Manifold Sculpting signal extraction — step_manifold

step_manifold_sculpting() creates a specification of a recipe step that converts numeric data into one or more new dimensions with Manifold Sculpting.

Usage

step_manifold_sculpting(
  recipe,
  ...,
  role = "predictor",
  trained = FALSE,
  num_comp = 2,
  neighbors = 20,
  squishing_rate = 0.99,
  options = list(),
  seed = sample.int(10^5, 1),
  res = NULL,
  columns = NULL,
  prefix = "MS",
  keep_original_cols = FALSE,
  skip = FALSE,
  id = recipes::rand_id("manifold_sculpting")
)

# S3 method for class 'step_manifold_sculpting'
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 variables for this step. See recipes::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_comp: The number of dimensions of the embedding. It is reduced to one less than the number of selected columns when it is larger. With num_comp = 0, the data are returned unchanged.
neighbors: The number of nearest neighbors that define the local relationships to preserve.
squishing_rate: The factor by which the dimensions to remove are scaled down at each iteration, in (0, 1).
options: A list of other arguments to manifold_sculpting(): nstart, max_iter, patience, nn_method and verbose.
seed: A single integer, the seed of the random numbers used when the step is trained, for reproducible results.
res: The manifold_sculpting() fit, once the step has been trained by recipes::prep().
columns: A character string of the selected variable names. This field is a placeholder and will be populated once prep() is used.
prefix: The prefix of the names of the new columns, which are numbered from 1 (MS1, MS2, ...).
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.
x: A step_manifold_sculpting object.

Value

An updated version of recipe with the new step added to the sequence of any existing operations.

Details

Manifold Sculpting (Gashler, Ventura and Martinez, 2008) finds a low-dimensional embedding that preserves the distances and angles between neighboring samples; see manifold_sculpting() for the algorithm. It is based on Euclidean distances, so the predictors should usually be centered and scaled first, with recipes::step_normalize().

New samples, given to recipes::bake(), are embedded from their nearest training samples by predict.manifold_sculpting(). The training set gets the embedding found by the algorithm.

Tidying

When you tidy() this step, a tibble is returned with the columns terms (the selectors or variables selected) and id.

Tuning parameters

This step has 3 tuning parameters: num_comp (# Components), neighbors (# Nearest Neighbors) and squishing_rate (Squishing Rate, see squishing_rate()).

Case weights

The underlying operation does not allow for case weights.

References

Gashler, M., Ventura, D. and Martinez, T. (2008). Iterative non-linear dimensionality reduction with manifold sculpting. In Advances in Neural Information Processing Systems 20, 513–520.

Examples

library(recipes)

set.seed(1)
roll <- sim_swiss_roll(1000)
train <- roll[1:800, ]
test <- roll[801:1000, ]

rec <- recipe(~ x + y + z, data = train) |>
  step_manifold_sculpting(all_numeric_predictors(), num_comp = 2, seed = 1)

rec_trained <- prep(rec)
rec_trained
#> 
#> ── Recipe ──────────────────────────────────────────────────────────────────────
#> 
#> ── Inputs 
#> Number of variables by role
#> predictor: 3
#> 
#> ── Training information 
#> Training data contained 800 data points and no incomplete rows.
#> 
#> ── Operations 
#> • Manifold Sculpting extraction with: x, y, z | Trained
bake(rec_trained, new_data = test)
#> # A tibble: 200 × 2
#>      MS1   MS2
#>    <dbl> <dbl>
#>  1 10.3   18.0
#>  2 17.7   11.5
#>  3  9.35  19.0
#>  4 11.4   17.3
#>  5 15.7   13.5
#>  6 12.1   16.8
#>  7 15.1   14.2
#>  8  9.78  19.1
#>  9 15.3   14.3
#> 10 18.1   11.9
#> # ℹ 190 more rows
tidy(rec_trained, number = 1)
#> # A tibble: 3 × 2
#>   terms id                      
#>   <chr> <chr>                   
#> 1 x     manifold_sculpting_JtE6m
#> 2 y     manifold_sculpting_JtE6m
#> 3 z     manifold_sculpting_JtE6m