Spatial-Temporal Data Mining Wei Wang Data Mining Lab Computer Science Department UCLA
Outline <ul><li>Introduction </li></ul><ul><li>Active Spatial Data Mining </li></ul><ul><ul><li>Spatial data mining trigge...
Introduction <ul><li>Huge amount of spatial data are generated everyday. </li></ul><ul><ul><li>Earth Observing System </li...
Introduction <ul><li>Knowledge discovery processes are computationally expensive. </li></ul><ul><li>Today’s technology adv...
Outline <ul><li>Introduction </li></ul><ul><li>STING+: An approach to active spatial data mining </li></ul><ul><li>Tempora...
STING+ <ul><li>Since data evolves over time, interesting patterns are likely to emerge or change. </li></ul><ul><li>Goal: ...
STING+ <ul><li>Traditional database triggers can not be directly applied: </li></ul><ul><ul><li>Expressive power of tradit...
STING+ <ul><li>STING+ was designed to introduce and support  spatial triggers  efficiently. </li></ul><ul><li>Observation ...
STING+ <ul><li>STING+ Strategy:  Monitor   only the area occupied by potential clusters and their neighborhoods. </li></ul...
STING+ <ul><ul><li>Space is recursively divided into smaller rectangular cells down to a specified granularity and is orga...
STING+ <ul><ul><li>STING+ decomposes a trigger into a set of  sub-triggers  associated with individual cells in the hierar...
STING+ <ul><ul><li>Updates/insertions are  suspended  at various levels in the hierarchy until such time that the cumulati...
STING+ Level 3 . . . . . . . . . . . . . . . . . . . . . . . . + + + + . . . . . . . . . . . . . . . . . . . . . . . . Lev...
STING+ <ul><li>Primitive event:   insertion ,  deletion ,  update </li></ul><ul><li>Composite event:  a set of primitive e...
STING+ <ul><li>STING+ Strategy:  Two sets of composite events are considered: </li></ul><ul><ul><li>the set of composite e...
STING+ <ul><li>Observation:  Trigger condition  C T  is a conjunction of predicates  P 1      P 2     …     P n  and ca...
STING+ <ul><li>PK-tree  is used to index  instantiated   cells </li></ul><ul><ul><li>Bound on height </li></ul></ul><ul><u...
STING+ <ul><li>Comparison with periodic re-examination via STING </li></ul><ul><ul><li>200,000 synthetic point objects </l...
Outline <ul><li>Introduction </li></ul><ul><li>STING+: An approach to active spatial data mining </li></ul><ul><li>Tempora...
Temporal Association Rules <ul><li>Now we are considering general databases with evolving numerical attributes. </li></ul>...
Temporal Association Rules <ul><li>Earlier work on association rules mainly focused on binary attributes and intra-transac...
Temporal Association Rules <ul><li>Consider a set of objects, each of which has a unique ID and a set of time varying nume...
Temporal Association Rules <ul><ul><li>Given a sequence of snapshots, the  trace  of an employee can be mapped to a point ...
Temporal Association Rules <ul><li>Temporal association rules  represent the correlation among object evolutions. </li></u...
Temporal Association Rules <ul><li>Observation:   The domain of a numerical attribute might contain a large number of dist...
Temporal Association Rules <ul><li>Attribute evolution </li></ul>50000 56000 54000 salary 58000 60000 52000 E 1 ( salary )...
Temporal Association Rules Snapshot 1 Snapshot 2 Snapshot 3 Evolution space Evolution cube of  E 1 ( salary ) Evolution cu...
Temporal Association Rules <ul><ul><li>The subcube-supercube  relationship defines a  lattice  among all evolution cubes w...
Temporal Association Rules <ul><li>Some properties of the metrics enable us to search efficiently through the lattice in a...
Temporal Association Rules <ul><li>Observation:   Many valid but trivial rules may exist. </li></ul><ul><ul><li>( salary :...
Temporal Association Rules <ul><li>Strategy:  An interval can be included in a rule only if there are some minimum number ...
Temporal Association Rules <ul><li>General Model: </li></ul><ul><ul><li>Data set  D </li></ul></ul><ul><ul><li>Language  L...
Temporal Association Rules <ul><li>Temporal Association Rule: </li></ul><ul><ul><li>Language  L :  each sentence        ...
Temporal Association Rules <ul><li>partial order  on  q i  with respect to  < </li></ul><ul><ul><li>support( D ,   )    ...
Temporal Association Rules <ul><li>Efficiency of space pruning </li></ul><ul><ul><li>SR algorithm: after quantization, bas...
Conclusions and Future Work <ul><li>STING+ was developed to support  spatial data mining triggers  very efficiently by  </...
Conclusions and Future Work <ul><li>Selected future work </li></ul><ul><ul><li>Data mining over Internet </li></ul></ul><u...
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  • The topic of my talk today is Spatial temporal data mining. My name is Wei Wang. I am a Ph.D. candidate in this department. This work was supported by NASA and NCR funds.
  • I will first give a brief introduction on the motivation of our research. In the first half of the talk, I will explain an approach to active spatial data mining. Similar to conventional databases, it is also desirable for the data mining system to support triggers. We will see shortly how this can be done efficiently on spatial databases. The second half of my talk focuses on mining temporal association rules with numerical attributes. As opposite to the traditional association rule on binary attribute and intra-transaction relationships, association rules with numerical attributes and temporal evolutions are often much more complicated. How to mine this type of association rules is quite challenging. Finally, I’ll conclude my talk and mention some of the future work.
  • 1. Earth Observing System: generate terabytes data everyday. One meter resolution data will be available later this year commercially. Our vice president also promote the concept of digital earth which provides seamless access of the spatial data. 2. Such hidden information could be aggregate information, clustering, or even more general type of patterns.
  • Most previous research focuses on passive data mining, i.e., efficient query processing. However, people may want to monitor the appearance of some pattern and take action accordingly. Therefore, we introduced an approach called STING+ to support spatial data mining triggers efficiently.
  • 1. As I mentioned at the beginning, ….. 2. Our goal is to identify and find most of these interesting patterns if not all. 3.2. One alternative would be examining the data periodically, say every 1000 updates.
  • 2. Moreover, the expressive power of traditional database triggers is limited. Especially in describing spatial relationships. 3. For example, to guarantee the quality of service, a cellular phone company may want to dynamically reallocation bandwidth to different area according to the customer usage. 3.1. How to express the notion of cluster? 3.2 since data change very frequently, current clusters may move, vanish, and new clusters may appear, how to monitor such evolution efficiently?
  • This is the set of cells to approximate the shaded area. A sub-trigger is set on each cell. At higher level, a sub-trigger is set on a cell iff any of its subcells (children) has a subtrigger.
  • Remember that we need at least 4 insertions/updates to satisfy the trigger condition.
  • Spatial Temporal Data Mining

    1. 1. Spatial-Temporal Data Mining Wei Wang Data Mining Lab Computer Science Department UCLA
    2. 2. Outline <ul><li>Introduction </li></ul><ul><li>Active Spatial Data Mining </li></ul><ul><ul><li>Spatial data mining trigger </li></ul></ul><ul><li>Temporal Association Rule with Numerical Attributes </li></ul><ul><ul><li>Correlation among object evolutions </li></ul></ul><ul><li>Conclusions and Future Work </li></ul>
    3. 3. Introduction <ul><li>Huge amount of spatial data are generated everyday. </li></ul><ul><ul><li>Earth Observing System </li></ul></ul><ul><ul><li>National Spatial Data Infrastructure </li></ul></ul><ul><ul><li>National Image Mapping Agency </li></ul></ul><ul><ul><li>One meter resolution data </li></ul></ul><ul><ul><li>Digital earth </li></ul></ul><ul><li>Users are usually interested in the hidden information. </li></ul><ul><ul><li>Aggregate information </li></ul></ul><ul><ul><li>Clustering </li></ul></ul><ul><ul><li>Patterns </li></ul></ul>
    4. 4. Introduction <ul><li>Knowledge discovery processes are computationally expensive. </li></ul><ul><li>Today’s technology advances provide necessary computing power to carry out such complicated processes. </li></ul>
    5. 5. Outline <ul><li>Introduction </li></ul><ul><li>STING+: An approach to active spatial data mining </li></ul><ul><li>Temporal association rules with numerical attributes </li></ul><ul><li>Conclusions and Future Work </li></ul>
    6. 6. STING+ <ul><li>Since data evolves over time, interesting patterns are likely to emerge or change. </li></ul><ul><li>Goal: identify and find (most) interesting patterns </li></ul><ul><li>Problems: </li></ul><ul><ul><li>Knowledge discovery processes are expensive. </li></ul></ul><ul><ul><ul><li>It is not feasible to re-process the entire data set for every change. </li></ul></ul></ul><ul><ul><li>Periodically examine the data. </li></ul></ul><ul><ul><ul><li>Long delays </li></ul></ul></ul><ul><ul><ul><li>Transient patterns might be missed </li></ul></ul></ul><ul><li>Natural solution: Usage of triggers . </li></ul>
    7. 7. STING+ <ul><li>Traditional database triggers can not be directly applied: </li></ul><ul><ul><li>Expressive power of traditional database triggers is limited, especially in describing spatial relationships. </li></ul></ul><ul><ul><li>Example: Trigger investigation when the size of any cluster exceeds 20. </li></ul></ul>. . . . . . . . . . . . . . . . . . . . . . . .
    8. 8. STING+ <ul><li>STING+ was designed to introduce and support spatial triggers efficiently. </li></ul><ul><li>Observation (spatial locality): Only objects added to the shaded area will contribute to the growth of cluster size at this moment. </li></ul>. . . . . . . . . . . . . . . . . . . . . . . .
    9. 9. STING+ <ul><li>STING+ Strategy: Monitor only the area occupied by potential clusters and their neighborhoods. </li></ul><ul><li>Observation (cumulative effect): at least 4 more objects are needed in order to make the cluster size be 20. </li></ul><ul><li>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. </li></ul>
    10. 10. STING+ <ul><ul><li>Space is recursively divided into smaller rectangular cells down to a specified granularity and is organized via the inherit pyramid hierarchy. </li></ul></ul>. . . . . . . . . . . . . . . . . . . . . . . . Level 1 . . . . . . . . . . . . . . . . . . . . . . . . Level 2
    11. 11. STING+ <ul><ul><li>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. </li></ul></ul>Level 4 . . . . . . . . . . . . . . . . . . . . . . . . Sub-trigger on cell Level 3 . . . . . . . . . . . . . . . . . . . . . . . . Higher level sub-trigger on cell
    12. 12. STING+ <ul><ul><li>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. </li></ul></ul>. . . . . . . . . . . . . . . . . . . . . . . . Level 1 . . . . . . . . . . . . . . . . . . . . . . . . Level 0 + + + + + + + +
    13. 13. STING+ Level 3 . . . . . . . . . . . . . . . . . . . . . . . . + + + + . . . . . . . . . . . . . . . . . . . . . . . . Level 2 + + + + No update of cluster !
    14. 14. STING+ <ul><li>Primitive event: insertion , deletion , update </li></ul><ul><li>Composite event: a set of primitive events </li></ul><ul><li>In general, evaluating a trigger T usually involves two aspects: </li></ul><ul><ul><li>Find a set of composite events E ( s ) that may cause the trigger condition C T to become true. </li></ul></ul><ul><ul><li>Each time some composite event in E ( s ) occurs, check the status (false or true) of C T (given that C T was false previously). </li></ul></ul><ul><li>Observation: As a side effect of the occurrence of some composite event, E(s) might also evolve over time. </li></ul>
    15. 15. STING+ <ul><li>STING+ Strategy: Two sets of composite events are considered: </li></ul><ul><ul><li>the set of composite events E ( s ) that can cause C T to become true </li></ul></ul><ul><ul><ul><li>need to re-evaluate C T </li></ul></ul></ul><ul><ul><li>the set of composite events F ( s ) that can cause a change to E ( s ) </li></ul></ul><ul><ul><ul><li>need to update E ( s ) </li></ul></ul></ul><ul><ul><li>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 . </li></ul></ul>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
    16. 16. STING+ <ul><li>Observation: Trigger condition C T is a conjunction of predicates P 1  P 2  …  P n and can not be true if one predicate is false. </li></ul><ul><ul><li>They can be evaluated in a specific order: the i th predicate is tested when all previous ( i -1) predicates are true. </li></ul></ul><ul><ul><li>The evaluation order should be chosen in such a way that the total cost is minimum. </li></ul></ul>
    17. 17. STING+ <ul><li>PK-tree is used to index instantiated cells </li></ul><ul><ul><li>Bound on height </li></ul></ul><ul><ul><li>Bounds on number of children </li></ul></ul><ul><ul><li>Uniqueness for any data set </li></ul></ul><ul><ul><ul><li>independent of order of insertion and deletion </li></ul></ul></ul><ul><ul><li>Solid theoretical foundation </li></ul></ul><ul><ul><li>Fast retrieval and efficient maintenance </li></ul></ul><ul><li>Statistical information maintained at each node is used to facilitate the trigger process. </li></ul><ul><ul><li>Sub-trigger </li></ul></ul>
    18. 18. STING+ <ul><li>Comparison with periodic re-examination via STING </li></ul><ul><ul><li>200,000 synthetic point objects </li></ul></ul><ul><ul><li>10,000 insertions/deletions/updates </li></ul></ul><ul><ul><li>If the period is set to be less than 4000 updates, STING+ consumes less CPU cycles. </li></ul></ul><ul><ul><li>Significant delay and transient patterns misses can occur for larger period. </li></ul></ul><ul><ul><ul><li>Not acceptable in many applications </li></ul></ul></ul><ul><ul><li>No delay and no transient patterns missed with STING+. </li></ul></ul>
    19. 19. Outline <ul><li>Introduction </li></ul><ul><li>STING+: An approach to active spatial data mining </li></ul><ul><li>Temporal association rules with numerical attributes </li></ul><ul><li>Conclusions and Future Work </li></ul>
    20. 20. Temporal Association Rules <ul><li>Now we are considering general databases with evolving numerical attributes. </li></ul><ul><li>Interesting patterns exhibited in the data are often numerous and complicated. </li></ul><ul><ul><li>Customer churning: If a customer’s phone bill increases by at least $10 each month for six months, then he is likely to change his long distance telephone carrier. </li></ul></ul><ul><ul><li>Real estate: People who receive a raise of at least 20% of their salary are likely to move away from big city. </li></ul></ul><ul><li>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. </li></ul>
    21. 21. Temporal Association Rules <ul><li>Earlier work on association rules mainly focused on binary attributes and intra-transaction relationship. </li></ul><ul><ul><li>E.g., ham  bread </li></ul></ul><ul><ul><li>Support and strength are two metrics used to qualify interesting rules. </li></ul></ul><ul><ul><ul><li>support : number of instances to follow the rule </li></ul></ul></ul><ul><ul><ul><ul><li>N ( ham , bread ) </li></ul></ul></ul></ul><ul><ul><ul><li>strength : how strong the correlation is </li></ul></ul></ul>
    22. 22. Temporal Association Rules <ul><li>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. </li></ul><ul><ul><li>E.g., in an employee database, two attributes are considered: salary and monthly housing expense. </li></ul></ul><ul><ul><li>For a given snapshot, each employee can be mapped to a point in a two dimensional space. </li></ul></ul>salary monthly housing expense . . . . . .
    23. 23. Temporal Association Rules <ul><ul><li>Given a sequence of snapshots, the trace of an employee can be mapped to a point in a high dimensional space. </li></ul></ul><ul><ul><ul><li>(< s 1 , mhe 1 >, < s 2 , mhe 2 >, < s 3 , mhe 3 >, < s 4 , mhe 4 >, < s 5 , mhe 5 >) </li></ul></ul></ul>salary monthly housing expense . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Snapshot 1 Snapshot 2 Snapshot 3 Snapshot 4 Snapshot 5 time
    24. 24. Temporal Association Rules <ul><li>Temporal association rules represent the correlation among object evolutions. </li></ul><ul><ul><li>( salary : [52000, 56000]  [54000, 58000])  ( monthly_housing_expense : [1200, 1400]  [1400, 1600]) </li></ul></ul><ul><ul><li>Each temporal association rule can also be viewed as an interpretation of a cluster (with certain shape) of points. </li></ul></ul>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . monthly_housing_expense salary
    25. 25. Temporal Association Rules <ul><li>Observation: The domain of a numerical attribute might contain a large number of distinct values and might even be continuous. </li></ul><ul><ul><li>E.g., domain( salary ) = [50000, 60000]. </li></ul></ul><ul><ul><li>Any sub-ranges can appear in a rule. </li></ul></ul><ul><ul><li>The number of possible rules may be very large if not infinite. </li></ul></ul><ul><li>Strategy: Each attribute domain is quantized into a set of equi-length base intervals . </li></ul><ul><ul><li>The domain of salary could be quantized into base intervals of length $2000: </li></ul></ul><ul><ul><li>Values within the same interval are not distinguished. </li></ul></ul><ul><ul><ul><li>E.g., $51000 and $51500 are considered as the same. </li></ul></ul></ul>50000 60000
    26. 26. Temporal Association Rules <ul><li>Attribute evolution </li></ul>50000 56000 54000 salary 58000 60000 52000 E 1 ( salary ) = [52000, 54000]  [52000, 54000]  [54000, 56000] E 2 ( salary ) = [52000, 56000]  [52000, 54000]  [52000, 56000]
    27. 27. Temporal Association Rules Snapshot 1 Snapshot 2 Snapshot 3 Evolution space Evolution cube of E 1 ( salary ) Evolution cube of E 2 ( salary ) Base cube
    28. 28. Temporal Association Rules <ul><ul><li>The subcube-supercube relationship defines a lattice among all evolution cubes within the evolution space. </li></ul></ul><ul><ul><li>This also holds for the evolution space of more than one attributes. </li></ul></ul>salary 50000 60000 monthly housing expense 1000 2000
    29. 29. Temporal Association Rules <ul><li>Some properties of the metrics enable us to search efficiently through the lattice in a bottom-up manner. </li></ul>... ... ... . . . . ... Property of strength : The strength of an evolution cube is less than or equal to the highest strength of its subcubes. Property of support : The support of an evolution cube is great than or equal to support of its subcube.
    30. 30. Temporal Association Rules <ul><li>Observation: Many valid but trivial rules may exist. </li></ul><ul><ul><li>( salary : [52000, 56000])  ( monthly_housing_expense : [1200, 1400]) </li></ul></ul><ul><ul><li>( salary : [50000, 56000])  ( monthly_housing_expense : [1200, 1400]) </li></ul></ul><ul><ul><li>Both rules have the same value of support and strength since no employee’s salary is between 50000 and 52000. However, the first rule conveys more precise information. </li></ul></ul>salary 50000 60000 monthly housing expense 1000 2000 . . . . . .
    31. 31. Temporal Association Rules <ul><li>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. </li></ul><ul><ul><li>The density of each base cube within the evolution cube of a rule has to meet some threshold. </li></ul></ul><ul><ul><li>In the previous example, the second rule can be eliminated. </li></ul></ul><ul><li>Property of density : An evolution cube could satisfy the density threshold only when all of its subcubes satisfy the density threshold. </li></ul>min_density = 2 . . . . . . . . . . . . . . . . . .
    32. 32. Temporal Association Rules <ul><li>General Model: </li></ul><ul><ul><li>Data set D </li></ul></ul><ul><ul><li>Language L </li></ul></ul><ul><ul><ul><li>express properties or define subgroup of data </li></ul></ul></ul><ul><ul><li>Selection predicate q </li></ul></ul><ul><ul><ul><li>evaluate whether a sentence   L defines a potentially interesting class of D </li></ul></ul></ul><ul><ul><li>Task: find the set {   | q ( D ,  ) is true} </li></ul></ul><ul><li>If </li></ul><ul><ul><li>a lattice can be formed on sentences in L and </li></ul></ul><ul><ul><li>partial order exists on selection predicate </li></ul></ul><ul><li>then the level-wise algorithm can be used to prune search space efficiently. </li></ul>
    33. 33. Temporal Association Rules <ul><li>Temporal Association Rule: </li></ul><ul><ul><li>Language L : each sentence   L is a temporal association rule. </li></ul></ul><ul><ul><li>The selection predicate q ( D ,  ) is true iff </li></ul></ul><ul><ul><ul><li>support( D ,  )  min_support and </li></ul></ul></ul><ul><ul><ul><li>strength( D ,  )  min_strength and </li></ul></ul></ul><ul><ul><ul><li>density( D ,  )  min_density </li></ul></ul></ul><ul><ul><li>Task: find the set of temporal association rules which satisfy all three predicates. </li></ul></ul><ul><li>Specialization relation <  a lattice on the sentences in L </li></ul><ul><ul><li>subcube/supercube relationship </li></ul></ul>q 1 q 2 q 3
    34. 34. Temporal Association Rules <ul><li>partial order on q i with respect to < </li></ul><ul><ul><li>support( D ,  )  support( D ,  ) if  <  </li></ul></ul><ul><ul><li>if strength ( D ,  ) < min_strength for all  <  , then strength( D ,  ) < min_strength </li></ul></ul><ul><ul><li>density( D ,  )  density( D ,  ) if  <  </li></ul></ul><ul><li>level-wise algorithm </li></ul><ul><ul><li>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. </li></ul></ul><ul><li>Efficient space pruning </li></ul><ul><ul><li>Starting point </li></ul></ul><ul><ul><li>Random sampling </li></ul></ul><ul><ul><li>Order of predicate evaluation </li></ul></ul>
    35. 35. Temporal Association Rules <ul><li>Efficiency of space pruning </li></ul><ul><ul><li>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. </li></ul></ul>100000 objects 100 snapshots 5 attributes 500 rules of length 5 density = 2 support = 5% strength = 1.4
    36. 36. Conclusions and Future Work <ul><li>STING+ was developed to support spatial data mining triggers very efficiently by </li></ul><ul><ul><li>employing spatial locality property and </li></ul></ul><ul><ul><li>postponing the trigger condition evaluation until the cumulative effect might cause the trigger to be fired. </li></ul></ul><ul><li>Temporal association rules were introduced to capture relationship among object evolutions . </li></ul><ul><li>Selected continuous work </li></ul><ul><ul><li>Patterns whose cause and consequence do not happen together </li></ul></ul><ul><ul><ul><li>There is a delay for the consequence to show up. </li></ul></ul></ul><ul><ul><li>Patterns involving relationships among objects </li></ul></ul><ul><ul><ul><li>e.g., children tend to live further away from their parent when they grow up. </li></ul></ul></ul>
    37. 37. Conclusions and Future Work <ul><li>Selected future work </li></ul><ul><ul><li>Data mining over Internet </li></ul></ul><ul><ul><ul><li>data type </li></ul></ul></ul><ul><ul><ul><li>networking issue </li></ul></ul></ul><ul><ul><li>Analytical model </li></ul></ul><ul><ul><ul><li>classify data mining problems </li></ul></ul></ul><ul><ul><ul><li>devise efficient general approach </li></ul></ul></ul><ul><ul><li>Applications </li></ul></ul><ul><ul><ul><li>compiler/programming language </li></ul></ul></ul><ul><ul><ul><li>WWW </li></ul></ul></ul>
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