K-Nearest Neighbors Imputation

Imputes missing values from the k nearest complete observations. Numeric and factor variables are both supported.

Usage

imputeKnn(
  x,
  k = 10,
  scale = TRUE,
  method = c("weighted", "median"),
  distData = NULL
)

Arguments

x

a data frame with missing values.

k

positive integer, the number of nearest neighbours to draw on.

scale

logical; if TRUE (default), numeric variables are standardized before distances are computed. This affects the distances only, not the imputed values.

method

the aggregation applied to the neighbours' values, either "weighted" for a distance-weighted mean (numeric) or weighted mode (factor), or "median" for a median (numeric) or mode (factor).

distData

optional data frame supplying the pool of potential neighbours. If given, neighbours are drawn from distData only, while x alone is imputed. It must have the same variables as x.

Value

a data frame of the same shape as x, with missing values replaced.

Details

Distance is Gower-style: numeric variables contribute their squared differences and factor variables a 0/1 mismatch penalty, summed and square-rooted. Numeric variables are standardized beforehand when scale = TRUE, so that no variable dominates through its unit alone. The standardization affects distances only; imputed values are always taken from the original data.

Continuous and categorical contributions are combined without further weighting, so a factor mismatch counts as much as a one-standard-deviation numeric gap. Whether that balance suits the data is for the caller to judge.

Each incomplete observation is compared with the complete ones on the variables it does observe, so rows missing different variables use different distances. Observations are therefore grouped by their pattern of missingness and each pattern is solved in one pass.

With method = "weighted" the neighbours are weighted by \(\exp(-d)\). Because that decays on the scale of the distances themselves, it is meaningful only when those are of moderate size, which is another reason to keep scale = TRUE. Weights are normalized against their maximum before exponentiation, so that widely separated neighbours cannot all underflow to zero.

When dbscan is installed it is used to find the neighbours via a kd-tree, which is markedly faster on large data. The result is the same either way, apart from the resolution of exact ties.

See also

Other impute: impute()

Examples

set.seed(123)
dat <- data.frame(
  x = c(1, 2, 3, 4, 5, 6),
  y = c(1, 2, 3, 4, 5, 6),
  z = factor(c("a", "b", "a", "b", "a", "b"))
)

dat[c(1, 3), "x"] <- NA
dat[c(2, 5), "y"] <- NA

imputeKnn(dat, k = 2)
#>          x       y z
#> 1 4.599849 1.00000 a
#> 2 2.000000 4.47332 b
#> 3 4.688363 3.00000 a
#> 4 4.000000 4.00000 b
#> 5 5.000000 5.00000 a
#> 6 6.000000 6.00000 b

# neighbours drawn from a separate reference set
ref <- data.frame(
  x = c(1.5, 2.5, 3.5, 4.5),
  y = c(1.5, 2.5, 3.5, 4.5),
  z = factor(c("a", "b", "a", "b"), levels = c("a", "b"))
)

imputeKnn(dat, k = 2, distData = ref)
#>          x        y z
#> 1 1.758634 1.000000 a
#> 2 2.000000 2.174485 b
#> 3 2.798218 3.000000 a
#> 4 4.000000 4.000000 b
#> 5 5.000000 3.978892 a
#> 6 6.000000 6.000000 b