## K-nearest neighbor in 2D dimension space

## K-nearest neighbor

There are miscellaneous algorithms for searching nearest neighbors.

An alternative method is to use grid indexing strategy.

Slowly expand the grid boxes from the center to find the k-nearest neighbors.

The grid is used as a filtering mechanism to reduce the search space.

This works fast for distributed data across the space and is a good alternative algorithm for dynamic data that changes position frequently.

### Reference links:

Project implemented in C# is available at Github:

A survey of techniques for fixed radius near neighbor searching:

The origin is in ring 0.

The origin can anywhere in the box and the distance to test on first iteration must be at least 1 x grid distance. The first iteration starts with data from ring 0 and 1.

**The algorithm goes like this:**

i = 0 Point origin list currRing = empty list nextRing = empty list temp while all rings not explored i = i + 1 temp = empty for all point in nextRing test distance between origin and point if distance is within i * grid put it in currRing else put it in temp nextRing = empty Add all from temp to nextRing temp = empty if(i==1) temp = points from ring 0 and ring 1 else temp = points from ring i For all point in temp test distance between origin and point if distance is within i * grid put it in currRing else put it in nextRing If there are at least k points in currRing then exit while loop end while loop if currRing count is < k then add all from nextRing to currRing sort currRing by distance take first k from currRing

**Grid version algorithm:**

Apply algorithm described above.

Searching: `O(n * m)`

where m is grid cells and k << n.

**Naive version algorithm:**

For origin point check the distance to every other point.

Take k first items sorted by distance.

Searching: `O(n log n)`

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