Calculate and Plot k-Nearest Neighbor Distances

Fast calculation of the k-nearest neighbor distances for a dataset represented as a matrix of points. The kNN distance is defined as the distance from a point to its k nearest neighbor. The kNN distance plot displays the kNN distance of all points sorted from smallest to largest. The plot can be used to help find suitable parameter values for dbscan().

Usage

kNNdist(x, k, all = FALSE, ...)

kNNdistplot(x, k, minPts, ...)

Arguments

x

the data set as a matrix of points (Euclidean distance is used) or a precalculated dist object.

k

number of nearest neighbors used for the distance calculation. For kNNdistplot() also a range of values for k or minPts can be specified.

all

should a matrix with the distances to all k nearest neighbors be returned?

...

further arguments (e.g., kd-tree related parameters) are passed on to kNN().

minPts

to use a k-NN plot to determine a suitable eps value for dbscan(), minPts used in dbscan can be specified and will set k = minPts - 1.

Value

kNNdist() returns a numeric vector with the distance to its k nearest neighbor. If all = TRUE then a matrix with k columns containing the distances to all 1st, 2nd, ..., kth nearest neighbors is returned instead.

See also

Other Outlier Detection Functions: glosh(), lof(), pointdensity()

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

Author

Michael Hahsler

Examples

data(iris)
iris <- as.matrix(iris[, 1:4])

## Find the 4-NN distance for each observation (see ?kNN
## for different search strategies)
kNNdist(iris, k = 4)
#>   [1] 0.1414214 0.1732051 0.2645751 0.2449490 0.1732051 0.3741657 0.3162278
#>   [8] 0.2000000 0.3464102 0.1732051 0.3316625 0.3000000 0.2000000 0.4795832
#>  [15] 0.5567764 0.6164414 0.3872983 0.1732051 0.5099020 0.2645751 0.3605551
#>  [22] 0.2645751 0.5196152 0.3872983 0.4242641 0.2236068 0.2449490 0.1732051
#>  [29] 0.1732051 0.2236068 0.2236068 0.3162278 0.4242641 0.4123106 0.1732051
#>  [36] 0.3316625 0.3464102 0.2645751 0.3000000 0.1414214 0.2449490 0.7810250
#>  [43] 0.3000000 0.3741657 0.4123106 0.2449490 0.3000000 0.2236068 0.2449490
#>  [50] 0.2236068 0.4582576 0.3741657 0.3464102 0.4358899 0.3741657 0.3316625
#>  [57] 0.4582576 0.7211103 0.3162278 0.5291503 0.7141428 0.3605551 0.5830952
#>  [64] 0.4242641 0.5196152 0.3464102 0.4123106 0.3605551 0.6782330 0.2645751
#>  [71] 0.4242641 0.4000000 0.4242641 0.4358899 0.3872983 0.3162278 0.3741657
#>  [78] 0.4242641 0.3464102 0.4472136 0.3000000 0.4358899 0.3000000 0.3741657
#>  [85] 0.4898979 0.4690416 0.3316625 0.6082763 0.3162278 0.3000000 0.4242641
#>  [92] 0.3464102 0.2645751 0.6480741 0.3000000 0.3316625 0.2236068 0.3464102
#>  [99] 0.7937254 0.2449490 0.5567764 0.3316625 0.4582576 0.3872983 0.3872983
#> [106] 0.5477226 0.8774964 0.5477226 0.6164414 0.7549834 0.4242641 0.3872983
#> [113] 0.3741657 0.5196152 0.5196152 0.3872983 0.3872983 1.0049876 0.9273618
#> [120] 0.5830952 0.3000000 0.4582576 0.6782330 0.3605551 0.3741657 0.4690416
#> [127] 0.3872983 0.3000000 0.3741657 0.5567764 0.5099020 0.9327379 0.4358899
#> [134] 0.4358899 0.6633250 0.6782330 0.4358899 0.4358899 0.3162278 0.3741657
#> [141] 0.3464102 0.5099020 0.3316625 0.3464102 0.4000000 0.3741657 0.4123106
#> [148] 0.3605551 0.6164414 0.3316625

## Get a matrix with distances to the 1st, 2nd, ..., 4th NN.
kNNdist(iris, k = 4, all = TRUE)
#>                1         2         3         4
#>   [1,] 0.1000000 0.1414214 0.1414214 0.1414214
#>   [2,] 0.1414214 0.1414214 0.1414214 0.1732051
#>   [3,] 0.1414214 0.2449490 0.2645751 0.2645751
#>   [4,] 0.1414214 0.1732051 0.2236068 0.2449490
#>   [5,] 0.1414214 0.1414214 0.1732051 0.1732051
#>   [6,] 0.3316625 0.3464102 0.3605551 0.3741657
#>   [7,] 0.2236068 0.2645751 0.3000000 0.3162278
#>   [8,] 0.1000000 0.1414214 0.1732051 0.2000000
#>   [9,] 0.1414214 0.3000000 0.3162278 0.3464102
#>  [10,] 0.1000000 0.1732051 0.1732051 0.1732051
#>  [11,] 0.1000000 0.2828427 0.3000000 0.3316625
#>  [12,] 0.2236068 0.2236068 0.2828427 0.3000000
#>  [13,] 0.1414214 0.1732051 0.2000000 0.2000000
#>  [14,] 0.2449490 0.3162278 0.3464102 0.4795832
#>  [15,] 0.4123106 0.4690416 0.5477226 0.5567764
#>  [16,] 0.3605551 0.5477226 0.6164414 0.6164414
#>  [17,] 0.3464102 0.3605551 0.3872983 0.3872983
#>  [18,] 0.1000000 0.1414214 0.1732051 0.1732051
#>  [19,] 0.3316625 0.3872983 0.4690416 0.5099020
#>  [20,] 0.1414214 0.1414214 0.2449490 0.2645751
#>  [21,] 0.2828427 0.3000000 0.3605551 0.3605551
#>  [22,] 0.1414214 0.2449490 0.2449490 0.2645751
#>  [23,] 0.4582576 0.5099020 0.5099020 0.5196152
#>  [24,] 0.2000000 0.2645751 0.3741657 0.3872983
#>  [25,] 0.3000000 0.3741657 0.4123106 0.4242641
#>  [26,] 0.1732051 0.2000000 0.2236068 0.2236068
#>  [27,] 0.2000000 0.2236068 0.2236068 0.2449490
#>  [28,] 0.1414214 0.1414214 0.1414214 0.1732051
#>  [29,] 0.1414214 0.1414214 0.1414214 0.1732051
#>  [30,] 0.1414214 0.1732051 0.2236068 0.2236068
#>  [31,] 0.1414214 0.1414214 0.1732051 0.2236068
#>  [32,] 0.2828427 0.3000000 0.3000000 0.3162278
#>  [33,] 0.3464102 0.3464102 0.3741657 0.4242641
#>  [34,] 0.3464102 0.3605551 0.3872983 0.4123106
#>  [35,] 0.1000000 0.1414214 0.1414214 0.1732051
#>  [36,] 0.2236068 0.3000000 0.3162278 0.3316625
#>  [37,] 0.3000000 0.3162278 0.3316625 0.3464102
#>  [38,] 0.1414214 0.2449490 0.2645751 0.2645751
#>  [39,] 0.1414214 0.2000000 0.2449490 0.3000000
#>  [40,] 0.1000000 0.1414214 0.1414214 0.1414214
#>  [41,] 0.1414214 0.1732051 0.1732051 0.2449490
#>  [42,] 0.6244998 0.7141428 0.7681146 0.7810250
#>  [43,] 0.2000000 0.2236068 0.3000000 0.3000000
#>  [44,] 0.2236068 0.2645751 0.3162278 0.3741657
#>  [45,] 0.3605551 0.3741657 0.4123106 0.4123106
#>  [46,] 0.1414214 0.2000000 0.2000000 0.2449490
#>  [47,] 0.1414214 0.2449490 0.2449490 0.3000000
#>  [48,] 0.1414214 0.1414214 0.2236068 0.2236068
#>  [49,] 0.1000000 0.2236068 0.2449490 0.2449490
#>  [50,] 0.1414214 0.1732051 0.2236068 0.2236068
#>  [51,] 0.2645751 0.3316625 0.4358899 0.4582576
#>  [52,] 0.2645751 0.3162278 0.3464102 0.3741657
#>  [53,] 0.2645751 0.2828427 0.3162278 0.3464102
#>  [54,] 0.2000000 0.3000000 0.3162278 0.4358899
#>  [55,] 0.2449490 0.3162278 0.3741657 0.3741657
#>  [56,] 0.3000000 0.3162278 0.3162278 0.3316625
#>  [57,] 0.2645751 0.3741657 0.4242641 0.4582576
#>  [58,] 0.1414214 0.3872983 0.4582576 0.7211103
#>  [59,] 0.2449490 0.2449490 0.3162278 0.3162278
#>  [60,] 0.3872983 0.5099020 0.5196152 0.5291503
#>  [61,] 0.3605551 0.4582576 0.6708204 0.7141428
#>  [62,] 0.3000000 0.3316625 0.3605551 0.3605551
#>  [63,] 0.4898979 0.5196152 0.5477226 0.5830952
#>  [64,] 0.1414214 0.2236068 0.2449490 0.4242641
#>  [65,] 0.4242641 0.4472136 0.5099020 0.5196152
#>  [66,] 0.1414214 0.3162278 0.3162278 0.3464102
#>  [67,] 0.2000000 0.3000000 0.3872983 0.4123106
#>  [68,] 0.2449490 0.2828427 0.3316625 0.3605551
#>  [69,] 0.2645751 0.5099020 0.5385165 0.6782330
#>  [70,] 0.1732051 0.2449490 0.2645751 0.2645751
#>  [71,] 0.2236068 0.3000000 0.3605551 0.4242641
#>  [72,] 0.3316625 0.3464102 0.3741657 0.4000000
#>  [73,] 0.3605551 0.3605551 0.4123106 0.4242641
#>  [74,] 0.2236068 0.3000000 0.3872983 0.4358899
#>  [75,] 0.2000000 0.2645751 0.3605551 0.3872983
#>  [76,] 0.1414214 0.2449490 0.2645751 0.3162278
#>  [77,] 0.3162278 0.3464102 0.3464102 0.3741657
#>  [78,] 0.3162278 0.3741657 0.4123106 0.4242641
#>  [79,] 0.2000000 0.2449490 0.3316625 0.3464102
#>  [80,] 0.3464102 0.4242641 0.4358899 0.4472136
#>  [81,] 0.1414214 0.1732051 0.3000000 0.3000000
#>  [82,] 0.1414214 0.2645751 0.3464102 0.4358899
#>  [83,] 0.1414214 0.2645751 0.2828427 0.3000000
#>  [84,] 0.3316625 0.3605551 0.3605551 0.3741657
#>  [85,] 0.2000000 0.4123106 0.4795832 0.4898979
#>  [86,] 0.3741657 0.4242641 0.4582576 0.4690416
#>  [87,] 0.2828427 0.3162278 0.3162278 0.3316625
#>  [88,] 0.2645751 0.5744563 0.5916080 0.6082763
#>  [89,] 0.1732051 0.1732051 0.2236068 0.3162278
#>  [90,] 0.2000000 0.2449490 0.3000000 0.3000000
#>  [91,] 0.2645751 0.3162278 0.4242641 0.4242641
#>  [92,] 0.1414214 0.2000000 0.3000000 0.3464102
#>  [93,] 0.1414214 0.2449490 0.2645751 0.2645751
#>  [94,] 0.1414214 0.3605551 0.3872983 0.6480741
#>  [95,] 0.1732051 0.2236068 0.2645751 0.3000000
#>  [96,] 0.1414214 0.1732051 0.2449490 0.3316625
#>  [97,] 0.1414214 0.1414214 0.1732051 0.2236068
#>  [98,] 0.2000000 0.3316625 0.3464102 0.3464102
#>  [99,] 0.3872983 0.3872983 0.7211103 0.7937254
#> [100,] 0.1414214 0.1732051 0.2236068 0.2449490
#> [101,] 0.4242641 0.5000000 0.5099020 0.5567764
#> [102,] 0.0000000 0.2645751 0.3162278 0.3316625
#> [103,] 0.3872983 0.4000000 0.4123106 0.4582576
#> [104,] 0.2449490 0.2449490 0.3316625 0.3872983
#> [105,] 0.3000000 0.3162278 0.3605551 0.3872983
#> [106,] 0.2645751 0.5291503 0.5477226 0.5477226
#> [107,] 0.7348469 0.7615773 0.7937254 0.8774964
#> [108,] 0.2645751 0.4358899 0.5291503 0.5477226
#> [109,] 0.5567764 0.6000000 0.6164414 0.6164414
#> [110,] 0.6324555 0.6708204 0.7071068 0.7549834
#> [111,] 0.2236068 0.3741657 0.4242641 0.4242641
#> [112,] 0.3464102 0.3741657 0.3741657 0.3872983
#> [113,] 0.1732051 0.3464102 0.3605551 0.3741657
#> [114,] 0.2645751 0.2645751 0.3316625 0.5196152
#> [115,] 0.4898979 0.5099020 0.5099020 0.5196152
#> [116,] 0.3000000 0.3741657 0.3741657 0.3872983
#> [117,] 0.1414214 0.2449490 0.3605551 0.3872983
#> [118,] 0.4123106 0.8185353 0.8602325 1.0049876
#> [119,] 0.4123106 0.5477226 0.8944272 0.9273618
#> [120,] 0.4358899 0.5196152 0.5385165 0.5830952
#> [121,] 0.2236068 0.2645751 0.3000000 0.3000000
#> [122,] 0.3162278 0.3162278 0.3316625 0.4582576
#> [123,] 0.2645751 0.4123106 0.6082763 0.6782330
#> [124,] 0.1732051 0.2449490 0.3605551 0.3605551
#> [125,] 0.3000000 0.3162278 0.3741657 0.3741657
#> [126,] 0.3464102 0.3872983 0.4358899 0.4690416
#> [127,] 0.1732051 0.2449490 0.2828427 0.3872983
#> [128,] 0.1414214 0.2449490 0.2828427 0.3000000
#> [129,] 0.1000000 0.3162278 0.3316625 0.3741657
#> [130,] 0.3464102 0.5099020 0.5196152 0.5567764
#> [131,] 0.2645751 0.4582576 0.4690416 0.5099020
#> [132,] 0.4123106 0.8831761 0.9273618 0.9327379
#> [133,] 0.1000000 0.3000000 0.4242641 0.4358899
#> [134,] 0.3316625 0.3605551 0.3741657 0.4358899
#> [135,] 0.5385165 0.5567764 0.5830952 0.6633250
#> [136,] 0.5385165 0.5477226 0.6633250 0.6782330
#> [137,] 0.2449490 0.3872983 0.4242641 0.4358899
#> [138,] 0.1414214 0.2449490 0.3872983 0.4358899
#> [139,] 0.1414214 0.2236068 0.2828427 0.3162278
#> [140,] 0.1732051 0.3605551 0.3605551 0.3741657
#> [141,] 0.2449490 0.2645751 0.3464102 0.3464102
#> [142,] 0.2449490 0.3605551 0.4690416 0.5099020
#> [143,] 0.0000000 0.2645751 0.3162278 0.3316625
#> [144,] 0.2236068 0.3162278 0.3162278 0.3464102
#> [145,] 0.2449490 0.3000000 0.3162278 0.4000000
#> [146,] 0.2449490 0.3605551 0.3605551 0.3741657
#> [147,] 0.2449490 0.3741657 0.3872983 0.4123106
#> [148,] 0.2236068 0.3464102 0.3605551 0.3605551
#> [149,] 0.2449490 0.3000000 0.5567764 0.6164414
#> [150,] 0.2828427 0.3162278 0.3316625 0.3316625

## Produce a k-NN distance plot to determine a suitable eps for
## DBSCAN with MinPts = 5. Use k = 4 (= MinPts -1).
## The knee is visible around a distance of .7
kNNdistplot(iris, k = 4)


## Look at all k-NN distance plots for a k of 1 to 10
## Note that k-NN distances are increasing in k
kNNdistplot(iris, k = 1:20)


cl <- dbscan(iris, eps = .7, minPts = 5)
pairs(iris, col = cl$cluster + 1L)

## Note: black points are noise points