Knowledge Discovery in Spatial Planning Data: A Concept for Cluster Understanding

Abstract

The objective of this paper is to present a methodology for discovering comprehensible, valid, potentially innovative, and useful patterns, i.e., new knowledge, in multidimensional spatial data. Techniques from statistics, machine learning, and data mining are applied in consecutive logical steps to allow the visualization of results and the application of validation procedures at each stage. However, the approach does not end with a data cluster; rather, if such a valid cluster has been achieved, then the question is posed: “What do the clusters mean?”. Symbolic machine learning methods are employed to produce an explanation of the clusters in terms of rules employing an understandable subset of the high-dimensional data variables. This combined with canonical representatives of a cluster and consideration of the spatial distribution of the clusters lead to hypothesis on emergent data structures, that is, potential new knowledge. The approach is demonstrated on an exemplary data set of German urban districts featuring seven dimensions of land use.

Appendices

Appendix 1

1.1 Nonlinear Transformations of the Variables in the UD Data

$\mathit{OpenSpaceMeshSize: log}$ $\mathit{BuildingArea: log}$ $\mathit{SettlementDensity: log}$ $\mathit{SealedSurface: sqrt}$ $\mathit{LandConsumption: sqrt}$ $\mathit{ProtectedAreas: sqrt}$ $\mathit{HemerobyIndex: identity}(\mathit{notransformation})$

Appendix 2

2.1 Cluster Representatives

U-matrix cluster	Urban district
UC1	Leverkusen
UC2	Heilbronn
UC3	Zweibrücken
UC4	Freiburg im Breisgau
UC5	Bremen
UC6	Aschaffenburg
UC7	Landau in der Pfalz
UC8	Berlin
UC9	Suhl

Appendix 3

3.1 Rules Explaining the U-Matrix Clustering

UD data belongs to Cluster UC1, if

$\mathit{log}(\mathit{SealedSurfaces}) \geq 48.3179$ and

$\mathit{log}(\mathit{OpenSpaceMeshSize}) \leq 72.6255$ and

$\mathit{log}(\mathit{BuildingArea}) < 65.4549$

UD data belongs to Cluster UC2, if

$\mathit{log}(\mathit{SealedSurfaces}) < 48.3179$ and

$\mathit{log}(\mathit{BuildingArea}) < 75.0076$ and

$\mathit{sqrt}(\mathit{ProtectedAreas}) < 60.8555$ or

$\mathit{log}(\mathit{SealedSurfaces}) \geq 48.3179$ and

$\mathit{log}(\mathit{BuildingArea}) \geq 65.4549$ and

$\mathit{log}(\mathit{OpenSpaceMeshSize}) < 72.6255$

UD data belongs to Cluster UC3, if

$\mathit{log}(\mathit{BuildingArea}) \geq 75.0076$ and

$\mathit{log}(\mathit{SealedSurfaces}) < 48.3179$

UD data belongs to Cluster UC4, if

$\mathit{sqrt}(\mathit{ProtectedAreas}) \geq 60.8555$ and

$\mathit{log}(\mathit{BuildingArea}) < 75.0076$ and

$\mathit{log}(\mathit{SealedSurfaces}) < 48.3179$

UD data belongs to Cluster UC5, if

$\mathit{log}(\mathit{OpenSpaceMeshSize}) \geq 72.6255$ and

$\mathit{log}(\mathit{SealedSurfaces}) \geq 48.3179$