R: Isomap Embedding

step_isomap {recipes} | R Documentation

## Isomap Embedding

### Description

`step_isomap` creates a specification of a recipe step that will convert numeric data into one or more new dimensions.

### Usage

    step_isomap(recipe, ..., role = "predictor", trained = FALSE, num = 5,
      options = list(knn = 50, .mute = c("message", "output")), res = NULL,
      prefix = "Isomap", skip = FALSE)

    ## S3 method for class 'step_isomap'
    tidy(x, ...)

### 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 variables will be used to compute the dimensions. See `selections()` for more details. For the `tidy` method, these are not currently used.
`role` | For model terms created by this step, what analysis role should they be assigned?. By default, the function assumes that the new dimension columns created by 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` | The number of isomap dimensions to retain as new predictors. If `num` is greater than the number of columns or the number of possible dimensions, a smaller value will be used.
`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.recipe()`.
`prefix` | A character string that will be the prefix to the resulting new variables. See notes below.
`skip` | A logical. Should the step be skipped when the recipe is baked by `bake.recipe()`? While all operations are baked when `prep.recipe()` 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
`x` | A `step_isomap` object

### 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.

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` 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 < 10`, their names will be `Isomap1` - `Isomap9`. If `num = 101`, the names would be `Isomap001` - `Isomap101`.

### 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` (the selectors or variables selected).

### 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

`step_pca()` `step_kpca()` `step_ica()` `recipe()` `prep.recipe()` `bake.recipe()`

### Examples

    data(biomass)

    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_predictors()) %>%
      step_center(all_predictors()) %>%
      step_scale(all_predictors()) %>%
      step_isomap(all_predictors(),
                  options = list(knn = 100),
                  num = 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 = 4)
    tidy(im_estimates, number = 4)

[Package recipes version 0.1.2 Index]