Kernel methods for point symmetry-based clustering

• Generalization (by kernelization) of a family of point symmetry distances.
• Kernelized-SBKM that offers new possibilities for point symmetry-based clustering.
• Empirical recognition of symmetric clusters using any proximity measure.
• Highlighting new simple examples, hard to manage by original methods.
• New complex examples well-managed with KSBKM by using implicit projections.

This paper deals with the point symmetry-based clustering task that consists in retrieving – from a data set – clusters having a point symmetric shape. Prototype-based algorithms are considered and a non-trivial generalization to kernel methods is proposed, thanks to the geometric properties satisfied by the point symmetry distances proposed until now. The proposed kernelized framework offers new opportunities to deal with non-Euclidean symmetries and to reconsider any intractable examples by means of implicit feature spaces.A deep experimental study is proposed that brings out, on artificial data sets, the capabilities and the limits of the current point symmetry-based clustering methods. It reveals that kernel methods are quite capable of stretching the current limits for the considered task and encourages new research on the kernel selection issue in order to design a fully unsupervised symmetric pattern recognition process.