# On Training Road Surface Classifiers by Data Augmentation
## 4 Experiments  
First, let us indicate the main elements of the experimental setup. All 10 channels (described in the previous section) were sampled at 48 KHz. The moving time window duration was selected to be 1.5 s, and the shift between two consecutive windows was 0.1 s. These values were selected in a rather experimental manner to maximize the classification accuracy. In every location of the time window, 56 features were extracted for every channel. Given that most of the channels are audio channels or vibration channels, our tests considered several spectral features that are commonly used for audio classification [33], namely:  
* Average power across all frequency bands. We compute 1 feature per channel. * Spectral contrast: ratio between the minimum and maximum spectral values in each octave. As in most applications on audio processing, the octaves are referenced to 440 Hz. Given the sampling frequency, we had 10 octaves. Therefore, we computed 10 features per channel. * Spectral slope: first-order polynomial trend of the power spectrum, assuming that the spectrum follows a power law of the frequency. We compute 1 feature per channel. * Spectral flatness: measure of the variability of the spectrum in a given band, obtained as the ratio of the geometric and arithmetic means of the power spectrum. As per the MPEG7 standard, we considered bands of one quarter of an octave. We had 10 octaves; therefore, we computed 40 features per channel. * Centroid frequency, 1 feature per channel. * Maximum frequency, 1 feature per channel. * We also considered the following high-order statistics:
* Third-order autocorrelation, 1 feature per channel. * Time reversibility, 1 feature per channel. This resulted in a total of 56 features extracted from each of the 10 available channels, which provides a total of 560 features at every window location. Table 1 shows the mathematical definitions of all features. Figure 2: Description of the oversampling method GANSO. OFV, Original Feature Vector; SFV, Synthetic Feature Vector. The feature ranking method proposed in [13] was applied, retaining the best ranked feature of every channel to get 10 selected features. Resuming, 56 features are extracted for every sensor signal interval corresponding to the location of the moving window, as described in Figure 1. Then, a feature vector having 56 \(\times\) 10 = 560 components is computed for every location of the moving window by aggregating the 56 features of the 10 channels. After feature ranking, we only retain the best ranked feature of every channel. Thus, a feature vector of just 10 components is finally computed for every location of the moving window of Figure 1. Thus, we guarantee that all channels are involved in the overall procedure. Among the large number of possible classifiers, we have considered two methods. The first one is the well-known Linear Discriminant Analysis (LDA) [34]. This is a practical option from the point of view of maximum simplicity for the possible commercial implementation of the on-board road surface classifier. It implies simple linear computations on the elements of the extracted feature vector. Training of LDA is also simple as it amounts to estimating correlations on the training set and solving linear systems of equations. On the other extreme, we have also tested the Random Decision Forest (RDF) classifier [35]. This is a complex method that combines the outputs of many decision trees. Training of the RDF is rather complex as an iterative search is required to obtain optimum decision trees to be combined. Implementation is also complex as every element of the extracted feature vector is to be compared with a properly selected threshold to define every branch of the many decision trees. A total number of 63 10-channel captures (multichannel signal acquisitions) were made.