Fuzzy Clustering Guided by Spectral Rotation and Scaling

Representing data in different spaces becomes more powerful and suitable for solving downstream learning tasks. The membership degrees obtained through fuzzy C-means (FCM) clustering cannot capture data structures sufficiently, as they represent samples from a single Euclidean geometrical perspective. To address this issue, we propose a novel fuzzy clustering model guided by spectral rotation and scaling (FCSR). In FCSR, both spectral embeddings and membership degrees are considered as new representations of data. They can complement each other from different perspectives which enables the model to engage more structural properties of the data. The process of solving the problem of membership degrees not only inherits the merits of traditional FCM but also preserves data neighborhood structures revealed by the spectral decomposition based on an affinity matrix. Furthermore, to improve the adaptability and extensibility of FCSR, the projected and kernel versions of FCSR (FCSR-P and FCSR-K) are formed. We demonstrate that FCSR-P is suitable for high-dimensional scenarios and FCSR-K can improve the linear separability among data. Extensive experiments conducted on various well-known data sets illustrate the validity of the proposed ideas.