## 3 Results  
In this section, we will present the results obtained for the proposed unsupervised anomaly detection algorithm. The algorithm was tested on 17 datasets sourced from the Outlier Detection DataSets (ODDSs), available at [[https://odds.cs.stonybrook.edu/](https://odds.cs.stonybrook.edu/)]([https://odds.cs.stonybrook.edu/](https://odds.cs.stonybrook.edu/)) (accessed on 10 September 2024). Additional information can be found at [[https://paperswithcode.com/dataset/odds](https://paperswithcode.com/dataset/odds)]([https://paperswithcode.com/dataset/odds](https://paperswithcode.com/dataset/odds)) (accessed on 10 September 2024). These data represent various problem domains and are characterized by diverse numbers of features, numbers of examples, and proportions of examples recognized as anomalies. Each of these datasets includes built-in information about which examples are considered anomalies. However, this is not used during the operation of the negative selection algorithm, which uses the entire dataset--as training data--including both normal data and anomalies; the aim of the analysis is to precisely indicate which records in the dataset should be considered anomalies. Having the correct classifications allows, however, for the calculation of many informative metrics. Basic statistical information about the used datasets is presented in Table 1. More information regarding the domain of each dataset can be found on the source website. The proposed algorithm was tested in the following configuration. An ensemble of 20 detection models that vote by majority was used. Each of them consisted of spherical detectors generated by an algorithm generating detectors with variable radii using the strategy of generating larger ones first. No data normalization was performed; hence, a strategy was proposed to estimate the minimal radius parameter for specific data. It is estimated as the value:  
\[\text{radius\_min}=\frac{\text{mean\_dist}+\text{std}\times\text{std\_mult}} {2} \tag{1}\]  
where mean_dist is a mean distance between pairs of nearest neighbors in the training data, std is standard deviation, and std_mult is a parameter. In the experiments, for each dataset, std_mult was tried from the set {0.1, 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0}. Since for different data, different levels of the decision threshold parameter for considering as an anomaly are better, values of anomaly_threshold were tried from the set {50%, 60%, 70%, 80%}. The parameter max_tries had a value of 500, while the parameter \(\eta\) (for decreasing the radius value of generated detectors) had a value of 0.95. In the unsupervised negative selection algorithm, the parameter perc, controlling the size of the neighborhood, had a value of 0.01, and 100 test points were generated. The results of the proposed algorithm were compared with the results of classical unsupervised anomaly detection algorithms implemented in the PyCaret library [46]. The following algorithms were used along with parameters tuned in the library:  
* abod--Angle-base Outlier Detection
* cluster--Clustering-Based Local Outlier
* cof--Connectivity-Based Outlier Factor
* histogram--Histogram-based Outlier Detection