## 4 Proposed Models
### Selected Models  
The five selected models chosen to solve the problem are logistic regression [15], quadratic discriminant analysis (QDA) [16], linear discriminant analysis (LDA) [17], SVM, and the random forest model [18].  
As mentioned, it was finally decided to use the convention of dividing the sample into two classes (class \"0\": no-turn and slight turns; class \"1\": turns close to 90 degrees). For the two-class classification problem, the logistic regression model is often chosen as the first one checked. Logistic regression is one of the simplest machine learning tools. This method is based on a logit function defined as the logarithm of odds [19] (Equation (2)):  
\[\textit{chance}=\frac{\textit{the probability of success}}{\textit{the probability of failure}}. \tag{2}\]  
The next two models (QDA and LDA) were also initially designed for the two-class classification, although their generalizations for the multi-class problem are also widely used. The LDA method finds a linear combination of features (introduced into the model) to distinguish the classes in the best way possible. This method has a very wide range of possible applications, more advanced applications being, for instance, face-recognition algorithms. LDA method assumes that observations from each of the classes have a Gaussian distribution, and covariances are identical. The QDA model is a generalization of the LDA model. It can also be used when the assumption of equal covariance is not met.  
Another model considered in the article is the Support Vector Machine, which is an extension of the support vector classifier, which enables enlarging the feature space by using different kernels. This allows for non-linear boundaries between the classes. SVM models tend to perform well in a variety of different settings.  
Figure 5: Most significant relationships between variables and searched classes found during exploratory analysis: (**A**) Minimum to maximum range and median; (**B**) Interquartile range and kurtosis; (**C**) Kurtosis and standard deviation. Kurtosis and standard deviation have been presented in logarithmic scale.  
The last of the considered models is the random forest model. That method is based on the construction of multiple decision trees. Each of the trees assigns a given observation to one of the considered classes, and then the final assignment is being made based on those individual predictions. Single, deep decision trees very often overfit the training data, especially when lots of input parameters are considered. This means that the decision trees can have great accuracy when predicting samples from the training dataset (90-100%), but when given new data, the accuracy often drops to very low level, often not significantly better than a coin-flip in the case of a two-class problem. Additionally, single trees are often very non-robust, meaning that relatively small changes in the training sample can greatly impact the final estimated trees. The random forest model counteracts this phenomenon; therefore, it was chosen in this case.  
All of the described models were implemented by using the sklearn library available in Python. It was established that 70% of the sample will be used to train the model and the remaining 30% will be used as a test sample.