## 4 Results
### Description of the Empirical Study  
Based on the assumptions stated in Section 3.3.1, several ensemble classifiers were applied to the available dataset, both before and after its processing, using different sampling strategies, including our proposal. We compared the results of the classifiers obtained from preprocessed data using our sampling approach in comparison with those obtained from the original dataset, as well as from the datasets resulting from the application of SMOTE (resampling the minority class 100% and 500%) and RUS sampling methods. RUS was used with a distribution spread of 4 (ratio 4:1 of majority to minority class instances). Since we handle a very imbalanced data set, the RUS ratio should be high enough to improve the classification of the minority class but at the same time as low as possible to lose the minimum information. In our experiments we found that values higher than 4 hardly affect the improvement of the results, so the ratio chosen was 1:4.  
The KnowledgeFlow tool of Weka ([[https://www.cs.waikato.ac.nz](https://www.cs.waikato.ac.nz)]([https://www.cs.waikato.ac.nz](https://www.cs.waikato.ac.nz))) was used to apply the algorithms. All were run with the default parameters.  
The dataset used in the study comprises information about 4616 patients hospitalized in the ICU of the University Hospital of Salamanca. We focused on predictive factors of infections; since some attributes such as days of stay or death are not known until the end of the stay, they were discarded. The attributes used in the learning process were the following:  
* Gender  
Figure 1: Process of inducing and validating classification models when using the clustering based random undersampling approach.  
* Acute Physiology and Chronic Health Evaluation (APACHE II)
* Emergency surgery
* Immunosuppression
* Neutropenia
* Immunodeficiency
* Mechanical Ventilation
* Central venous catheter (CVC)
* Urinary Catheter
* Parenteral nutrition
* Patient origin
* 48 h of antibiotic treatment
* Previous surgery
* Extrarenal depuration  
Year and APACHE are numerical attributes. Origin can take one of four nominal values, while previous surgery can take one of 13 nominal values (no surgery and 12 types of surgery). The rest of the attributes are binary, taking the values YES/NO, except gender, which takes MALE/FEMALE values. The label attribute is infection, which can take the values YES or NO.  
Classification algorithms were applied to induce models that make it possible to predict infections in ICU patients. In order to do a comparative study of the results, two kinds of algorithms were used, single classifiers and multiclassifiers, or more specifically, ensemble classifiers. These were tested with several base classifiers. The results of some algorithms providing very poor results (accuracy less than 60%) are not reported. We highlight the fact that, applied in different ways, SVM yielded a minority class precision close to 0%, even though this algorithm has been successfully used for dealing with the problem of imbalanced data in other application domains.  
Ten-fold cross-validation was used in the validation of all classifiers. In the experiments carried out with the resampled data using SMOTE, the folders were created before the resampling process in order to ensure that the test set does not contain \"synthetic\" examples, which could mask the right performance and result in unreal values due to overfitting. The same procedure was used for undersampling.  
In the implementation of the clustering-RUS process, two clusters were created, which split the space of characteristics into two regions with imbalance ratios of 6.03 and 17.33. The threshold to perform undersampling was set to 10.0, hence only the cluster with the lower value of imbalance ratio was undersampled. To do that, we also used RUS with a distribution spread of 4.