^{1},\mathbf{x}_{geo}^{2},\ldots,\mathbf{x }_{geo}^{n}]\)  4. Score beauty vector \(\mathbf{Y}=[y_{1},y_{2},\ldots,y_{l},0,0,0,\ldots]\) (\(l\) images are scored)  5. Parameters \(\mu\), \(\gamma\) Output:  Prediction scores for all images \(\mathbf{F}=[f_{1},f_{2},\ldots,f_{l},f_{l+1},f_{l+2},\ldots,f_{n}]\). Process:  Construct three different data graphs \(\mathbf{W}_{fc6}\), \(\mathbf{W}_{resnet}\), \(\mathbf{W}_{geo}\) (\(M=3\));  Calculate their corresponding Laplacian matrices \(\mathbf{L}_{fc6}\), \(\mathbf{L}_{resnet}\) and \(\mathbf{L}_{geo}\)  Set the data matrix to \(\mathbf{X}=[\mathbf{X}_{fc6};\mathbf{X}_{resnet};\mathbf{X}_{geo}]\)  Initialize the soft score vector \(\mathbf{F}=\mathbf{Y}\) for t = 1: Maxiteration  Generate the correlation graph \(\mathbf{W}_{corr}\) based on \(\mathbf{F}\) using Equation (7). Obtain the global Laplacian \(\hat{\mathbf{L}}\) by fusing the \(M+1\) Laplacian matrices (Equation (8)).