Condensed Nearest Neighbors

step_cnn() creates a specification of a recipe step that removes redundant majority class observations, keeping only a consistent subset that correctly classifies the data using a 1-nearest-neighbor rule.

Usage

step_cnn(
  recipe,
  ...,
  role = NA,
  trained = FALSE,
  column = NULL,
  distance = "euclidean",
  skip = TRUE,
  seed = sample.int(10^5, 1),
  distance_with = recipes::all_predictors(),
  id = rand_id("cnn")
)

Arguments

recipe

A recipe object. The step will be added to the sequence of operations for this recipe.

...

One or more selector functions to choose which variable is used to sample the data. See recipes::selections for more details. The selection should result in single factor variable. For the tidy method, these are not currently used.

role

Not used by this step since no new variables are created.

trained

A logical to indicate if the quantities for preprocessing have been estimated.

column

A character string of the variable name that will be populated (eventually) by the ... selectors.

distance

A character string specifying the distance metric used for nearest neighbor calculations, defaulting to "euclidean". The available metrics fall into three groups.

"euclidean", "cosine", and "mahalanobis" use approximate nearest neighbors via the RANN package and scale well to large datasets.

"squared_chord", "matusita", "hellinger", and "bhattacharyya" are probability-divergence measures that treat each row as a distribution over the predictors, so they require non-negative values. "hellinger" and "bhattacharyya" further require each row to sum to 1. All four also use the RANN package and scale well to large datasets.

"manhattan", "chebyshev", "canberra", "soergel", "lorentzian", "jeffreys", "topsoe", "jensen-shannon", "jensen_difference", "taneja", and "kumar-johnson" compute an exact all-pairs distance matrix. This takes time and memory proportional to the square of the number of observations in a class, so these are best suited to smaller datasets. Everything from "canberra" onwards is a probability divergence requiring non-negative values, is provided by the philentropy package (which must be installed separately), and in the case of "jeffreys", "taneja", and "kumar-johnson" requires strictly positive values, since those divide by individual predictor values.

The probability divergences are meaningful for compositional predictors such as proportions or counts normalized per observation, and are generally not appropriate for standardized predictors.

skip

A logical. Should the step be skipped when the recipe is baked by bake()? While all operations are baked when prep() is run, some operations may not be able to be conducted on new data (e.g. processing the outcome variable(s)). Care should be taken when using skip = TRUE as it may affect the computations for subsequent operations.

seed

An integer that will be used as the seed when applied.

distance_with

A call to a selector function to choose which variables are used for distance calculations. Defaults to recipes::all_predictors(). The variable selected by ... is always excluded from the distance calculations.

id

A character string that is unique to this step to identify it.

Value

An updated version of recipe with the new step added to the sequence of existing steps (if any). For the tidy method, a tibble with columns terms which is the variable used to sample.

Details

Condensed Nearest Neighbors (CNN) is an under-sampling method that reduces the majority classes to a consistent subset: a subset that classifies the original data correctly using a 1-nearest-neighbor rule. It starts with a "store" containing all minority class observations and one randomly chosen majority class observation. It then repeatedly scans the remaining majority class observations and moves any that are misclassified by a 1-nearest neighbor fit on the current store into the store. This continues until a full pass adds no new observations. The observations left outside the store are removed.

The smallest class is treated as the minority class and is always kept. CNN tends to keep observations near the decision boundary while discarding redundant interior observations. Because the seed observation and the scan order are random, results depend on the random seed.

All variables selected by distance_with must be numeric with no missing data.

All columns in the data are sampled and returned by recipes::juice() and recipes::bake().

When used in modeling, users should strongly consider using the option skip = TRUE so that the extra sampling is not conducted outside of the training set.

Tidying

When you tidy() this step, a tibble is returned with columns terms and id:

terms

character, the selectors or variables selected

id

character, id of this step

Case weights

The underlying operation does not allow for case weights. Supplying data with a case weights column to this step results in an error.

References

Hart, P. (1968). The condensed nearest neighbor rule. IEEE Transactions on Information Theory, 14(3), 515-516.

See also

cnn() for direct implementation

Other Steps for under-sampling: step_cluster_centroids(), step_downsample(), step_enn(), step_instance_hardness(), step_ncl(), step_nearmiss(), step_oss(), step_tomek()

Examples

library(recipes)
library(modeldata)
data(hpc_data)

hpc_data0 <- hpc_data |>
  select(-protocol, -day)

orig <- count(hpc_data0, class, name = "orig")
orig
#> # A tibble: 4 × 2
#>   class  orig
#>   <fct> <int>
#> 1 VF     2211
#> 2 F      1347
#> 3 M       514
#> 4 L       259

up_rec <- recipe(class ~ ., data = hpc_data0) |>
  step_cnn(class) |>
  prep()

training <- up_rec |>
  bake(new_data = NULL) |>
  count(class, name = "training")
training
#> # A tibble: 4 × 2
#>   class training
#>   <fct>    <int>
#> 1 VF         933
#> 2 F          803
#> 3 M          339
#> 4 L          259

# Since `skip` defaults to TRUE, baking the step has no effect
baked <- up_rec |>
  bake(new_data = hpc_data0) |>
  count(class, name = "baked")
baked
#> # A tibble: 4 × 2
#>   class baked
#>   <fct> <int>
#> 1 VF     2211
#> 2 F      1347
#> 3 M       514
#> 4 L       259

orig |>
  left_join(training, by = "class") |>
  left_join(baked, by = "class")
#> # A tibble: 4 × 4
#>   class  orig training baked
#>   <fct> <int>    <int> <int>
#> 1 VF     2211      933  2211
#> 2 F      1347      803  1347
#> 3 M       514      339   514
#> 4 L       259      259   259

library(ggplot2)

ggplot(circle_example, aes(x, y, color = class)) +
  geom_point() +
  labs(title = "Without CNN") +
  xlim(c(1, 15)) +
  ylim(c(1, 15))


recipe(class ~ x + y, data = circle_example) |>
  step_cnn(class) |>
  prep() |>
  bake(new_data = NULL) |>
  ggplot(aes(x, y, color = class)) +
  geom_point() +
  labs(title = "With CNN") +
  xlim(c(1, 15)) +
  ylim(c(1, 15))