Fuzzy C-Means Algorithm for Heterogeneous Data Using Multiple Kernels

The difficult unsupervised learning task of clustering samples according to an efficient metric and/or vector space representation has numerous practical applications. K-means and its kernelized version are still popular among clustering algorithms due to their conceptual ease and practical effectiveness. However, due to its inherent square scaling in memory with the number of samples, the kernelized version of C-means cannot be applied consistently. In this contribution, we develop a rough method to reduce the kernel C-means cost function, where the system memory available automatically determines the trade-off between accuracy and velocity. In addition, we provide an ad hoc parallelization strategy that works well with hybrid state-of-the-art parallel systems. On common UCI datasets, we demonstrated the efficiency of the parallelization method as well as the approximation scheme. In this practical context, clustering can be crucial for both qualitatively summarizing the underlying chemical phenomenon under investigation in a way that is human compatible and quantitatively predicting kinetics rates via Markov state models. We chose it as a useful real-world application situation for these reasons.