# Healthy Knee Kinematic Phenotypes Identification Based on a Clustering Data Analysis
###### Abstract  
The purpose of this study is to identify healthy phenotypes in knee kinematics based on clustering data analysis. Our analysis uses the 3D knee kinematics curves, namely, flexion/extension, abduction/adduction, and tibial internal/external rotation, measured via a KneeKG(tm) system during a gait task. We investigated two data representation approaches that are based on the joint analysis of the three dimensions. The first is a _global approach_ that is considered a concatenation of the kinematic data without any dimensionality reduction. The second is a _local approach_ that is considered a set of 69 biomechanical parameters of interest extracted from the 3D kinematic curves. The data representations are followed by a clustering process, based on the BIRCH (balanced iterative reducing and clustering using hierarchies) discriminant model, to separate 3D knee kinematics into homogeneous groups or clusters. Phenotypes were obtained by averaging those groups. We validated the clusters using inter-cluster correlation and statistical hypothesis tests. The simulation results showed that the global approach is more efficient, and it allows the identification of three descriptive 3D kinematic phenotypes within a healthy knee population. kinematic data phenotype; gait analysis; healthy subjects; clustering analysis +
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patterns [2; 8; 9], other studies used 3D kinematic and kinetic to identify how age, sex, and body mass index (BMI) can influence normal gait [10]. However, both the high variability and high dimensionality of biomechanical data have forced many studies to limit their analyses to using simple descriptions, e.g., the mean or the local extrema. Indeed there have been various biomechanical patterns describing normal three-dimensional (3D) kinematic patterns of the knee (flexion/extension, abduction/adduction, and tibial internal/external rotation) during functional activities such as level walking [7; 11; 12; 13; 14; 15; 16; 17]--where a single normal pattern with bands of deviation is used as a reference to identify abnormalities in a patient's pattern [18]. Most previous studies have focused on assessing pathological rather than healthy asymptomatic kinematics [12]. Pattern recognition and machine learning techniques are typically used to characterize gait patterns. Various clustering techniques have been applied such as hierarchical clustering [19; 20; 21], \(c\)-means [22; 23; 24; 25], artificial neural networks [26], and fuzzy clustering [27]. Hierarchical clustering was used to distinguish five gait patterns in young subjects using 3D peak muscle powers [19; 20]. Hierarchical \(c\)-means clustering algorithms were employed to derive gait patterns [22], to classify kinematic data of patients following a stroke [23], and to identify gait pattern deviations in children with cerebral palsy [24; 25; 21]. In this same pathological population, fuzzy clustering was applied to normal and pathological subjects [27]. Similarly, artificial neural networks were used to distinguish between asymptomatic and osteoarthritis gaits [26]. Previous studies used only a small set of descriptors such as the mean of the measured data or local information to identify patterns in the data. The use of a small set of descriptors seriously limits the analysis and interpretation of the data due to the complexity of the kinematic data [28]. Therefore, the objective of this study is to identify healthy gait phenotypes using a clustering model that deals with high dimensional data analysis, i.e., the BIRCH (balanced iterative reducing and clustering using hierarchies) model. We investigated two data representation approaches based on a joint analysis of the three dimensions. The first, named _global approach_, considered the raw data without any dimensionality reduction. The second is a _local approach_, which is considered a large set of biomechanical parameters of interest extracted on the 3D kinematic patterns.