# On Training Road Surface Classifiers by Data Augmentation
## 4 Experiments
Each capture corresponded to a straight line path of the car with an average time duration of 14.59 s. The captures considered different configurations of the following four properties: (i) worm-gear interface configuration (three configurations to simulate different noise and vibration conditions on the driver); (ii) hands on or off the wheel; (iii) vehicle \begin{table}
\begin{tabular}{c c} \hline \hline
**Feature** & **Definition (In All Cases A Is the Number of Samples within the Time Window)** \\ \hline Average power & \(\frac{1}{\Delta}\sum\limits_{n=1}^{\Delta}x^{2}(n)\) & **1 feature** \\ Spectral contrast & \(\frac{\max\limits_{i=1}\left|X(f)\right|}{\min\left|X(f)\right|}\) & where \(f_{01}\), \(f_{02}\) are the start and end indices of \(o\)th octaves, respectively. 440 Hz was the reference (end limit of the 4 th octave) [26], 10 octaves were considered. \\  & \(f_{01}\leq f\leq f_{02}\) & **10 features** \\ Spectral slope & Trend \(a\) of the model & \(\log\left|X(f)\right|=a\log f+b\), \\ Spectral flatness & \(\frac{\left(\prod_{i=f_{02}}^{f_{02}}\left|X(f)\right|\right)^{1/(f_{02}-f_{01})} }{f_{02}^{\Delta}\prod_{i=f_{02}}^{\Delta}\left|X(f)\right|}\) & where \(f_{01}\), \(f_{02}\) are respectively the start and end indices of the \(o\)th quarter of octave [26]. 10 octaves were considered. \\ Centroid frequency & \(\frac{f_{0}}{\Delta}\frac{\sum\limits_{n=1}^{\Delta}f_{1}X(f)|^{2}}{\sum\limits _{n=1}^{\Delta}\left|X(f)\right|^{2}}\) & where \(X(f)\) is the direct Fourier transform of \(x\) within the epoch taken at \(\Delta\) points, and \(f_{s}\) is the sampling rate. \\ Maximum frequency & \(\frac{f_{0}}{\Delta}\left(\underset{f}{\mathrm{argmax}}\left|X(f)\right|\right)\) & **1 feature** \\ Third-order autocorrelation & \(\frac{1}{\Delta-2}\sum\limits_{n=3}^{\Delta}x(n)\cdot x(n-1)\cdot x(n-2)\) & **1 feature** \\ Time reversibility & \(\left(\frac{1}{\Delta}\sum\limits_{n=1}^{\Delta}x^{2}(n)\right)^{-3/2}\frac{1} {\Delta-1}\sum\limits_{n=2}^{\Delta}\left(x(n)-x(n-1)\right)^{3}\) & **1 feature** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Extracted feature definitions. speed (constant speed of 10, 15, 20, 30 km/h, or accelerating from 0 to 30 km/h); (iv) road surface (smooth flat asphalt, stripes, or cobblestones). A dataset consisting of 8039 10-dimensional feature vectors was obtained from the 63 10-channel captures using the setup described above. Notice that the overall duration of the captures is directly related to the size of the dataset. Thus, it will be relevant any reduction in the dataset size, not affecting the training quality. We define the training set (\(TS\)) as the set of captured feature vectors from the total set that will be used for training. The cardinality of the \(TS\) will be denominated training set size (\(TSS\)). Thus, a variable TSS was reserved for training. A fixed size of 500 was considered for the testing set, not including members of the \(TS\) to avoid overfitting. Let us now consider the most significant results of the experiment. Figure 3 shows the mean accuracy (percentage of correct classification in the testing set) for TSS varying from 377 to 1505 in steps of 125. Mean accuracy was obtained by averaging 100 iterations, where every iteration corresponded to a different random partition of the training and testing sets. In every iteration, accuracy has been computed from sample estimates: quotient between the number of correct road surface classifications and the total number of cases to be classified. Then, it is multiplied by 100 to express it as a percentage. Figure 3 represents six curves. Three of them (blue) correspond to LDA and the other three (red) to RDF. Notice that for every type of classifier, the solid line corresponds to training without data augmentation, while the dot-dash line and dot line correspond to training with data augmentation, where the TS was duplicated by adding the appropriate number of synthetic 10-dimensional feature vectors.