## 3 Results and Discussion
The correlation between C1 and C2 is strongly negative. The correlation between C3 and each one of C1 and C2 is negligible because the angle between each pair of clusters (C1, C3) and (C2, C3) is apparently right, so that the correlation is almost null. CCA, which is a linear subspace analysis, involves the projection of two variable sets \(\mathbf{X}\) and \(\mathbf{Y}\) onto a joint subspace such that the correlations between the projected vectors of variables are maximized. The correlation between clusters (between all variables) is quantifying, as explained before, by means of the first two canonical correlations values corresponding to the first two dimensions which are equal to 0.80 and 0.79, respectively. Figure 1: Correlation variable representation with a threshold \(=\) 0.35. The radius of the inner circle represents the correlation with a cut-off \(=\) 0.5. The representation of cross-correlation variable is shown by the heatmap in Figure 2 and relevance network in Figure 3. For the hierarchical clustering in the heatmap, the Euclidean distance was used as proximity measure and the [PERSON]'s method was used for the agglomeration hierarchical clustering procedure [33, 34]. The correlation between groups of the variable \(\mathbf{X}\) and \(\mathbf{Y}\) is represented by a colored block. The two clusters C1 and C2 identified in Figure 1 are clearly highlighted in Figure 2 by the blue and red blocks that correspond to the two long sections of the dendrograms and are summarized in a single subnetwork in Figure 3, which visualizes simultaneously positive and negative correlations of variables to represent only the strongest cross-correlations. Figure 3: Cross-correlation variable representation by relevance networks with a cut-off \(=0.35\). Figure 2: Cross-correlation variable representation by heatmap with a threshold \(=0.35\). The red and blue color indicate the positive and negative correlation, respectively. The representation of canonical variables (Figure 1) and of the cross-correlation variables (Figures 2 and 3) highlights the importance of a combined analysis. For instance, the cluster C3 in Figure 1, which combines the pair of parameters \(\{Y3,X46\}\), is not visualized by the cross-correlation variable representations in Figures 2 and 3 because of the neglected correlation between C3 and the other two clusters C1 and C2. For that reason, the combination of correlation and cross-correlation variable representations implies to consider the cluster 3 with the clusters 1 and 2 as the groups of variables highlighting the highest correlations. From a clinical point of view the cluster C3 is important. As, it emphases the relationship between the BMI and internal/external tibial rotation angle at the end of push-off phase. Following the combination of these representations, the correlated clinical and kinematic parameters are described in Table 2. Cluster C1 regroups kinematic parameter in the sagittal plane related to flexion/extension ROM (\(X_{52}\)) and transverse plane, which include only the tibial rotation variation value between the end of loading phase and initial contact. Each of these parameters in sagittal and transverse plane are highly and positively correlated with the functional tests indicating the active knee flexion ROM (\(Y_{37}\)) and flexion contracture (\(Y_{38}\)) (or extension ROM). The couple of parameters that is important is the one that connects the flexion/extension ROM (\(X_{52}\)) with the index of joint extension ROM (\(Y_{38}\)), this corresponds to the red rectangle in the heatmap (2) where correlation are higher than 0.5. The second cluster C2 regroups five clinical parameters and seven kinematic parameters.