In this paper, we present an evolving data-based approach to automatically cluster Twitter users according to their behavior. The clustering method is based on the Gaussian probability density distribution combined with a Takagi–Sugeno fuzzy consequent part of order zero (eGauss0). This means that this method can be used as a classifier that is actually a mapping from the feature space to the class label space. The eGauss method is very flexible, is computed recursively, and the most important thing is that it starts learning “from scratch”. The structure adapts to the new data using adding and merging mechanisms. The most important feature of the evolving method is that it can process data from thousands of Twitter profiles in real time, which can be characterized as a Big Data problem. The final clusters yield classes of Twitter profiles, which are represented as different activity levels of each profile. In this way, we could classify each member as ordinary, very active, influential and unusual user. The proposed method was also tested on the Iris and Breast Cancer Wisconsin datasets and compared with other methods. In both cases, the proposed method achieves high classification rates and shows competitive results.