• 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.

• 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.

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

• 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.
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• 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.

• 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.
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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
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• Minimum Bounding Rectangle
• Smallest rectangle that completely contains the object
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• 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.
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Tree Structures
• Quad Tree: every four quadrants in one layer forms a parent quadrant in an upper layer
– An example

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

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,
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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)
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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?
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