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kNN query |
- 1-NN query of
has true answer ![](images/img59.png)
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- Applying 1-NN on l projections gives l collision sets:
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- 2,9,13:
![](images/img59.png)
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- 7,10,14:
![](images/img280.png)
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- 1,5,11:
![](images/img281.png)
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- 8,12,14:
![](images/img282.png)
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- Now majority counting gives
![](images/img59.png)
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- No guarantee of correct answer
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- Accuracy increases with more runs
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- It can be proved that
is approximately distance preserving provided is so ( already is so!)
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- Therefore, this is a Monte Carlo algorithm
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- Time:
where is the dimensionality (here, 3)
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