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6. Spatial Mining

Spatial Data and Structures

Images

Spatial Mining Algorithms

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Definitions

• Spatial data is about instances located in a physical space

• Spatial data has location or geo-referenced features

• Some of these features are: – Address, latitude/longitude (explicit)

– Location-based partitions in databases (implicit)

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Applications and Problems

• Geographic information systems (GIS) store information related to geographic locations on Earth– Weather, climate monitoring, community infrastructure

needs, disaster management, and hazardous waste

• Homeland security issues such as prediction of unexpected events and planning of evacuation

• Remote sensing and image classification• Biomedical applications include medical imaging

and illness diagnosis

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Use of Spatial Data

• Map overlay – merging disparate data– Different views of the same area: (Level 1) streets, power

lines, phone lines, sewer lines, (Level 2) actual elevations, building locations, and rivers

• Spatial selection – find all houses near ASU• Spatial join – nearest for points, intersection for areas• Other basic spatial operations

– Region/range query for objects intersecting a region

– Nearest neighbor query for objects closest to a given place

– Distance scan asking for objects within a certain radius

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Spatial Data Structures

• Minimum bounding rectangles (MBR)• Different tree structures

– Quad tree

– R-Tree

– kd-Tree

• Image databases

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MBR

• Representing a spatial object by the smallest rectangle [(x1,y1), (x2,y2)] or rectangles

(x1,y1)

(x2,y2)

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Tree Structures

• Quad Tree: every four quadrants in one layer forms a parent quadrant in an upper layer– An example

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R-Tree

• Indexing MBRs in a tree– An R-tree order of m has at most m entries in one node

– An example (order of 3)

R8

R1

R2R3

R6

R5R4

R7

R8

R7R6

R3R2R1 R5R4

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kd-Tree

• Indexing multi-dimensional data, one dimension for a level in a tree– An example

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Common Tasks dealing with Spatial Data

• Data focusing– Spatial queries– Identifying interesting parts in spatial data– Progress refinement can be applied in a tree structure

• Feature extraction– Extracting important/relevant features for an

application

• Classification or others– Using training data to create classifiers– Many mining algorithms can be used

• Classification, clustering, associations

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Spatial Mining Tasks

• Spatial classification• Spatial clustering• Spatial association rules

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Spatial Classification

• Use spatial information at different (coarse/fine) levels (in different indexing trees) for data focusing

• Determine relevant spatial or non-spatial features• Perform normal supervised learning algorithms

– e.g., Decision trees, NBC, etc.

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Spatial Clustering

• Use tree structures to index spatial data• Cluster locally

– DBSCAN: R-tree

– CLIQUE: Grid or Quad tree

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Spatial Association Rules

• Spatial objects are of major interest, not transactions• A B

– A, B can be either spatial or non-spatial (3 combinations)

– What is the fourth combination?

• Association rules can be found w.r.t. the 3 types

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Summary

• Spatial data can contain both spatial and non-spatial features.

• When spatial information becomes dominant interest, spatial data mining should be applied.

• Spatial data structures can facilitate spatial mining.

• Standard data mining algorithms can be modified for spatial data mining, with a substantial part of preprocessing to take into account of spatial information.

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Bibliography

• M. H. Dunham. Data Mining – Introductory and Advanced Topics. Prentice Hall. 2003.

• R.O. Duda, P.E. Hart, D.G. Stork. Pattern Classification, 2nd edition. Wiley-Interscience.

• J. Han and M. Kamber. Data Mining – Concepts and Techniques. 2001. Morgan Kaufmann.