Data Management+ Laboratory

V*-kNN: an Efficient Algorithm forMoving k Nearest Neighbor Queries

Speaker: AdamAdviser: Yuling Hsueh

2009 IEEE International Conference on Data Engineering

Sarana Nutanong, Rui Zhang, Egemen Tanin, Lars Kulik

INTRODUCTION

What is “Moving k Nearest Neighbor Queries(MkNN)” ?- K Nearest Neighbor Query(kNN)

- Example of MkNN: Ambulance

Purpose: reduce the computation costs

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INTRODUCTION

To avoid unnecessary data access(computation): Safe region

Safe region: a region in which the query point can move without changing the result

This V*-kNN is based on two types of safe regions, the fixed-rank region (FRR) and the safe region with regard to a data point

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INTRODUCTION

Using a safe region-based method, an MkNN query can be processed :

(i) finding the current k NNs

(ii) calculating a region that the current k NNs are valid, i.e., a safe-region of the kNN;

(iii) repeating the first two steps when the query point moves out of the safe region.

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Fixed-Rank Region

Compute regions (F(p1,p2,…,pn) or F(L)) where the ranking of all the objects (based on their distances) is the same

Need: list of points and corresponding list of bisectors

List of points: sorted in ascending order by their distances to the query point

Corresponding list of bisectors: for n points, it requires at most (n-1) bisectors of the (n-1) pairs of rank-adjacent points

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Fixed-Rank Region

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Each time the query point crosses a bisector, the ranks of the two corresponding points are swapped and the list of rank-adjacent bisectors are updated.

Only rank-adjacent points can swap their ranks

Fixed-Rank Region

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(a, c, b, f, e, d) , ( Bac, Bbc, Bbf , Bef , Bde )

(a, c, b, e, f, d) , ( Bac, Bbc, Bbe , Bef , Bfd )

Safe Region With Regard To A Data Point

kNN (k+x)NN , where x is the number of auxiliary points

assume that z is the farthest known point to qb, i.e., the (k + x)th NN of qb

Known region

Reliable

Reliable region : dist(q′, p) ≤ dist(qb, z) − dist(qb, q′).

Safe region with regard to the data point

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Safe Region With Regard To A Data Point

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V*-kNN

Combine Fixed-Rank Region with Safe Region With Regard To A Data Point integrated safe region (ISR)

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ALGORITHM

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EXAMPLE

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ADVANTAGES

The V*-kNN has the following key advantages:

(i) It requires no precomputation

(ii) It incrementally computes answers and therefore efficiently adapts to changes – such as insertions and deletions of objects, as well as, dynamically changing values of k

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EXPERIMENT

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THE END

Thank you for listening!

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THE END

Q & A

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