## 4 Discussion  
The purpose of this study was to investigate a generalization of the Kohonen neural network that encodes samples of multidimensional data vectors rather than single such vectors, and apply it to knee kinematic data for osteoarthritis pathology classification. Knee kinematic data, which describe the temporal variation of each of the three fundamental angles of knee three-dimensional rotation (flexion/extension angle, with respect to the sagittal plane, abduction/adduction angle, with respect to the frontal plane, and internal/external angle, with respect to the transverse plane) during a walking cycle, are recorded in the form of a small sample of repeated measurements. To confront the curse of dimensionality [11], the original high-dimensional kinematic data was mapped to a significantly lower dimensional space by Daubechies Db1 wavelet decomposition at level 6 to yield representation vectors of dimension 4. The training input of the sample-encoding Kohonen network consisted of this 4-dimensional representation applied to the abduction/adduction and internal/external original kinematic data. The selection of these two reference planes (discarding the third) has been determined by recognition rate maximization. This result is consistent with findings in previous studies on biomechanical data of knee pathologies. In these studies, several biomechanical parameters measured in the sagittal plane, related to the varus or valgus thrust during the loading phase, have been identified as the most useful parameters and serve diagnostic as biomarkers [8; 39]. In addition, the range of motion of the abduction/adduction angle during loading phase has been identified as a component of burden of disease biomarkers to discriminate between moderate OA  
Figure 7: Comparison of the proposed sample-encoding Kohonen network method with other classifiers using a leave-one-out cross validation. grades and severe OA [8]. In addition, a study which compared a set of biomechanical parameters of patients categorized as sufferers of moderate to severe OA grades [39; 40], reported that both the peak knee adduction moment and the knee adduction angular impulse increased with knee radiographic grade. Network training and the ensuing classification function of the network both use the Hotelling \(T^{2}\) statistic to evaluate the underlying similarity of pattern samples, affording robust class membership assignments to observed data. Applied to knee osteoarthritis pathology discrimination, the scheme improves on the state-of-the-art results by other methods. The classification rate reached 90.47% for the classification of FR and FT classes and 71.4% for the classification of FR, FT and FR-FT classes. As [PERSON] and [PERSON] and others [11] have argued, the small size of this application dataset instructs us to use leave-one-out cross validation in the experimental evaluation of classification accuracy. There are two basic reasons for the choice of leave-one-out validation over \(k\)-fold cross validation with \(k\
eq n\), where \(n\) is the number of elements in the dataset (leave-one-out validation is \(n\)-fold cross validation). One obvious reason is that, while every data element serves testing once, training is done with as much data as possible, therefore using as much information about the underlying data classes as available to give a classifier more representative of the classes than it would otherwise be. This is so because when \(n\) is small and \(k\
eq n\), the smaller training set, due to the larger test set, is more likely to cause class information to be left out of classifier design. Another somewhat secondary reason to prefer leave-one-out validation is that proper random choice of folds for \(k\
eq n\) may take a great deal of computation and produce unbalanced test set sizes, causing some data elements to dominate testing and bias classification results. However, this is not a serious issue in practice because one may use pseudo-random routines, such as ones found in Matlab, that produce balanced test folds.