Watersheds on Hypergraphs for Data Clustering

Fabio Dias (1) , Moussa R Mansour (2) , Paola R Valdivia (3, 2) , Jean Cousty (4) , Laurent Najman (4)

1 NYU Tandon School of Engineering
2 ICMC-USP - Instituto de Ciências Mathemàticas e de Computação [São Carlos]
3 AVIZ - Analysis and Visualization
4 LIGM - Laboratoire d'Informatique Gaspard-Monge

We present a novel extension of watershed cuts to hyper-graphs, allowing the clustering of data represented as an hypergraph, in the context of data sciences. Contrarily to the methods in the literature , instances of data are not represented as nodes, but as edges of the hypergraph. The properties associated with each instance are used to define nodes and feature vectors associated to the edges. This rich representation is unexplored and leads to a data clustering algorithm that considers the induced topology and data similarity concomitantly. We illustrate the capabilities of our method considering a dataset of movies, demonstrating that knowledge from mathematical morphology can be used beyond image processing, for the visual analytics of network data. More results, the data, and the source code used in this work are available at https://github.com/015988/hypershed.

Keywords: Hypergraphs; Watershed algorithm; Data clustering

Domains: Computer Science [cs]; Discrete Mathematics [cs.DM]; Computer Science [cs]; Computer Vision and Pattern Recognition [cs.CV]; Computer Science [cs]; Signal and Image Processing

Fabio Dias, Moussa R Mansour, Paola R Valdivia, Jean Cousty, Laurent Najman. Watersheds on Hypergraphs for Data Clustering. ISMM 2017 - 13th International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing, May 2017, Fontainebleau, France. pp.211-221, ⟨10.1007/978-3-319-57240-6_17⟩. ⟨hal-01592155⟩