Uncertain Spatiotemporal Databases

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Uncertain Spatiotemporal Databases

• Yufei Tao
• Chinese University of Hong Kong

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Spatial databases

• Query processing Retrieval of stationary
  locations.
• Range search
• Nearest neighbor retrieval
• Object location changes are captured by explicit
  updates to the database.

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Retrospect

• First (?) SIGMOD/VLDB/ICDE/PODS paper about query
  processing on spatiotemporal data
• G. Kollios, D. Gunopulos, and V. Tsotras. On
  Indexing Mobile Objects. PODS, 1999.
• 2006 1999 7 years.

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The current literature

• Historical retrieval
• A direct (but non-trivial) extension of the
  traditional temporal databases
• The database stores the historical location of
  each object at every single past timestamp.

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The current literature (cont.)

• Find all vehicles that were in the 1km vicinity
  of the crime scene at 7pm on Nov 1 2006.
• Find the 10 vehicles that were closest to the
  crime scene at 7pm on Nov 1 2006.

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The current literature (cont.)

• Future prediction
• A novel area specific to spatiotemporal
• The database stores the current location and
  velocity of each object.
• The objective is to retrieve objects expected to
  satisfy certain predicates in the future.

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The current literature (cont.)
Current movements
Locations 1 timestamp later

• Find the aircrafts expected to appear in the air
  space of Hong Kong in 10 minutes.
• Find the aircraft nearest to UA801 in 10
  minutes.

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The current literature (cont.)
Current movements

• Future prediction captures the conventional
  spatial databases as a special case.
• Queries concern objects current locations only.
• Hence, object velocities do not matter.

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The current literature (cont.)

• Indexing
• HR-, MVR-, 3D R-trees,
• TPR-, TPR-, STRIPES, Bx-, Bdual-trees,
• Range search
• Nearest neighbor
• Time parameterized NN
• Continuous NN
• Location based NN
• Selectivity estimation
• Histograms
• Sampling
• Stream processing
• Fact Harder and harder to impress the database
  community.

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A new twist?

• All the above work assumes that the database has
  the exact location of each object.
• This is rarely possible.

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Uncertainty
An objects location is described by a
probability density function.
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Probabilistic range search
Find the clients that are currently in the town
center with at least 50 probability.
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Qualification probability
Qualification probability
Example uniform
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Qualification probability (cont.)

• Probabilistic modeling in practice

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Qualification probability (cont.)
must be calculated numerically
Calculation time of an appearance probability in
2D space 1.3ms
Time for a random I/O access 10ms
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Exciting opportunities

• Uncertain range search
• Reynold et al. VLDB 04, Tao et al. VLDB 05
• Uncertain nearest neighbor search
• Reynold et al. TKDE 04
• Uncertain selectivity estimation
• No work
• Uncertain stream processing
• No work
• All existing work considers only uncertain
  stationary objects.
• Location updates need to be reported to the
  database through explicit updates.
• Combined with future prediction or historical
  retrieval.
• No existing work.

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In this talk

• Goal Motivate query processing on uncertain
  spatiotemporal objects
• Uncertain range search on stationary objects
• If time permits
• Indexing of historical uncertain data

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Nonfuzzy queries

• Find all objects that appear in a search region
  rq with a probability ? tq.

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Fuzzy queries

• Find all objects whose distances to an uncertain
  object q are ? eq with a probability ? tq.

Example q the cab with suspects objects
police cars
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Goal

• Support any pdf.
• Convex/concave uncertainty regions
• Minimize the number of page accesses
• Minimize the number of qualification probability
  calculations.
• Minimize the total cost (I/O CPU)

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Review MBR and why

• Minimum bounding rectangle (MBR)

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Main Idea

• For each object, pre-compute some auxiliary
  information that can be used to
• efficiently decide whether an object appears in a
  region with at least a certain probability
• without calculating its actual appearance
  probability.
• Auxiliary information Probabilistically
  constrained rectangle

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Probabilistically Constrained Rectangle (PCR)
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PCR in pruning
Probability threshold tq 0.8.
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PCR in pruning
Probability threshold tq 0.2.
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PCR in validating
tq 0.9
tq 0.8
tq 0.1
o.pcr(0.1)
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PCR in validating (cont.)
tq 0.6
tq 0.8
tq 0.7
o.pcr(0.1)
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Still down the road

• Only a finite number of PCRs can be stored for
  each object. Which ones to store?
• How to index these PCRs to reduce query cost?
• Cost model analysis?
• Fuzzy range search (repeat all the above issues)

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In this talk

• Goal Motivate query processing on uncertain
  spatiotemporal objects
• Uncertain range search on stationary objects
• If time permits
• Indexing of historical uncertain data

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Historical uncertain spatiotemporal databases

• Application
• A database stores the locations of each vehicle
  on a 10-minute basis in the whole past year.
• Possible queries
• Find all vehicles that appeared in the town
  center sometime during 6pm-7pm with a probability
  at least 50.
• Find all vehicles that appeared in the town
  center during the entire period of 6pm-7pm with a
  probability at least 50.
• Nearest neighbor search counterparts

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Existing Uncertainty Models

• The linear model

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Existing Uncertainty Models (cont.)

• The ellipse model Pfoser et al. SSTD 99

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Existing Uncertainty Models (cont.)

• The cylinder model Trajcevski et al. TODS 04

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A general modeling

• Each object o is associated with an o.pdf(x, t),
  which captures the probability that o is at
  location x at any timestamp t in history.

Conceptually, one pdf like this at every past
timestamp.
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Query semantics Trajcevski et al. TODS 04

• Based on the cylinder model

possibly sometime
possibly always
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Query semantics (cont.)

• Based on the cylinder model

always possibly
definitely always
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Query semantics (cont.)

• Based on the cylinder model

definitely sometime
sometime definitely
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Query processing
Conceptually, one pdf like this at every past
timestamp.

• Difficulties
• There are infinitely number of timestamps in the
  past. How to compute the pdfs at all of them?
• How to index them?
• Can PCRs help?
• Algorithms for supporting all the previous
  semantics based on the index structure?

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Conclusions

• Uncertain spatiotemporal query processing
• Data
• Stationary, historical, and moving
• Queries
• Range search, NN, selectivity estimation,
• New query types fuzzy range search,
• Combinations of the above two.