# Detection and Monitoring of Bottom-Up Cracks in Road Pavement Using a Machine-Learning Approach
## 3 Innovative Method
### The Machine Learning Classifiers Used  
In this study, ANNs, random forest classifiers, and a set of support vector machine models were implemented in order to compare the efficiency of the developed ANN models. As is well known [48], three practical issues must be faced in learning from samples: (1) capacity of the network (i.e., the number of patterns that can be stored, and the functions and the decision boundaries can be formed), (2) sample complexity (i.e., the number of training patterns needed to obtain a good generalization and avoid the \"over-fitting\", namely obtaining good results in the training phase, and poor results in the test phase), and (3) computational complexity (i.e., the time required to estimate a solution from the training patterns). In more detail, the quality of the results of an ANN depends on the following variables, which should be carefully defined by the mean of trial-and-error approaches, and bearing in mind the following theoretical considerations and issues [49; 50]: (i) data preprocessing (e.g., balancing an over- or underestimated class of signal, or enrichment using augmentation techniques such as scaling, translation, random noise addition, etc.) is recommended to accelerate the convergence of the testing results to the training results, (ii) input data set size (it should be sufficiently large to cover any variation in the problem domain), (iii) input data set partitioning (the percentages of signals of the data set used for learning and testing phases should be defined using the user experience, or the trial-and-error approach, or some statistical regression rule, (iv) learning rate (a high learning rate may lead to the overshooting of the optimal. This happens when the learning phase is too fast and the network is not able to carry out the classification, while a slow learning rate can make the network inefficient), (v) activation function (data non-linearity and noisiness should be considered before the selection of the activation function), (vi) hidden layers and node sizes (few hidden layers may underestimate complex patterns (under-parameterization), while too many hidden layers can lead the network to learn from the noise of the data (poor generalization). Furthermore, numerous hidden nodes may lead to time-consuming networks, while few hidden nodes can lead to the under-fitting of the network (network unable to obtain the underlying rules embedded in the data)), and (vii) training modes (weights updating) that refer to the size of the section of samples that are used in each testing iteration (i.e., the batch size). A trade-off between the batch size = 1 and the batch size = data set size should be found. If the batch size is equal to the data set size (a.k.a., batch training mode), a large storage for the weights is required, a better estimation of the error gradient can be obtained, but it is more likely that the network will be trapped in local minima. While, if a batch size = 1 is used (a.k.a., stochastic mode), an example-to-example training will be carried out, and this means smaller storage requirements for the weights, and fewer possibilities of entrapment in local minima. (viii) Convergence criteria or stopping criteria, namely the criteria used to stop the training, which can belong to the type \"training error (i.e., error function \(\leq\) small real number)\", \"gradient error (i.e., gradient of the error function \(\leq\) small real number)\", and \"cross-validation (i.e., training the network using a part of the data set, and then validating the network using the remaining part of the data)\". Generally, during the training process the related error decreases when the number of nodes or training cycles increases. Examples of stopping criteria are the coefficient of determination and the sum of squared errors.