# Detection and Monitoring of Bottom-Up Cracks in Road Pavement Using a Machine-Learning Approach
## 3 Innovative Method
### The Machine Learning Classifiers Used
Finally, confusion matrixes, or the hit (or miss) rate representing the percentage of examples classified correctly (or incorrectly) can be used as an error metric in classification problems, rather than the absolute deviation of the network classification from the target classification. Based on the above, the following tasks were carried out: (a) the data set was preprocessed using the augmentation procedure described above in order to obtain an adequate input data set size (i.e., from an initial data set of 40 signals related to 4 SHSs, another 5 data sets were produced. The new data sets consist of 400, 800, 1600, 3200, and 4000 signals; see Table 1), (b) the data set was partitioned considering as a starting point the use of 50% of the ARs the training and the use of the remaining part (50%) for testing, (c) values extracted from an exponential scale starting from 0.001 (\(y\) = \(a\times b^{x}\), where \(a\) = 0.001, and \(b\) = 2.5) were used as the learning rate, (d) the ReLu function was selected as activation function for the classification purpose (this activation function,\(f\) (\(z\) ), is zero when \(z\) is less than zero, and it is equal to \(z\) when \(z\) is above or equal to zero, i.e., _relu ( \(x\) ):=max ( 0, \(x\))_), and (e) the modelaccuracy (i.e., the ratio between the number of signals of the testing data set correctly classified and the total number of signals belonging to the testing data set to be classified), derived from confusion matrixes, were used to show the results of the classification. Furthermore, the Adadelta Optimized was selected as an optimizer function (for the adjustment of weights and biases). ANNs are the basic classification approach considered in this study. The following ANN types were developed:  
* Multilayer perceptron (MLP);
* Convolutional neural network (CNN). The MLP consists of two fully connected hidden layers that are dedicated to the pattern recognition (using the ReLu as the activation function). CNNs are commonly used for the classification of images (e.g., [31]), while, in this study, pseudorandom time series were used as input. These types of networks try to take advantage from the potentialities offered by the convolutional and pooling layers of the CNN (i.e., feature extraction and processing). The CNN used in this study consists of one convolution layer (feature extraction), one pooling layer (average pooling of the features extracted, applying the valid padding), and the same two fully connection layers used in the MLP (pattern recognition using the activation function ReLu). The activation function softmax cross entropy (i.e., measures the probability error in discrete classification tasks), and confusion matrixes were used to show and analyze the results of the classification. In addition to ANNs, the following advanced ML-classifiers were developed:  
* Random forest classifier (RFC): an ensemble learning method for classification that operates by constructing a set of decision trees and returning the class that is the mode of the classes (classification) of the individual trees [38];
* Support vector classifier (SVC): a supervised learning classifier with associated learning algorithms that can perform a nonlinear classification, implicitly mapping the model inputs into high-dimensional feature spaces. The essential parameter of a RFC model is the number of estimators (the number of trees in the forest). The following types of SVC were implemented in the study:  
* SVC with linear kernel;
* SVC with radial basis function (RBF) kernel;
* SVC with polynomial kernel. As it is stated in the scikit-learn documentation [47], two basic characteristics are used to parameterize SVC: (1) a kernel coefficient (gamma) and (2) the penalty parameter (C). The gamma