## 1 Introduction  
Novelty detection has been presented as a one-class problem where the main goal is to discriminate examples from the normal class and everything else that does not fit into the current understanding of normalcy. The learning phase for the novelty detection problem, formalized in such a way, is based only on examples from one class, which is also referred to as the normal concept. Therefore, in the application phase, the stream of new unlabelled examples can be classified as either normal (instance belongs to the normal concept, which was learned during the training phase) or unknown (instance does not belong to the normal concept). The unknown examples can indicate the presence of a new class, known as novelty, which was not learned in the training phase, or they can be anomalous data not belonging to any class. The latter can result from measurement errors, noise or other factors. In this study, novelty detection is treated as a multi-class task, to be more specific, it is assumed that the normal concept may be composed not by one but by multiple classes. Moreover, new instances or test examples can also form multiple novel classes, or they can indicate new features of the known classes, or, lastly, they can be anomalies. It should be noted that the new classes result in a concept evolution [1], while new features of the known classes are the subject of the concept drift [2]. Thus, the decision model should be able to evolve to represent the new emergent classes or patterns. Let us examine continuous data produced according to some probability distribution, which can change over time. These data are also denoted as data streams, and with data streams not only can novel concepts appear, but the known concepts can also evolve [3]. Thus, the dynamic nature of the normal and novel classes renders novelty detection a challenging task [4]. In this study, we propose a new algorithm, named HPFuzzNDA (Hybrid Possibilisitic Fuzzy approach with Automatically adjusted number of clusters), which is a modification of the Possibilisitic Fuzzy multi-class Novelty Detector for continuous multi-class data stream problems [5]. The new approach employs the NL-SHADE-RSP algorithm [6], which is a modification of the well-known evolutionary algorithm L-SHADE [7]. Namely, NL-SHADE-RSP is used to design clusters for each known class and to determine the number of these clusters. It should be noted that the objective function for the NL-SHADE-RSP approach was the same as that proposed for the Possibilisitic Fuzzy C-Means (PFCM) method [8]. Additionally, a new mechanism based on the fuzzy clustering similarity metric [9], the generalized soft C index metric [10] and mini-batch approach, is proposed to reduce the number of designed clusters where necessary. Thus, the main contributions of this paper are as follows:  
* NL-SHADE-RSP is able to design a more appropriate number of clusters for each class, normal or novel, which is supported by the experimental results, thus, the NL-SHADE-RSP algorithm presents a more flexible approach for clustering as it is not limited by a predefined number of clusters unlike the PFCM approach used for PFuzzND. * For each class, the number of clusters is not fixed and can increase or decrease over time, so the final decision model can be simplified and vice versa, depending on the given dataset, and as a result, better classification results can be achieved. * A new additional mechanism, proposed for the automated adjustment of the number of clusters, helps to increase the classification accuracy as the \"borders\" of clusters of different classes, and consequently, the \"borders\" of these classes, are better distinguished compared to the PFuzzND approach.