Isomap embedding

step_isomap() creates a specification of a recipe step that uses multidimensional scaling to convert numeric data into one or more new dimensions.

step_isomap(
  recipe,
  ...,
  role = "predictor",
  trained = FALSE,
  num_terms = 5,
  neighbors = 50,
  options = list(.mute = c("message", "output")),
  res = NULL,
  columns = NULL,
  prefix = "Isomap",
  keep_original_cols = FALSE,
  skip = FALSE,
  id = rand_id("isomap")
)

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 variables for this step. See selections() for more details.

role

For model terms created by this step, what analysis role should they be assigned? By default, the new columns created by this step from the original variables will be used as predictors in a model.

trained

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

num_terms

The number of isomap dimensions to retain as new predictors. If num_terms is greater than the number of columns or the number of possible dimensions, a smaller value will be used.

neighbors

The number of neighbors.

options

A list of options to `dimRed::Isomap()“.

res

The `dimRed::Isomap()“ object is stored here once this preprocessing step has be trained by prep().

columns

A character string of the selected variable names. This field is a placeholder and will be populated once prep() is used.

prefix

A character string for the prefix of the resulting new variables. See notes below.

keep_original_cols

A logical to keep the original variables in the output. Defaults to FALSE.

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.

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 any existing operations.

Details

Isomap is a form of multidimensional scaling (MDS). MDS methods try to find a reduced set of dimensions such that the geometric distances between the original data points are preserved. This version of MDS uses nearest neighbors in the data as a method for increasing the fidelity of the new dimensions to the original data values.

This step requires the dimRed, RSpectra, igraph, and RANN packages. If not installed, the step will stop with a note about installing these packages.

It is advisable to center and scale the variables prior to running Isomap (step_center and step_scale can be used for this purpose).

The argument num_terms controls the number of components that will be retained (the original variables that are used to derive the components are removed from the data). The new components will have names that begin with prefix and a sequence of numbers. The variable names are padded with zeros. For example, if num_terms < 10, their names will be Isomap1 - Isomap9. If num_terms = 101, the names would be Isomap001 - Isomap101.

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

Tuning Parameters

This step has 2 tuning parameters:

• num_terms: # Model Terms (type: integer, default: 5)

• neighbors: # Nearest Neighbors (type: integer, default: 50)

Case weights

The underlying operation does not allow for case weights.

References

De Silva, V., and Tenenbaum, J. B. (2003). Global versus local methods in nonlinear dimensionality reduction. Advances in Neural Information Processing Systems. 721-728.

dimRed, a framework for dimensionality reduction, https://github.com/gdkrmr

See also

Other multivariate transformation steps: step_classdist(), step_classdist_shrunken(), step_depth(), step_geodist(), step_ica(), step_kpca(), step_kpca_poly(), step_kpca_rbf(), step_mutate_at(), step_nnmf(), step_nnmf_sparse(), step_pca(), step_pls(), step_ratio(), step_spatialsign()

Examples

if (FALSE) {
data(biomass, package = "modeldata")

biomass_tr <- biomass[biomass$dataset == "Training", ]
biomass_te <- biomass[biomass$dataset == "Testing", ]

rec <- recipe(
  HHV ~ carbon + hydrogen + oxygen + nitrogen + sulfur,
  data = biomass_tr
)

im_trans <- rec |>
  step_YeoJohnson(all_numeric_predictors()) |>
  step_normalize(all_numeric_predictors()) |>
  step_isomap(all_numeric_predictors(), neighbors = 100, num_terms = 2)

im_estimates <- prep(im_trans, training = biomass_tr)

im_te <- bake(im_estimates, biomass_te)

rng <- extendrange(c(im_te$Isomap1, im_te$Isomap2))
plot(im_te$Isomap1, im_te$Isomap2,
  xlim = rng, ylim = rng
)

tidy(im_trans, number = 3)
tidy(im_estimates, number = 3)
}