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Find the k Nearest Neighbors

Source: R/kNN.R
kNN.Rd

This function uses a kd-tree to find all k nearest neighbors in a data matrix (including distances) fast.

Usage

kNN(
  x,
  k,
  query = NULL,
  sort = TRUE,
  search = "kdtree",
  bucketSize = 10,
  splitRule = "suggest",
  approx = 0
)

# S3 method for class 'kNN'
sort(x, decreasing = FALSE, ...)

# S3 method for class 'kNN'
adjacencylist(x, ...)

# S3 method for class 'kNN'
print(x, ...)

Arguments

x

a data matrix, a dist object or a kNN object.

k

number of neighbors to find.

query

a data matrix with the points to query. If query is not specified, the NN for all the points in x is returned. If query is specified then x needs to be a data matrix.

sort

sort the neighbors by distance? Note that some search methods already sort the results. Sorting is expensive and sort = FALSE may be much faster for some search methods. kNN objects can be sorted using sort().

nearest neighbor search strategy (one of "kdtree", "linear" or "dist").

bucketSize

max size of the kd-tree leafs.

splitRule

rule to split the kd-tree. One of "STD", "MIDPT", "FAIR", "SL_MIDPT", "SL_FAIR" or "SUGGEST" (SL stands for sliding). "SUGGEST" uses ANNs best guess.

approx

use approximate nearest neighbors. All NN up to a distance of a factor of 1 + approx eps may be used. Some actual NN may be omitted leading to spurious clusters and noise points. However, the algorithm will enjoy a significant speedup.

decreasing

sort in decreasing order?

...

further arguments

Value

An object of class kNN (subclass of NN) containing a list with the following components:

dist

a matrix with distances.

id

a matrix with ids.

k

number k used.

metric

used distance metric.

Details

Handling of ties and self-matches

  • Ties: If the kth and the (k+1)th nearest neighbor are tied, then the neighbor found first is returned and the other one is ignored.

  • Self-matches: If no query is specified, then self-matches are removed.

Details on the search parameters:

  • search controls if a kd-tree or linear search (both implemented in the ANN library; see Mount and Arya, 2010). Note, that these implementations cannot handle NAs. search = "dist" precomputes Euclidean distances first using R. NAs are handled, but the resulting distance matrix cannot contain NAs. To use other distance measures, a precomputed distance matrix can be provided as x (search is ignored).

  • bucketSize and splitRule influence how the kd-tree is built. approx uses the approximate nearest neighbor search implemented in ANN. All nearest neighbors up to a distance of eps / (1 + approx) will be considered and all with a distance greater than eps will not be considered. The other points might be considered. Note that this results in some actual nearest neighbors being omitted leading to spurious clusters and noise points. However, the algorithm will enjoy a significant speedup. For more details see Mount and Arya (2010).

References

David M. Mount and Sunil Arya (2010). ANN: A Library for Approximate Nearest Neighbor Searching, http://www.cs.umd.edu/~mount/ANN/.

See also

Other NN functions: NN, comps(), frNN(), kNNdist(), sNN()

Author

Michael Hahsler

Examples

data(iris)
x <- iris[, -5]

# Example 1: finding kNN for all points in a data matrix (using a kd-tree)
nn <- kNN(x, k = 5)
nn
#> k-nearest neighbors for 150 objects (k=5).
#> Distance metric: euclidean 
#> 
#> Available fields: dist, id, k, sort, metric

# explore neighborhood of point 10
i <- 10
nn$id[i,]
#>  1  2  3  4  5 
#> 35  2 31 13 26 
plot(x, col = ifelse(seq_len(nrow(iris)) %in% nn$id[i,], "red", "black"))


# visualize the 5 nearest neighbors
plot(nn, x)


# visualize a reduced 2-NN graph
plot(kNN(nn, k = 2), x)


# Example 2: find kNN for query points
q <- x[c(1,100),]
nn <- kNN(x, k = 10, query = q)

plot(nn, x, col = "grey")
points(q, pch = 3, lwd = 2)


# Example 3: find kNN using distances
d <- dist(x, method = "manhattan")
nn <- kNN(d, k = 1)
plot(nn, x)