# Healthy Knee Kinematic Phenotypes Identification Based on a Clustering Data Analysis
## 4 Discussion  
The SPM analysis showed that the _global_ approach was more efficient than the _local_ approach to identify distinct clusters (Figure 4). Indeed, there was an overall statistical difference in all three planes (throughout 100% of the gait cycle). The statistical difference between clusters was limited to 80% of the gait cycle in the frontal plane based on the _local_ representation method (Figure 5). Notably, the optimum number of clusters determined by the CH-index was similar using both approaches. It is interesting to highlight that the mean ICC in the sagittal plane was lower than the two other planes and that this was true for the majority of the clusters. This result was predictable, as the bundle of curves is narrower for the sagittal plane (Figure 2b) than for the two other planes (Figure 2a,c). This makes the partition of the data into three groups more difficult and hence the obtained phenotypes more similar. The _global_ approach further led to a separation of the 3D kinematic data into homogeneous groups and meaningful phenotypes. Based on the _ICC_ values, the kinematical similarity between members of the same cluster was maximized in the frontal plane (i.e., varus-valgus alignment). Although the local approach gathers a representative list of parameters of interest, it performs less well than the global approach. Indeed, the latter keeps all the kinematic curves and thus naturally includes the totality of the information. The use of the _global_ representation that assumes high-dimensional data vectors (a vector of 300 dimensions corresponding to the concatenation of the 3 planes of kinematic data) is made possible by the utilization of the BIRCH algorithm. It is especially suitable for clustering very large datasets [35] and the first clustering algorithm to be proposed that handles noise \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Clusters** & **Frontal** & **Sagittal** & **Transverse** \\
**(Adduction/Abduction)** & **(Flexion/Extension)** & **(Int/External Rotation)** \\ \hline Cluster 1 & 0.74 & 0.54 & 0.39 \\ Cluster 2 & 0.51 & 0.27 & 0.60 \\ Cluster 3 & 0.76 & 0.34 & 0.60 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Intracluster correlation coefficient (ICC) using the _global_ representation. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Characteristics** & **All Participants** & **Cluster 1** & **Cluster 2** & **Cluster 3** \\ \hline Number of knees & 150 & 48 & 30 & 72 \\ Age (years) & \(33.11\pm 10.14\) & \(32.89\pm 9.69\) & \(31.62\pm 8.52\) & \(33.85\pm 11.04\) \\ Height (m) & \(1.69\pm 0.11\) & \(1.71\pm 0.12\) & \(1.68\pm 0.11\) & \(1.69\pm 0.10\) \\ Weight (kg) & \(70.75\pm 16.12\) & \(69.57\pm 14.68\) & \(72.56\pm 15.91\) & \(70.79\pm 17.23\) \\ BMI (kg/m\({}^{2}\)) * & \(24.42\pm 4.07\) & \(23.68\pm 3.43\) & \(25.61\pm 4.0\) & \(24.42\pm 4.41\) \\ Ratio Men/Women * & \(68/82\) & \(29/19\) & \(9/21\) & \(30/42\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Between-cluster differences on the demographic characteristics of the participants (units \(\pm\) SD). effectively [38]. These strengths made it very suitable for kinematic data analysis as it can handle high dimensional data compared to other clustering algorithms. This is due to the fact that when dimensionality increases, only a small number of dimensions are relevant for certain clusters. Thus, data in irrelevant dimensions may act as noise and mask the formation of the real clusters, which can be avoided with the BIRCH algorithm. The three clusters allow the occurrence of three specific phenotypes of knee kinematics. The first phenotype (Cluster 1, c.f. blue curve of Figure 4) describes participants walking with a predominant dynamic varus alignment (i.e., adduction) through the entire GC, starting with a mean varus angle at heel strike greater than 5\({}^{\circ}\). In the transversal plane, these participants accentuate their internal tibia rotation during the first half of their swing phase. Participants from Cluster 2 (c.f.