###### Abstract  
This paper proposes a new evolving algorithm named Macro SOStream with entirely online learning and based on self-organizing density for data stream clustering. The Macro SOStream is based on the SOStream algorithm, but we incorporate macroclusters composed of microclusters. While microclusters have spherical shapes, macroclusters can have arbitrary shapes. Moreover, the Macro SOStream has the macrocluster merge functionality specially designed to improve its performance under data drift contexts. The Macro SOStream's performance is compared to SOStream and DenStream algorithms' performance using four synthetic datasets and the ARI performance metric to validate our proposal. Furthermore, we carry out an exhaustive analysis on the influence of adequate hyperparameter setup on these algorithms' performance. As a result, the Macro SOStream presents good performance mainly in the context of data drift and for demands of non-spherical clusters. evolving systems; data stream; online learning; clustering +
Footnote †: journal: Medical Imaging  
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Footnote 1: [[https://www.mdpi.com/journal/applsci](https://www.mdpi.com/journal/applsci)]([https://www.mdpi.com/journal/applsci](https://www.mdpi.com/journal/applsci))  
Footnote †: journal: Medical Imaging  
the entire dataset available a priori because the processing takes place sample by sampling in a serial manner [6]. For this reason, when dealing with online grouping methods, characteristics such as volume, density, shape, or temporal order of the data are used to form the grouping, as it is impracticable to store all data [7]. Thus, algorithms and systems that work online are more viable in environments with limited memory, single data pass, and that require real-time response [7]. Moreover, algorithms need to have the ability to dynamically evolve the internal structure of the model because, in such a scenario, data are generally not stationary. That is, there may be a change in the data pattern or data deviation caused, for example, by variation in the quality of the raw material in oil refining, and the lighting of image processing [8; 9]. In a data clustering context, algorithms that can adapt their cluster parameters (such as center position and density) for data drift are considered adaptive algorithms. Simultaneously, algorithms that can not only adapt to data drift, but also to the emergence of new clusters and the elimination of non-active clusters (data evolution) are considered to be evolving algorithms [8; 9]. Thus, evolving algorithms can develop and update unfamiliar environments and have no problems with non-stationary data [8; 9; 10]. Some evolving clustering algorithms proposed in the literature are Clustream [11], DenStream [12], C-DenStream [13], SDStream [14], SOStream [15], Online Elliptical Clustering--OEC [16], and Auto-Cloud [17]. In this paper, we propose a new evolving clustering algorithm named Macro SOStream. The Macro SOStream is based on SOStream [15] and uses entirely online learning based on self-organizing density for data stream clustering. Therefore our contributions are:  
* The creation of macroclusters with arbitrary shapes. The difference between SOStream and Macro SOStream is the creation of macroclusters from microclusters, where this process takes place entirely online. Unlike microclusters, macroclusters can assume arbitrary shapes. * A merging mechanism for macroclusters to improve their performance and robustness to noisy data. The primary motivation of the proposal is to improve the SOStream algorithm. Thus, the proposal expands the technique already utilized in SOStream with microclusters to the creation of macroclusters. The significant differeeces between SOStream to other evolving algorithms based on density is the technology used to perform clustering on the data stream. The SOStream is based on a self-organizing map (SOM), or Kohonen network. Through the research carried out in the literature, we pre-selected DenStream to compare with the proposed algorithm.