## 6 Conclusions and Future Work  
In this study, a new HPFuzzNDA approach for novelty detection is introduced. It is able to classify data and determine anomalies better than the original PFuzzNDM algorithm owing to HPFuzzNDA's use of an evolutionary algorithm, namely NL-SHADE-RSP, and a specific merging mechanism, which allows a more flexible partition of data instances into clusters. Experimental results demonstrated HPFuzzNDA's workability and usefulness. The obtained numerical results confirmed the following:  
* NL-SHADE-RSP is able to design a more appropriate number of clusters for each class, normal or novel, as it is not limited by the predefined number of clusters like the PFCM approach that is used for PFuzzNDM.
* The final decision model, designed by the proposed HPFuzzNDA approach, can be simplified or the other way around depending on the given dataset, and consequently, better classification results can be achieved.
* An adaptation strategy, proposed to control the number of clusters belonging to each class, allows increases in classification accuracy as the \"borders\" of clusters of different classes, and consequently, the \"borders\" of these classes, are better distinguished compared to the PFuzzNDM approach.
* The proposed algorithm is able to learn novel concepts or extensions of the known concepts and can better detect anomalies that do belong to any of the classes (known or novel) than the original PFuzzNDM method in terms of classification accuracy, macro \(F\)-score metric and the unknown rate measure.  
However, we introduced several new parameters in this study for the HPFuzzNDA approach and did not attempt to adjust them, although it is clear that inadequate parameter choice can lead to poor classification results. Moreover, the new algorithm was tested only on synthetic datasets, which did not contain many features, and is thus not entirely representative of real-world problems. In addition, as previously mentioned in Section 3, the evolutionary algorithm NL-SHADE-RSP is used for determining the centres of all clusters. As a result, NL-SHADE-RSP may suffer from the curse of dimensionality when used for more complex data, as the number of features may increase significantly. Therefore, there is a need for a feature selection technique that should be applied before NL-SHADE-RSP to pre-process data and decrease the number of features describing each data instance. Thus, the future work should be focused on the following:  
* Execution of additional experiments to better understand the influence of each parameter (not only the parameters of the original PFuzzND approach but also the parameters introduced in this study).
* Development of adaptation strategies for the most important parameters determined during the conducted experiments.  
Figure 10: Example of instances from the \(DS_{9}\), classified by HPFuzzNDA (the **left** graph) and PFuzzND (the **right** graph) algorithms.  
* Introduction of the feature selection operator to reduce the dimensionality of the data.
* Application of the proposed algorithm for more complex datasets, for example, image or video data.  
Conceptualization, S.A. and V.S.; methodology, S.A.; software, S.A.; validation, S.A. and V.S.; formal analysis, Y.K.; investigation, S.A.; resources, Y.K.; data curation, Y.K.; writing--original draft preparation, S.A.; writing--review and editing, S.A. and V.S.; visualization, V.S.; supervision, S.A. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.