1. Uncertain Data
Mobile Group
报告人：郝兴

2. Paper List
Querying Imprecise Data in Moving Object Environments. [TKDE 2004] Reynold Cheng, Dmitri V. Kalashnikov, and Sunil Prabhakar.
Indexing Multi-Dimensional Uncertain Data with Arbitrary Probability Density Functions. [VLDB 2005 ] Yufei Tao, Reynold Cheng, Xiaokui Xiao, Wang Kay Ngai, Ben Kao, Sunil Prabhakar.
Efficient Evaluation of Imprecise Location-Dependent Queries. [ICDE 2007] Jinchuan Chen, Reynold Cheng
Preserving User Location Privacy in Mobile Data Management Infrastructures. [PET 2006]
Reynold Cheng, Yu Zhang, Elisa Bertino, and Sunil Prabhakar.
Probabilistic Spatial Queries on Existentially Uncertain Data. [SSTD 2005]
Xiangyuan Dai, Man Lung Yiu, Nikos Mamoulis, Yufei Tao, and Michail Vaitis.
Probabilistic Skylines on Uncertain Data. [VLDB 2007]
Jian Pei, Bin Jiang, Xuemin Lin, Yidong Yuan

3. Efficient Evaluation of Imprecise Location-Dependent Queries
Jinchuan Chen Reynold Cheng
Department of Computing
The Hong Kong Polytechnic University

4. Outline A Classification of ILDQ 3 methods: The Minkowski Sum
Query-Data Duality
Exploiting Probability Threshold

5. IPQ and IUQ A A q Point object R Uncertainty of Uncertain object
Query issuer
Uncertain object
IPQ: Imprecise Location-Dependent
Queries over Point Objects
IUQ: Imprecise Location-Dependent
Queries over Uncertain Objects

6. Method 1: The Minkowski SumA U
利用Minkowski Sum找到最大的基于不确定区域U的最大查询框，然后利用这个最大的查询框来做pruning R B

7. Method 2: Query-Data Duality
Point
Point
Object R w h R w h R
Intuition: The role of query issuer and the point objects can be exchanged
Lead to simpler evaluation of IPQ and IUQ
Query Point
Point
Object

8. Query-Data Duality and IPQ
Uncertainty of Query Issuer U
Query at the point object!
Enables simpler probability evaluation

9. Method 3: Probability Threshold
p-expanded-query U R
R Ф U

10. The p-bound [VLDB04] p p-bound 0.1 0.3 0.5 p p p Uncertainty region
The p-bounds shrink with increasing value of p.
In practice, a few p-bounds are pre-computed and stored p

11. Deriving p-expanded-query with p-bound
p-bound (top) d d U
p-expanded-query
R Ф U
p-bound (left)

12. Pruning Uncertain Objects for C-IUQ (1)
Strategy 1: Use p-bound A
Uncertain object U
The concept of p-bound and p-expanded-query can also be used for C-IUQ. We have developed 3 strategies. The first one uses the p-bound, 2nd one uses p-expanded query, and the 3rd one uses both. Their details can be found in our paper.
p-bound
R Ф U

13. Pruning Uncertain Objects for C-IUQ (2)
Strategy 2: Use p-expanded query A
p-expanded-query U
R Ф U

14. Pruning Uncertain Objects for C-IUQ (3)
Strategy 3: Use both p-bound and p-expanded query
Qp-expanded-query
y-expanded-query
If x  y < p,
then A can be pruned. A U
R Ф U
x-bound
Qp-bound

15. Probabilistic Spatial Queries on Existentially Uncertain Data
Xiangyuan Dai (HKU), Man Lung Yiu (HKU),Nikos Mamoulis (HKU)
Yufei Tao (CityU,HK)
Michail Vaitis (U Aegean, GR)

16. Outline Introduction Definitions Evaluation of Probabilistic Queries
- range queries
- nearest neighbor queries

17. Introduction

18. Definitions
We refer to Ex as existential probability or confidence of x.
We identify two types of probabilistic spatial queries on existentially uncertain objects.
- Thresholding query
- Ranking query

19. Evaluation of Probabilistic Queries
range queries
􀂾A depth-first search algorithm applied on
the R-tree to retrieve the qualified objects
􀂾Let Px = Ex
􀂾Thresholding query: t is used to filter out objects with Px< t
􀂾Ranking query: a priority queue maintains the m results with the highest Px

20. Evaluation of Probabilistic Queries
nearest neighbor queries
Pfirst = 1
p7:Px=0.1 [not a result] Pfirst=1-0.1=0.9
p8:Px=0.9*0.2 = 0.18 [not a result] Pfirst = 0.9*(1-0.2)=0.72
p6:Px=0.72 x 0.1 = [not a result] Pfirst = 0.72*(1-0.1)=0.648
p4,:Px=0.648 x 0.5 = [result !!!] Pfirst = 0.648*(1-0.5)=0.342
p5:Px=0.342 x 0.9 = [result !!!] Pfirst = 0.342*(1-0.9)=0.034
Since Pfirst = < t = 0.3, the algorithm terminates!
Pm = 0 Pm

21. Probabilistic Skylines
on Uncertain Data
Jian Pei
Simon Fraser University, Canada
Bin Jiang, Xuemin Lin, Yidong Yuan
The University of New South Wales & NICTA, Australia

22. Outline Introduction Probabilistic Skyline Computation
Bounding-Pruning-Refining
Bottom-Up Method
Top-Down Method

23. ——Conventional Skylines
Introduction
——Conventional Skylines
n-dimensional numeric space D = (D1, …, Dn)
Large values are preferable
Two points, u dominates v (u ≻ v), if
" Di (1 ≤ i ≤ n), u.Di ≥ v.Di
$ Dj (1 ≤ j ≤ n), u.Dj > v.Dj
Given a set of points S, skyline = {u | uÎS and u is not dominated by any other point}
Example
C ≻ B, C ≻ D
skyline = {A, C, E}

24. ——Skylines on Uncertain Data
Introduction
——Skylines on Uncertain Data
Example
A set of object S = {A, B, C}
Each instance takes equal probability (0.5) to appear
Probabilistic Dominance
Pr(A ≻ C) = 3/4
Pr(B ≻ C) = 1/2
Pr((A ≻ C) ∨ (B ≻ C)) = 1
Pr(C is in the skyline) ≠ (1 - Pr(A ≻ C)) × (1 - Pr(B ≻ C))
Probabilistic dominance ≠≻ Probabilistic skyline

25. Probabilistic Skyline Computation
Bottom-Up Method
" u at layer-k, $ u′at layer-(k-1), s.t., u′≻ u and Pr(u′) ³ Pr(u)
max{Pr(u) | u is at layer-(k-1)} ³ max{Pr(u) | u is at layer-k}

26. Probabilistic Skyline Computation
Top-Down Method
Partition Tree
Bounding with Partition Trees

27. Thank you
Thank you