Obtaining homogeneous regions, yet connected (if possible)
Networks, and in particular spatial networks, capture the idea of proximity and neighbourhood between nodes (spatial weights). Nodes themselves are characterized by uni- or multivariate profiles. Taking into account both the spatial information (the "where") and the intrinsic information (the "what") is a fascinating challenge, of interest to many disciplines.
Flow Analysis and Spatial Autocorrelation
Reconstructing space from inter-regional flow
Spatial flow count the number of units (people, goods, matter, information...) issued from the origin regions and moving to the destination regions during some observation time. To the gravity or quasisymmetric flow correspond reversible Markov chains (spatial weights), defining an unoriented weighted network. This graph specifies the spatial autocorrelation structure, and induces regional clustering and factorial visualization strategies. In this approach, space appears as generated by the flow, rather than the other way round.
Data Mining and Information Theory
Towards the construction of aggregation-invariant methods
More often than not, the objects encountered in Data Mining can be merged or refined (regions, texts, categories...). Their treatment (clustering, visualisation) hence calls for weighted, or even fuzzy methods. Two main ingredients of the associated formalism are the concept of entropy, measuring the uncertainty, as well as the use of Euclidean distances between objects, possibly transformed.