# Analysis of Factors Influencing the Prices of Tourist Offers
## 3 Selecting Optimal Price Predictors
### Feature Selection  
Feature selection is the process of reducing the size of the set containing all original attributes describing the data. The dimensionality reduction achieved in this way not only reduces the computational and space complexity, but may also influence the accuracy of \begin{table}
\begin{tabular}{c c c c c c} \hline \(n\) & **Metric** & **Down** & **No Change** & **Up** & **Avg** \\ \hline \multirow{4}{*}{7} & Precision [\%] & 99.6 & 55.27 & 98.55 & 84.47 \\  & Recall [\%] & 64.35 & 99.14 & 49.78 & 71.09 \\  & F1 score [\%] & 77.01 & 70.4 & 62.05 & 69.82 \\ \hline \multirow{4}{*}{14} & Precision [\%] & 95.59 & 56.88 & 87.85 & 80.11 \\  & Recall [\%] & 84.76 & 93.49 & 38.36 & 72.2 \\  & F1 score [\%] & 89.64 & 70.32 & 50.73 & 70.23 \\ \hline \multirow{4}{*}{21} & Precision [\%] & 93.97 & 53.92 & 69.59 & 72.49 \\  & Recall [\%] & 69.92 & 84.87 & 46.12 & 66.97 \\ \cline{1-1}  & F1 score [\%] & 79.66 & 65.03 & 53.89 & 66.19 \\ \hline \multirow{4}{*}{28} & Precision [\%] & 92.68 & 64.53 & 61.95 & 73.05 \\ \cline{1-1}  & Recall [\%] & 64.32 & 76.27 & 63.35 & 67.98 \\ \cline{1-1}  & F1 score[\%] & 75.08 & 68.96 & 58.22 & 67.42 \\ \hline \end{tabular}
\end{table} 
Table 6: Classification results [%] for data from tour operator T2 and series length 3. \begin{table}
\begin{tabular}{c c c c c c} \hline \(n\) & **Metric** & **Down** & **No Change** & **Up** & **Avg** \\ \hline \multirow{4}{*}{7} & Precision [\%] & 89.05 & 82.03 & 78.67 & 83.25 \\  & Recall [\%] & 75.4 & 85.25 & 84.21 & 81.62 \\  & F1 score [\%] & 81.19 & 83.07 & 80.6 & 81.62 \\ \hline \multirow{4}{*}{14} & Precision [\%] & 77.66 & 81.67 & 60.05 & 73.13 \\  & Recall [\%] & 64.69 & 56.44 & 80.23 & 67.12 \\  & F1 score [\%] & 69.45 & 63.12 & 66.8 & 66.46 \\ \hline \multirow{4}{*}{21} & Precision [\%] & 63.64 & 57.71 & 48.03 & 56.46 \\  & Recall [\%] & 56.48 & 33.59 & 69.96 & 53.34 \\ \cline{1-1}  & F1 score [\%] & 57.76 & 40.22 & 55.31 & 51.1 \\ \hline \multirow{4}{*}{28} & Precision [\%] & 52.78 & 49.56 & 53.74 & 52.03 \\ \cline{1-1}  & Recall [\%] & 57.03 & 43.43 & 53.18 & 51.21 \\ \cline{1-1}  & F1 score [\%] & 53.87 & 44.83 & 50.96 & 49.89 \\ \hline \end{tabular}
\end{table} 
Table 5: Classification results [%] for data from tour operator T1 and series length 3.  
the trained model, which may have better generalization ability. Feature selection methods fall into one of the following categories:  
* Filter methods apply an evaluation function measuring the dependence between a given feature and a target value. Example criteria used as the evaluation function are Pearson coefficient, Spearman coefficient, mutual information. The advantage of filter methods is their low computational cost, but the drawback is the fact that they treat the predictors independently, neglecting potential correlations between them. A feature that is useless alone may be significant in combination with other features [27]. * Wrapper methods apply a trained model to evaluate the effectiveness of a selected feature subset. Depending on a given task, the model may be either a classifier or a regression model. These methods require choosing a feature space search strategy, leading to an iterative process. In each iteration, a new subset of features is generated, a model is trained and the subset is evaluated according to the model's performance. Searching the whole space of feature subsets is infeasible; therefore, some heuristics are applied. One of the most popular ones are sequential methods, where in each iteration, features are either added to or removed from the current subset. The computational cost of wrapper methods is high, due to the need of training a model whenever a new subset of features has to be evaluated. To reduce the computational complexity, the recursive feature elimination proposed in [28] may be applied. This algorithm reduces the necessary number of repetitions of the model training procedure. In each stage, after creating a model, features are ranked and the least important predictor is eliminated.