## 4 Vibroarthrography of the Knee Joint
### Feature Extraction and Classification
#### 4.3.1 Feature Extraction and Selection
The shape factor (SF) can be defined as a dimensionless function that is based on the form and distribution of signal attributes, which include peaks and troughs in the time domain [126]. The coefficient value is higher for signals of people with knee joint pathologies compared to regular VAG signals. The impulse factor (IF) is useful in understanding the occurrence of abnormal peak levels in vibration signals [127]. The use of IF can provide information on the occurrence of abnormal friction between the knee joint surfaces in the VAG signals. Margin factor (MF) shows higher values for abnormal VAG signals compared to normal signals. The crest factor (CF) is considered appropriate for signals characterising pathological behaviour of the knee joint. Despite this, in that work, the crest factor showed a correlation of \(<\)10% with the categorisation of VAG signals. In addition to the time domain features, spectral domain features were also extracted, such as the spectral mean and spectral peak, spectral flux, spectral slope, spectral skewness, and spectral kurtosis. The measure of the quantitative change in spectral shape is the spectral flux. Its output range is dependent on the frequency transformation as well as normalisation of the vibration signal. Low spectral flux is observed when there is no abrasion of moving parts causing vibrations, as well as spikes at the vibration peaks. Another important feature is the spectral slope, which concerns the distribution of energy at different frequencies. Spectral slope can be defined as the difference in amplitude between low and high frequencies. It is used to assess the knee joint condition where lower signal frequencies indicate smooth joint movements, while higher frequencies indicate pathological changes in the knee joint. The selection of extracted features in the time domain and spectral domain was performed using the mutual information test, Chi-square test, and ANOVA F-test. The obtained results indicated lower values of the features of healthy people compared to people with knee joint problems. [PERSON] et al. [59] also distinguished such features as the crest factor, impact factor, shape factor, and kurtosis described above, as well as the straightened average value (SA), root-mean-square (RMS), peak value (PV), peak-to-peak value (PPV), and variance (VAR). Straightened average value (SA) is used to assess the signal level regardless of its change in direction. It is especially useful in the analysis of oscillatory signals. Root-mean-square (RMS) is a measure of the energy of a signal. It is a key tool in evaluating signals with variable amplitude. Peak value (PV) is defined as the maximum value of the signal amplitude during its duration. It is used to assess the amount of fluctuation that may occur in the signal. Peak-to-peak value (PPV) can be defined as the difference between the highest positive and negative values in a signal. It is important in evaluating signals with variable amplitude. The last-mentioned determinant is variance (VAR), which can be described as a measure of the dispersion of the signal. High variance is directly related to the occurrence of large changes in signal amplitude, which, in turn, may result from the presence of interference. Statistical analysis was performed to determine the occurrence of statistically significant differences between the signal features for the recorded signals in the healthy group and in the group of people with knee OA. For this purpose, the Kolmogorov-Smirnov, Lilliefors, and Shapiro-Wilk tests were performed to determine whether the discriminant values of the acoustic signals were normally distributed in both groups [128; 129]. The [PERSON]'s, [PERSON]'s, and Brown and Forsyth tests were used for the analysis of equality of variances. The Student's t-test was used to test the equality of variances and normality of the distribution; for results with a normal distribution but a lack of equality of variances, the Cochran-Cox test was used [130].