Spatial Temporal Data Mining

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Spatial Temporal Data Mining

• Wei Wang
• Data Mining Lab, UCLA
• January 21, 1999

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Outline

• Introduction
• Statistical Clustering
• User-defined Trigger
• Spatial Index Structure for High Dimensional
  Point Data
• Temporal Spatial Pattern Detection
• ongoing research

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Introduction

• Spatial data mining has been an active research
  area during recent years.
• For some well know problem, e.g., clustering,
  many existing algorithms are not efficient
  enough.
• There is still room for improvement.
• There are a lot of interesting problems remaining
  uninvestigated.
• We classify a subset of problems and try to solve
  them efficiently.

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Outline

• STING a statistical information grid approach to
  spatial data mining
• STING an approach to active spatial data mining
• PK-tree a spatial index structure for high
  dimensional point data
• Temporal spatial pattern detection

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STING

• Spatial database is usually huge.
• Efficiency of the data mining algorithm is
  crucial.
• Example each person is an object
• Query Find high income area within California
• high income salary gt 50,000
• area gt 4 square miles
• Traditional Method
• Step 1 Select out all person whose salary are
  high.
• Step 2 Do clustering analysis on those persons
  selected out.
• Step 3 Form the region that each cluster
  occupies.
• Step 4 Return those regions larger than 4 square
  miles.
• If high income is defined as 80 persons have
  salary gt 50,000
• then the previous method can not even answer the
  query.
• STING was proposed to solve such problem
  efficiently.

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STING

• Region Query Example
• Select the maximal regions that have at least 100
  houses per unit area and at least 70 of the
  house prices are above 400K and with total area
  at least 100 units with 90 confidence.

SELECT REGION FROM house-map WHERE DENSITY IN
(100, ?) AND price RANGE (400000, ?) WITH
PERCENT (0.7, 1) AND AREA (100, ?) AND WITH
CONFIDENCE 0.9
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STING

• Objects are represented by points, each of which
  has associated spatial attributes, its location,
  and non-spatial (numerical) attributes.
• Space is recursively divided into smaller
  rectangular cells until certain level is reached.
• A hierarchical structure is employed.
• The average number of objects in a leaf cell is
  in the range from several dozens to several
  thousands.
• Preprocess data
• capture the statistical information

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STING
1st layer (root)
(i-1)th layer
ith layer
(i1)th layer (leaf layer)
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STING

• For each cell, we have
• attribute-independent parameter
• n number of objects
• attribute-dependent parameters (for each
  numerical attribute)
• mean mean value of the attribute
• std standard deviation of the attribute value
• min the minimum value of the attribute
• max the maximum value of the attribute
• distribution the type of distribution that best
  fits the attribute value (can be NONE)
• Bottom-up generation when the data is loaded into
  the database.
• Linear compilation time
• Only has to be done once ? not for each query.

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STING

• Take advantage of the statistical information
  captured.
• Only go through relevant cells at each level.
• Root is relevant.
• For each relevant cell, we exam its children at
  next level by statistical test and label them as
  relevant or not relevant.
• Form regions from relevant leaf level cells.
• Do not need to access full database.
• It is very efficient.

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STING

• The computational complexity of STING is linearly
  proportional to the number of leaf cells.
• We used the SEQUOIA 2000 benchmark as the data
  set to compare the performance of STING with
  other approaches.

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STING

• STING is a query-independent approach.
• The statistical information exists independently
  of queries.
• STING has a much smaller response time compared
  to other approaches
• The computational complexity is linearly
  proportional to the number of leaves.
• I/O cost is low.
• STING can support different resolution of query
  result.
• Regions returned by STING approach that returned
  by DBSCAN when the granularity approaches zero.
• Parameters in the hierarchical structure can be
  maintained efficiently by incremental update.

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Outline

• STING a statistical information grid approach to
  spatial data mining
• STING an approach to active spatial data mining
• PK-tree a spatial index structure for high
  dimensional point data
• Temporal spatial pattern detection

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STING

• Moreover, since objects evolve, interesting
  patterns may emerge or disappear over time.
• Example
• Trigger Do bandwidth reallocation when the
  average call length is greater than 10 minutes
  within the region where at least 10 cellular
  phones are in use per squared mile.
• This can not be supported by traditional database
  triggers efficiently
• due to the fact that the class membership of an
  object is not only determined by its non-spatial
  attributes but also by the attributes of objects
  in its neighborhood.
• Naïve approach re-evaluate condition
  periodically.
• Not efficient.

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STING

• STING was an extension of STING to support
  user-defined trigger.
• In spatial databases, object insertion, deletion,
  and update are primitive events.
• Observation Usually, only the cumulative effect
  of a set of primitive events may cause the
  trigger condition to be true.
• We refer such set of primitive events to as a
  composite events.

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STING

• Condition-Action paradigm
• In general, it is difficult or even impossible
  for user to specify all possible composite events
  that may cause the trigger condition to be true.
• In general, evaluating a user-defined trigger T
  usually involves two aspects
• Find a set of composite events E(s) that may
  cause the trigger condition CT to become true.
• Each time some composite event in E(s) occurs,
  check the status (false or true) of CT (given
  that CT was false previously).

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STING

• Observation As a side effect of the occurrence
  of some composite event, the set of composite
  events E(s) that could cause CT to transition
  from false to true might also evolve over time.
• Two set of composite events we need to consider
• the set of composite events E(s) that can cause
  CT to become true
• need to re-evaluate CT
• the set of composite events F(s) that can cause a
  change to E(s)
• need to update E(s)

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STING

• Observation In spatial databases, the effect of
  an event is usually local to its neighborhood.
• STING decomposes the user-defined trigger into a
  set of sub-triggers associated with individual
  cells in the hierarchical structure.
• These sub-triggers are used to monitor composite
  events in E(s) and F(s) and change accordingly
  when E(s) and F(s) evolves.

Level 4
Level 3
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STING

• Updates are suspended at some level in the
  hierarchy until such time that the cumulative
  effect of these updates might cause the trigger
  condition to become satisfied.

Level 2
Level 1
Level 1
Level 2
Level 3
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STING

• Example Trigger bandwidth reallocation when the
  total area occupied by those regions in
  California where at least 10 cellular phones are
  in use per squared mile and the average length of
  phone calls is at least 15 minutes with total
  area at least 50 squared miles increases by at
  least 10 squared miles.

DEFINE TRIGGER example ON cellular-phone WHEN
SELECT SIZE(REGION) INCREASE RANGE (10,
?) WHERE DENSITY IN RANGE (10, ?) AND
AVERAGE(length) IN RANGE (15, ?) AND AREA IN
RANGE (50, ?) LOCATION California DO
bandwidth-reallocation
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STING

• Observation Trigger condition CT is a
  conjunction of predicates P1 ? P2 ? ? Pn and
  can not be true if one predicate is false.
• They can be evaluated in a certain order the ith
  predicate is tested when all previous i -1
  predicates are true.
• The evaluation order should be chosen in such a
  way that the total cost is minimum.
• STING evaluates CT in the order location,
  density condition, attribute condition, each of
  which is evaluated in a different phase.
• Location only needs to be evaluated once and the
  cost can be regarded as constant in the trigger
  evaluation process.
• If the location is fixed, unnecessary
  sub-triggers set on cells outside the location
  can be avoided and hence save the evaluation cost
  of other predicates.
• Sub-triggers set during an earlier phase will
  exist longer than those set in a later phase.
• It is better to first evaluate the predicate that
  takes less time to handle.
• cost(density) lt cost(attribute)

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STING

• Average CPU cycles for handling each type of
  sub-trigger

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STING
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Outline

• STING a statistical information grid approach to
  spatial data mining
• STING an approach to active spatial data mining
• PK-tree a spatial index structure for high
  dimensional point data
• Temporal spatial pattern detection

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PK-tree

• As both the number of objects and the number of
  attributes are very large, it is essential to
  organize the set of objects by some dynamic
  indexing structure.
• Point index methods

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PK-tree
Spatial decomposition Space is recursively
divided until a level LD such that each cell
contains at most one point.
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PK-tree
16 intermediate nodes, height 3
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PK-tree
5 intermediate nodes, height 2
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PK-tree

• PK-tree employs a concept of K-instantiable cell
  to eliminate unnecessary nodes.
• Point cell a non-empty cell at level LD
• A cell C is K-instantiable iff
• C is a point cell, or
• there does not exist (K-1) or less K-instantiable
  sub-cells to cover all non-empty space in C
• Only K-instantiable cells serve as nodes in the
  PK-tree (expect the root).
• The parent-child relationship follows naturally
  from the cell-subcell relationship.

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PK-tree

• Properties
• Bounds on nodes outdegree
• allows allocating one node to a page
• Bounded storage space
• Existence and Uniqueness
• enables us to analyze the behavior of a PK-tree
  easier.
• Expected height
• log(N) under some general condition
• guarantees efficiency of retrieval and update.
• No overlapping among sibling nodes
• efficient retrieval
• Empirical studies shown that the PK-tree
  outperforms SR-tree and X-tree by a wide margin.

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PK-tree
Height of generated trees on 100,000 points
Size of index in MB
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PK-tree
KNN query on clustered data distribution
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PK-tree

• Real data set NASA Sky Telescope Data
• 200,000 two-dimensional points (they are the
  coordinates of crater locations on the surface of
  Mars)

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Outline

• STING a statistical information grid approach to
  spatial data mining
• STING an approach to active spatial data mining
• PK-tree a spatial index structure for high
  dimensional point data
• Temporal spatial pattern detection

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Temporal Spatial Pattern Detection

• When the number of attributes is large and/or the
  value of attributes evolve frequently, the
  complexity of patterns and the number of
  potential patterns increase.
• It is not desirable or even feasible to ask the
  user specify interesting patterns.
• E.g., the user wants to know any possible
  patterns involving certain attributes such as
  salary, rent, cellular phone usage, etc.
• Existing association rule algorithm can not be
  applied.
• Continuous attribute domain
• Temporal evolution
• Prior knowledge about relationships among
  attributes and objects

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Temporal Spatial Pattern Detection

• Object ? represented by point
• primitive attributes
• spatial attributes, i.e., coordinates of its
  position
• non-spatial attributes, e.g., name, weight,
  height, salary, rent
• derived attributes ? derived from primitive
  attribute(s)
• environment attributes, e.g., distance to a
  hospital, average income in the neighborhood area
• Consider a sequence of snapshots S1, S2, , Sn
• Temporal Spatial Pattern
• describes a possible relationship among evolution
  of attributes
• E.g., if the user want to know patterns involving
  salary and distance to big city, then one
  interesting pattern would be people receiving a
  raise tends to move further away from the big
  city from 1987 to 1993..

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Temporal Spatial Pattern Detection

• More complicated patterns
• Patterns on clustering evolution
• Patterns of high order
• Patterns whose cause and consequence do not
  happen together
• There is a delay for the consequence to show up.
• Patterns involving relationships among objects
• e.g., people who live far away from any doctor
  tend to move to a place closer to some doctor.
• Environment variables evolve independently over
  time.