Spatial-Temporal Data Mining

1
Spatial-Temporal Data Mining

• Wei Wang
• Data Mining Lab
• Computer Science Department UCLA

2
Outline

• Introduction
• Active Spatial Data Mining
• Spatial data mining trigger
• Temporal Association Rule with Numerical
  Attributes
• Correlation among object evolutions
• Conclusions and Future Work

3
Introduction

• Huge amount of spatial data are generated
  everyday.
• Earth Observing System
• National Spatial Data Infrastructure
• National Image Mapping Agency
• One meter resolution data
• Digital earth
• Users are usually interested in the hidden
  information.
• Aggregate information
• Clustering
• Patterns

4
Introduction

• Knowledge discovery processes are computationally
  expensive.
• Todays technology advances provide necessary
  computing power to carry out such complicated
  processes.

5
Outline

• Introduction
• STING An approach to active spatial data mining
• Temporal association rules with numerical
  attributes
• Conclusions and Future Work

6
STING

• Since data evolves over time, interesting
  patterns are likely to emerge or change.
• Goal identify and find (most) interesting
  patterns
• Problems
• Knowledge discovery processes are expensive.
• It is not feasible to re-process the entire
  data set for every change.
• Periodically examine the data.
• Long delays
• Transient patterns might be missed
• Natural solution Usage of triggers.

7
STING

• Traditional database triggers can not be directly
  applied
• Expressive power of traditional database triggers
  is limited, especially in describing spatial
  relationships.
• Example Trigger investigation when the size of
  any cluster exceeds 20.

8
STING

• STING was designed to introduce and support
  spatial triggers efficiently.
• Observation (spatial locality) Only objects
  added to the shaded area will contribute to the
  growth of cluster size at this moment.

9
STING

• STING Strategy Monitor only the area occupied
  by potential clusters and their neighborhoods.
• Observation (cumulative effect) at least 4 more
  objects are needed in order to make the cluster
  size be 20.
• STING Strategy Space is organized in a
  hierarchy so that updates can be suspended at
  various levels in the hierarchy until the
  cumulative effect might cause the trigger to be
  fired.

10
STING

• Space is recursively divided into smaller
  rectangular cells down to a specified granularity
  and is organized via the inherit pyramid
  hierarchy.

11
STING

• STING decomposes a trigger into a set of
  sub-triggers associated with individual cells in
  the hierarchical structure to monitor the
  cumulative effect of data changes within the cell.

Level 4
12
STING

• Updates/insertions are suspended at various
  levels in the hierarchy until such time that the
  cumulative effect of these insertions might cause
  the trigger condition to become satisfied.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.








.
.
.
.
.
.
.
.
.
.
Level 1
Level 0
13
STING
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.








.
.
.
.
.
.
.
.
.
.
Level 3
Level 2
No update of cluster !
14
STING

• Primitive event insertion, deletion, update
• Composite event a set of primitive events
• In general, evaluating a 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).
• Observation As a side effect of the occurrence
  of some composite event, E(s) might also evolve
  over time.

15
STING
.
.
.
.
.
.
.
.
.

• STING Strategy Two sets of composite events are
  considered
• 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)
• The sub-triggers are used to monitor composite
  events in E(s) and F(s) and change accordingly
  when E(s) and F(s) evolves.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
16
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 specific 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.

17
STING

• PK-tree is used to index instantiated cells
• Bound on height
• Bounds on number of children
• Uniqueness for any data set
• independent of order of insertion and deletion
• Solid theoretical foundation
• Fast retrieval and efficient maintenance
• Statistical information maintained at each node
  is used to facilitate the trigger process.
• Sub-trigger

18
STING

• Comparison with periodic re-examination via STING
• 200,000 synthetic point objects
• 10,000 insertions/deletions/updates
• If the period is set to be less than 4000
  updates, STING consumes less CPU cycles.
• Significant delay and transient patterns misses
  can occur for larger period.
• Not acceptable in many applications
• No delay and no transient patterns missed with
  STING.

19
Outline

• Introduction
• STING An approach to active spatial data mining
• Temporal association rules with numerical
  attributes
• Conclusions and Future Work

20
Temporal Association Rules

• Now we are considering general databases with
  evolving numerical attributes.
• Interesting patterns exhibited in the data are
  often numerous and complicated.
• Customer churning If a customers phone bill
  increases by at least 10 each month for six
  months, then he is likely to change his long
  distance telephone carrier.
• Real estate People who receive a raise of at
  least 20 of their salary are likely to move away
  from big city.
• Such patterns can be represented by association
  rules of the form X ? Y, which indicates that the
  occurrences of X and Y have high correlation.

21
Temporal Association Rules

• Earlier work on association rules mainly focused
  on binary attributes and intra-transaction
  relationship.
• E.g., ham ? bread
• Support and strength are two metrics used to
  qualify interesting rules.
• support number of instances to follow the rule
• N(ham, bread)
• strength how strong the correlation is

22
Temporal Association Rules

• Consider a set of objects, each of which has a
  unique ID and a set of time varying numerical
  attributes and a sequence of snapshots are taken
  at some frequency.
• E.g., in an employee database, two attributes are
  considered salary and monthly housing expense.
• For a given snapshot, each employee can be mapped
  to a point in a two dimensional space.

23
Temporal Association Rules

• Given a sequence of snapshots, the trace of an
  employee can be mapped to a point in a high
  dimensional space.
• (lts1, mhe1gt, lts2, mhe2gt, lts3, mhe3gt, lts4, mhe4gt,
  lts5, mhe5gt)

24
Temporal Association Rules

• Temporal association rules represent the
  correlation among object evolutions.
• (salary 52000, 56000?54000, 58000) ?
  (monthly_housing_expense 1200, 1400?1400,
  1600)
• Each temporal association rule can also be viewed
  as an interpretation of a cluster (with certain
  shape) of points.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
salary
.
.
.
.
.
.
.
.
.
.
.
.
.
.
monthly_housing_expense
25
Temporal Association Rules

• Observation The domain of a numerical attribute
  might contain a large number of distinct values
  and might even be continuous.
• E.g., domain(salary) 50000, 60000.
• Any sub-ranges can appear in a rule.
• The number of possible rules may be very large if
  not infinite.
• Strategy Each attribute domain is quantized into
  a set of equi-length base intervals.
• The domain of salary could be quantized into base
  intervals of length 2000
• Values within the same interval are not
  distinguished.
• E.g., 51000 and 51500 are considered as the
  same.

50000
60000
26
Temporal Association Rules

• Attribute evolution

60000
58000
56000
salary
54000
52000
50000
E1(salary) 52000, 54000 ? 52000, 54000 ?
54000, 56000
E2(salary) 52000, 56000 ? 52000, 54000 ?
52000, 56000
27
Temporal Association Rules
28
Temporal Association Rules

• The subcube-supercube relationship defines a
  lattice among all evolution cubes within the
  evolution space.
• This also holds for the evolution space of more
  than one attributes.

60000
salary
50000
1000
2000
monthly housing expense
29
Temporal Association Rules

• Some properties of the metrics enable us to
  search efficiently through the lattice in a
  bottom-up manner.

30
Temporal Association Rules

• Observation Many valid but trivial rules may
  exist.
• (salary 52000, 56000) ? (monthly_housing_expens
  e 1200, 1400)
• (salary 50000, 56000) ? (monthly_housing_expens
  e 1200, 1400)
• Both rules have the same value of support and
  strength since no employees salary is between
  50000 and 52000. However, the first rule conveys
  more precise information.

31
Temporal Association Rules

• Strategy An interval can be included in a rule
  only if there are some minimum number of objects
  whose attributes values fall into that interval.
• The density of each base cube within the
  evolution cube of a rule has to meet some
  threshold.
• In the previous example, the second rule can be
  eliminated.
• Property of density An evolution cube could
  satisfy the density threshold only when all of
  its subcubes satisfy the density threshold.

min_density 2
32
Temporal Association Rules

• General Model
• Data set D
• Language L
• express properties or define subgroup of data
• Selection predicate q
• evaluate whether a sentence ? ? L defines a
  potentially interesting class of D
• Task find the set ? ? q(D, ?) is true
• If
• a lattice can be formed on sentences in L and
• partial order exists on selection predicate
• then the level-wise algorithm can be used to
  prune search space efficiently.

33
Temporal Association Rules

• Temporal Association Rule
• Language L each sentence ? ? L is a temporal
  association rule.
• The selection predicate q(D, ?) is true iff
• support(D, ?) ? min_support and
• strength(D, ?) ? min_strength and
• density(D, ?) ? min_density
• Task find the set of temporal association rules
  which satisfy all three predicates.
• Specialization relation lt ? a lattice on the
  sentences in L
• subcube/supercube relationship

q1
q2
q3
34
Temporal Association Rules

• partial order on qi with respect to lt
• support(D, ?) ? support(D, ?) if ? lt ?
• if strength (D, ?) lt min_strength for all ? lt ?,
  then strength(D, ?) lt min_strength
• density(D, ?) ? density(D, ?) if ? lt ?
• level-wise algorithm
• basic scheme starting from the most special
  (general) sentences, and then evaluate more and
  more general (special) sentences excluding those
  sentences that can not be interesting given all
  the information obtained in earlier iterations.
• Efficient space pruning
• Starting point
• Random sampling
• Order of predicate evaluation

35
Temporal Association Rules

• Efficiency of space pruning
• SR algorithm after quantization, base intervals
  are combined as long as their density satisfies
  the threshold. The original base intervals and
  the combined intervals are treated as a set of
  items.

100000 objects 100 snapshots 5 attributes 500
rules of length 5 density 2 support
5 strength 1.4
36
Conclusions and Future Work

• STING was developed to support spatial data
  mining triggers very efficiently by
• employing spatial locality property and
• postponing the trigger condition evaluation until
  the cumulative effect might cause the trigger to
  be fired.
• Temporal association rules were introduced to
  capture relationship among object evolutions.
• Selected continuous work
• 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., children tend to live further away from
  their parent when they grow up.

37
Conclusions and Future Work

• Selected future work
• Data mining over Internet
• data type
• networking issue
• Analytical model
• classify data mining problems
• devise efficient general approach
• Applications
• compiler/programming language
• WWW