1. Spatial Mining

2. Introduction
Spatial Mining is a specialised domain of data mining whose goal is to find implicit knowledge in spatial data.
Spatial data may be viewed as objects with some location in physical space.
Spatial data also contain non-spatial attributes that may be either dependent or independent on location.

3. Spatial Data
Also known as geospatial data or geographic information it is the data or information that identifies the geographic location of features and boundaries on Earth, such as natural or constructed features, oceans, and more. Spatial data is usually stored as coordinates and topology, and is data that can be mapped.

4. Spatial Data Spatial data has location or geo-referenced features.
Some of these features are:
Address, latitude/longitude (explicit)
Location-based partitions in databases (implicit)

5. Spatial Object Contains both spatial and nonspatial attributes.
Must have a location type attributes:
Latitude/longitude
Zip code
Street address
May retrieve object using either (or both) spatial or nonspatial attributes.

6. Applications and Problems
Geographic information systems (GIS) store information related to geographic locations on Earth
Weather, 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.

7. Spatial Queries
Spatial selection may involve specialized selection comparison operations:
Near
North, South, East, West
Contained in
Overlap/intersect
Region (Range) Query – find objects that intersect a given region.
Nearest Neighbor Query – find object close to identified object.
Distance Scan – find object within a certain distance of an identified object where distance is made increasingly larger.

8. Spatial Data Structures
Data structures designed specifically to store or index spatial data
These are:-
Minimum bounding rectangles (MBR)
Different tree structures
Quad tree
R-Tree
kd-Tree
Image databases

9. MBR Minimum Bounding Rectangle
Smallest rectangle that completely contains the object

10. MBR Examples

11. Quad Tree
Hierarchical decomposition of the space into quadrants (MBRs)
Each level in the tree represents the object as the set of quadrants which contain any portion of the object.
Each level is a more exact representation of the object.
The number of levels is determined by the degree of accuracy desired.
© Prentice Hall

12. Tree Structures
Quad Tree: every four quadrants in one layer forms a parent quadrant in an upper layer
An example
Dunham Pp

13. R-Tree
As with Quad Tree the region is divided into successively smaller rectangles (MBRs).
Rectangles need not be of the same size or number at each level.
Rectangles may actually overlap.
Lowest level cell has only one object.
Tree maintenance algorithms similar to those for B-trees.

14. R-Tree Indexing MBRs in a tree
An R-tree of order m has at most m entries in one node
An example (order of 3) R8 R8 R1 R2 R3 R6 R5 R4 R7 R6 R7 R1 R2 R3 R4 R5

15. R-Tree Example

16. K-D Tree Designed for multi-attribute data, not necessarily spatial
Variation of binary search tree
Each level is used to index one of the dimensions of the spatial object.
Lowest level cell has only one object
Divisions not based on MBRs but successive divisions of the dimension range.

17. k-D Tree Example

18. kd-Tree
Indexing multi-dimensional data, one dimension for a level in a tree
An example

19. 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

20. Spatial Mining Tasks
Spatial classification
Spatial clustering
Spatial association rules

21. Spatial Classification
Use spatial information at different (coarse/fine) levels (different indexing trees) for data focusing
Determine relevant spatial or non-spatial features
Perform normal supervised learning algorithms
e.g., Decision trees,

22. Spatial Clustering
Use tree structures to index spatial data
DBSCAN: R-tree
CLIQUE: Grid or Quad tree
Clustering with spatial constraints (obstacles  need to adjust notion of distance)

23. 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? Pp