School of Computer Science and Engineering
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Transcript of School of Computer Science and Engineering
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School of Computer Science and Engineering
Finding Top k Most Influential Spatial Facilities over Uncertain Objects
Liming Zhan Ying Zhang Wenjie Zhang Xuemin Lin
The University of New South Wales, Australia
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Outline
Motivation Problem Definition Our Approach Experiments Conclusion
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Motivation example: NN, RNN, Influential Sites
I(F): influence score of F, which is the number of objects influenced by F, namely, treat F as the NN.
I(F1)=1I(F2)=2I(F3)=0
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Motivation
Warehouse Management SystemsRFID tags are attached to the items, whose locations can be
obtained by RFID readersFind top k popular dispatching points.
Location Based Service (LBS)Mobile to identify users’ locationFind the top k supermarkets which influence the largest
number of users.
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Influence Sites
Influence sets based on reverse nearest neighbor queries [SIGMOD 2000, Korn et al.]
On computing top-t most influential spatial sites (TkIS) [VLDB 2005, Xia et al.]
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Uncertainty exists
UncertaintyRFID Reader: noisyLocation of mobile users: imprecise
Uncertain objectsContinuous: PDFDiscrete: multiple instances
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Motivating example
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Challenge
Uncertain model Instances from an uncertain object may be influenced by several
facilities – How to model the query.
Efficiency of the algorithm More complicated than that of traditional objects
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Example
[TKDE 2011, Zheng et al.]
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Problem Statement
Given a set of uncertain objects O and a set of facilities F, find the k facilities with the highest expected influence scores.
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Naïve method
For each instance of an object, find the nearest facility f and increase the influential score of f by the probability of the instance.
Return k facilities with highest scores.
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Data Structure: Global R-tree
Global R-tree indexes the MBBs of all uncertain objects.
MBB of an object is the minimum bounding box containing all its instances.
Each leaf is a MBB of an object in the global R-tree.
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Data Structure: Local aR-tree (Aggregate R-tree)
For each uncertain object, a local aR-tree is built to organize its multiple instance.
For every intermediate entry E in the local aR-tree, the probability of E is the sum of probability of the instances considering E as an ancestor.
P(E)=P(E1)+P(E2)
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Framework
FilteringObtain tight lower and upper bounds for each facility and
prune unpromising facilities.Process on global index - no object loaded.
RefinementFor each candidate facility, compute influence score based
on local aR-tree.
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Filtering: Level by level
RU: Objects R-tree RF: Facility R-tree⋈⋈⋈
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Filtering: upper bound of facility score
I+(F1), I+(F2) ← number of objects in E1
max distancemin distance
maxdist(F1,E1)< mindist(Fi,E1)maxdist(F2,E1)< mindist(Fi,E1)
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Filtering: lower bound of facility score
min distancemax distance
I-(F1) ← number of objects in E1maxdist(F1,E1)< mindist(F2,E1)maxdist(F1,E1)< mindist(F3,E1)
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Filtering: get candidate
Sort facilities by lower bound in descending order
For top-K queryCompare the lower bound of the Kth facility with the upper
bound of the following facilities
Get candidate facilities dataset
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Refinement
For each candidate facility, traverse all the possible influenced objects aR-tree to get the exact score.
Get the top k facilities with the highest influence scores.
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U-Quadtree as global index
EDBT 2012, Zhang et al.
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Improvement by U-Quadtree
FilteringU-Quadtree build summaries of objects based on Quadtree,
so we can get tighter upper and lower bounds to prune more objects.
RefinementUse the leaf cell of U-Quadtree to intersect the entries of
aRtree to reduce the search space.
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Experiments
Algorithms: Naïve: The naïve implementation RTKIS: The technique based on R-tree UQuadTKIS: The technique based on U-Quadtree UTKIS: The technique presented in [TKDE 2011, Zheng et al.]
Environment: PC with Intel Xeon 2.40GHz dual CPU 4GB memory Debian Linux Disk page size is 4096 bytes
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Experiments (Cont.)
Real datasetsCenter distribution: CA (62k), US (200k), R-tree-portal(21K)Normalized to [0,10000]
Parameters
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Experiments (Cont.)
Expected Score VS Expected Rank – Result Comparison
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Experiments (Cont.)
Impact of Data Distribution
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Experiments (Cont.)
Varying m Varying ru
Varying #facilities Varying #objects
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Conclusion We propose a new model to evaluate the influences of the
facilities over a set of uncertain objects. Efficient R-tree and U-Quadtree based algorithms are presented
following the filtering and refinement paradigm. Novel pruning techniques are proposed to significantly improve
the performance of the algorithms by reducing the number of uncertain objects and facilities in the computation.
Comprehensive experiments demonstrate the effectiveness and efficiency of our techniques.
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Thank you!
Questions?