Spatial Classification Task

A Spatial Classification Task is a Classification Task that requires the an Entity's Location.

• AKA: Spatial Classification.
• Context:
  • It can be solved by a Spatial Classification Algorithm.
• See: Temporal Classification Task.

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References

2008

• (Diday, 2008) ⇒ Edwin Diday. (2008). “Spatial Classification.” In: Discrete Applied Mathematics, 156(8). doi:10.1016/j.dam.2007.04.031
  • ABSTRACT: The aim of a spatial classification is to position the units on a spatial network and to give simultaneously a set of structured classes of these units compatible with the network. We introduce the basic needed definitions: compatibility between a classification structure and a tessellation, (m,k)-networks as a case of tessellation, convex, maximal and connected subsets in such networks, spatial pyramids and spatial hierarchies. As like Robinsonian dissimilarities induced by indexed pyramids generalize ultrametrics induced by indexed hierarchies we show that a new kind of dissimilarity called Yadidean induced by spatial pyramids generalize Robinsonian dissimilarities. We focus on spatial pyramids where each class is a convex for a grid, and we show that there are several one-to-one correspondences with different kinds of Yadidean dissimilarities. These new results produce also, as a special case, several one-to-one correspondences between spatial hierarchies (resp. standard indexed pyramids) and Yadidean ultrametrics (resp. Robinsonian) dissimilarities. Qualities of spatial pyramids and their supremum under a given dissimilarity are considered. We give a constructive algorithm for convex spatial pyramids illustrated by an example. We show finally by a simple example that spatial pyramids on symbolic data can produce a geometrical representation of conceptual lattices of symbolic objects.

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