A Samplingbased Estimator for Topk Selection Query

1
A Sampling-based Estimator for Top-k Selection
Query

• Chung-Min Chen Yibei Ling
• ICDE 2002
• Presented by Kan Kin Fai

2
Outline

• Introduction
• Histogram-based Method
• Sampling-based Method
• Experimental Results
• Conclusion

3
Introduction

• Given a distance function and a query point q,
  the top-k query is to find the top k points from
  the dataset that are closest to q.
• Example searching an apartment by specifying a
  price and a location

4
Introduction

• Goal find a good approximation of the top-k
  points quickly
• Approach translate a top-k query into a range
  query
• Distance Functions
• Euclidean distance (L2-norm distance)
• Summation distance (L1-norm distance)
• Maximum distance (L?-norm distance)

5
Histogram-based Method

• To determine the range query for a top-k query
  with query point q using histograms
• Drawbacks
• poor scalability of histograms with data
  dimensionality
• non-trivial maintenance overhead of
  multidimensional histograms

6
Histogram-based Method

• Strategies NoRestart, Start, Inter1 and Inter2

7
Sampling-based Method

• Main idea
• take a random sample S of size s from the dataset
  D of size n. (sampling rate r s / n)
• given a query point q, compute the distances
  between q and all the points in S sort the
  sample points in ascending order of the computed
  distance.
• take the first l points from the sorted sequence
  where l k r and determine the range query
  from them.

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Sampling-based Method

• Determining the range query
• the Minimum Bounding Rectangle (MBR)
• Sym set the side length on the ith dimension to
  2di, where di max(qi - xi for all (x1,,xm)
  ? the l points).
• Squ set the side length on the ith dimension to
  2d, where d max(di) for 1?i ?m.
• the Minimum Bounding Square on Shape (MBSS)

9
Sampling-based Method
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Sampling-based Method

• Para
• use L? to sort the sampling points regardless of
  the distance function
• take l c ? r ? k 1 points from the sorted
  sequence c is the magnification factor (MF)
• set the range query to be the smallest square
  centered at q that encloses the l points.
• Pros give accurate result size

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Sampling-based Method

• Let Q(D) be the result of the range query Q and
  top(D,q,k) be the set containing the k closet
  points to q.

12
Sampling-based Method

• Deciding the magnification factor c for a given
  recall
• fixing k, plot a graph with recall vs. MF
• use linear interpolation to compute the needed
  magnification factor c from the graph

13
Experimental Results
14
Experimental Results
15
Experimental Results
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Experimental Results
17
Conclusions

• This paper presents a sampling-based method to
  process approximate top-k queries.
• Experimental results show that
• the proposed method outperforms the
  histogram-based method
• the mapping scheme scales well for
  high-dimensional data.
• Easy to implement and maintain!