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Session16

# Session16 - CSCI585 Nearest Neighbor Queries Instructor...

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CSCI585 CSCI585 Nearest Neighbor Queries Instructor: Cyrus Shahabi

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CSCI585 CSCI585 2 Nearest Neighbor Search Retrieve the nearest neighbor of query point Q Simple Strategy: convert the nearest neighbor search to range search. Guess a range around Q that contains at least one object say O if the current guess does not include any answers, increase range size until an object found. Compute distance d’ between Q and O re-execute the range query with the distance d’ around Q. Compute distance of Q from each retrieved object. The object at minimum distance is the nearest neighbor!!!
CSCI585 CSCI585 Naïve Approach A B C E F G H Query Point Q Issues: how to guess range? The retrieval may be sub-optimal if incorrect range guessed. Would be a problem in high dimensional spaces. B C E F G H A: B: C: 4 5 6 1 2 3 10 11 12 7 8 9 E F G H 6 7 2 3 1 4 5 8 9 10 11 12

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CSCI585 CSCI585 4 Given a query location q , find the nearest object. Depth First and Best-First Search using R-trees Goal: avoid visiting nodes that cannot contain results q a
CSCI585 CSCI585 5 Basic Pruning Metric: MINDIST Minimum distance between q and an MBR. mindist ( E 1 , q ) is a lower bound of d ( o , q ) for every object o in E 1 . If we have found a candidate NN p , we can prune every MBR whose mindist > d ( p , q ). E 1 p q mindist ( E 1 , q )

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CSCI585 CSCI585 MINDIST Property MINDIST is a lower bound of any k-NN distance (s1, s2) (t1, t2) (p1, p2) (p1, p2) (p1, p2) (p1, p2) (p1, p2) 6
CSCI585 CSCI585 7 Depth-First (DF) NN Algorithm Roussoulos et al., SIGMOD, 1995 2 0 4 6 8 10 2 4 6 8 10 x axis y axis b c a E 3 d e f g h i j k l m query E 4 E 5 E 1 E 2 E 6 E 7 1 2 5 9 5 2 13 a b c d e E 1 E 2 E 3 E 4 E 5 Root E 1 E 2 E 3 E 4 f g h E 5 l m E 7 i j k E 6 E 6 E 7 2 10 13 Note : distances not actually stored inside nodes. Only for illustration 5 Main idea Starting from the root visit nodes according to their mindist in depth-first manner

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CSCI585 CSCI585 8 DF Search – Visit E 1 2 0 4 6 8 10 2 4 6 8 10 x axis y axis b c a E 3 d e f g h i j k l m query E 4 E 5 E 1 E 2 E 6 E 7 1 2 5 9 5 2 13 a b c d e E 1 E 2 E 3 E 4 E 5 Root E 1 E 2 E 3 E 4 f g h E 5 l m E 7 i j k E 6 E 6 E 7 2 5
CSCI585 CSCI585 9 DF Search – Find Candidate NN a First Candidate NN: a with distance 1 2 5 9 5 2 13 a b c d e E 1 E 2 E 3 E 4 E 5 Root E 1 E 2 E 3 E 4 f g h E 5 l m E 7 i j k E 6 E 6 E 7 2 5 2 0 4 6 8 10 2 4 6 8 10 x axis y axis b c a E 3 d e f g h i j k l m query E 4 E 5 E 1 E 2 E 6 E 7 5

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CSCI585 CSCI585 10 DF Search – Backtrack to Root and Visit E 2
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Session16 - CSCI585 Nearest Neighbor Queries Instructor...

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