## 1 Introduction  
Frequent knee pain affects approximately one adult in four, limiting function and diminishing quality of life. Knee pain in people 50 years or older is predominantly caused by osteoarthritis (OA) and it is a major reason for knee replacements among knee osteoarthritis patients in general [1; 2]. This severe impact on human health and the soaring financial cost justify the recent accrued research interest in computer-aided, objective knee disease diagnosis methods. Such methods would facilitate diagnosis and improve its accuracy so that the disease can be treated more effectively. Several studies have addressed the problem of distinguishing asymptomatic and OA groups [3; 4; 5; 6; 7] and assessing the severity of the OA disease according to the Kellgren Lawrence (KL) score [8]. However, none has considered distinguishing two classes of knee OA pathologies, namely femoro-rotulian (FR) and femoro-tibilal (FT), or further consider, in addition to FR and FT, category FR-FT representing the incidence of both diseases FR and FT in a same individual. Currently, three-dimensional (3D) knee kinematic data, which can be easily acquired in clinical settings [9], is the foremost, most effective description of knee movement to develop a classification algorithm, an essential component in objective, computer-aided, knee pathology diagnosis [3; 10]. Knee kinematic data measurements consist of three high-dimensional vectors that describe the temporal variation during a full gait cycle of locomotion of the three fundamental angles of knee rotation, namely the knee angles with respect to the sagittal, frontal, and transverse planes (Figure 1). The curse of dimensionality [11], the high intra-class variability and inter-class similarity in applications such as osteoarthritis pathology classification, make knee kinematic data categorization difficult [12]. These are the angles in three-dimensional (3D) space between the tibia and femur, corresponding to flexion/extension in the sagittal plane, abduction/adduction in the frontal plane, and internal-external rotation in the transverse plane. To measure and record these angles, the participant walks at a self-paced, comfortable speed on a conventional treadmill with the non-invasive knee attachment of the KneeKG system [13]. The setup is illustrated in Figure 2. The device is first calibrated to define the origin and axes of the 3D Cartesian reference system of the knee angle coordinates. The measurements produce three discrete kinematic curves, one for each angle. Curves are normalized by resampling to some fixed number of equally spaced points [9], one hundred in this study. Figure 1: A family of twenty knee kinematic data curves measured for a particular participant: (**a**) flexion/extension, (**b**) abduction/adduction, and (**c**) internal/external rotation. Each curve was interpolated and re-sampled from 1% to 100% (100 points) of the gait cycle. Moreover, 1% corresponds to the initial contact (IC) and 100% to the end of the swing phase. Figure 2: The KneeKG system. Although the KneeKG system is accurate, a participant knee angle variation pattern varies in general, sometimes significantly, from one cycle to another during locomotion, due to the inherently uneven nature of a walker's cadence. However, current studies implicitly attribute these variations to noise, of the same structure across knee pathologies and individuals, and which does not, therefore, inform gait classification. As a result, an individual's measurements are repeated a few times, typically for ten to fifteen times, and the average of these is taken to be the individual's knee movement representative data for subsequent classification. However, summarizing a population by its average removes information about spread that might be essential to classification.