A review and proposal of (fuzzy) clustering for nonlinearly separable data

In many practical situations data may be characterized by nonlinearly separable clusters. Classical (hard or fuzzy) clustering algorithms produce a partition of objects by computing the Euclidean distance. As such, they are based on the linearity assumption and, therefore, do not identify properly clusters characterized by nonlinear structures. To overcome this limitation, several approaches can be followed: density-, kernel-, graph- or manifold-based clustering. A review of these approaches is offered and some new fuzzy manifold-based clustering algorithms, involving the so-called geodesic distance, are proposed. The effectiveness of such algorithms is shown by synthetic, benchmark and real data.