tdarec (version 0.2.0)

step_vpd_complex_polynomial: Complex Polynomial Vectorization of Persistent Homology

Description

The function step_vpd_complex_polynomial() creates a specification of a recipe step that will convert a list-column of 3-column matrices of persistence data to a list-column of 1-row matrices of vectorizations.

Usage

step_vpd_complex_polynomial(
  recipe,
  ...,
  role = "predictor",
  trained = FALSE,
  hom_degree = 0L,
  num_coef = 1L,
  poly_type = "R",
  columns = NULL,
  keep_original_cols = TRUE,
  skip = FALSE,
  id = rand_id("vpd_complex_polynomial")
)

Value

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

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.

hom_degree

The homological degree of the features to be transformed.

num_coef

The number of coefficients of a convex polynomial fitted to finite persistence pairs.

poly_type

The type of complex polynomial to fit ('R', 'S', or 'T').

columns

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

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.

Engine

The complex polynomial vectorization deploys TDAvec::computeComplexPolynomial(). See there for definitions and references.

Tuning Parameters

This step has 3 tuning parameters:

• hom_degree: Homological degree (type: integer, default: 0L)

• num_coef: # Polynomial coefficients (type: integer, default: 1L)

• poly_type: Type of polynomial (type: character, default: "R")

Details

Persistent homology is usually encoded as birth--death pairs (barcodes or diagrams), but the space of persistence data sets does not satisfy convenient statistical properties. Such applications as hypothesis testing and machine learning benefit from transformations of persistence data, often to Hilbert spaces (vector spaces with inner products and induced metrics).

Examples

library(recipes)

# inspect vectorized features
volc_dat <- data.frame(image = I(list(volcano / 10)))
recipe(~ image, data = volc_dat) %>% 
  step_pd_raster(image, method = "link_join") %>% 
  step_vpd_complex_polynomial(image, hom_degree = 1) %>% 
  print() -> volc_rec
print(volc_rec)
volc_rec %>% 
  prep(training = volc_dat) %>% 
  bake(new_data = volc_dat)

# dimension-reduce using vectorized features
data(permeability_qsar, package = "modeldata")
permeability_qsar %>% 
  transform(perm_cut = cut(permeability, breaks = seq(0, 60, 10))) %>% 
  subset(select = -permeability) %>% 
  tidyr::nest(chem_fp = -perm_cut) %>% 
  print() -> perm_dat
recipe(perm_cut ~ chem_fp, data = perm_dat) %>% 
  step_pd_point_cloud(chem_fp, max_hom_degree = 2) %>% 
  step_vpd_complex_polynomial(chem_fp, hom_degree = 1) %>% 
  step_pca(starts_with("chem_fp_"), num_comp = 2) %>%
  print() -> perm_rec
perm_est <- prep(perm_rec, training = perm_dat)
perm_res <- bake(perm_est, new_data = perm_dat)
# inspect results
tidy(perm_rec)
tidy(perm_rec, number = 2)
tidy(perm_est, number = 2)
# visualize results
with(perm_res, {
  plot(PC1, PC2, type = "n", asp = 1)
  text(PC1, PC2, labels = perm_cut)
})