predict_diagram_kpca {TDApplied}

Project persistence diagrams into a low-dimensional space via a pre-computed kernel PCA embedding.

Description

Compute the location in low-dimensional space of each element of a list of new persistence diagrams using a previously-computed kernel PCA embedding (from the diagram_kpca function).

Usage

predict_diagram_kpca(
  new_diagrams,
  K = NULL,
  embedding,
  num_workers = parallelly::availableCores(omit = 1)
)

Arguments

new_diagrams

a list of persistence diagrams which are either the output of a persistent homology calculation like ripsDiag/calculate_homology/PyH, or diagram_to_df. Only one of 'new_diagrams' and 'K' need to be supplied.

K

an optional precomputed cross-Gram matrix of the new diagrams and the ones used in 'embedding', default NULL. If not NULL then 'new_diagrams' does not need to be supplied.

embedding

the output of a diagram_kpca function call, of class 'diagram_kpca'.

num_workers

the number of cores used for parallel computation, default is one less than the number of cores on the machine.

Value

the data projection (rotation), stored as a numeric matrix. Each row corresponds to the same-index diagram in 'new_diagrams'.

Author(s)

Shael Brown - [e-mail]

See Also

diagram_kpca for embedding persistence diagrams into a low-dimensional space.

Examples

if(require("TDAstats"))
{
  # create six diagrams
  D1 <- TDAstats::calculate_homology(TDAstats::circle2d[sample(1:100,20),],
                      dim = 1,threshold = 2)
  D2 <- TDAstats::calculate_homology(TDAstats::circle2d[sample(1:100,20),],
                      dim = 1,threshold = 2)
  D3 <- TDAstats::calculate_homology(TDAstats::sphere3d[sample(1:100,20),],
                      dim = 1,threshold = 2)
  D4 <- TDAstats::calculate_homology(TDAstats::sphere3d[sample(1:100,20),],
                      dim = 1,threshold = 2)
  D5 <- TDAstats::calculate_homology(TDAstats::sphere3d[sample(1:100,20),],
                      dim = 1,threshold = 2)
  D6 <- TDAstats::calculate_homology(TDAstats::sphere3d[sample(1:100,20),],
                      dim = 1,threshold = 2)
  g <- list(D1,D2,D3,D4,D5,D6)

  # calculate their 2D PCA embedding with sigma = t = 2 in dimension 0
  pca <- diagram_kpca(diagrams = g,dim = 1,t = 2,sigma = 2,
                      features = 2,num_workers = 2,th = 1e-6)

  # project two new diagrams onto old model
  D7 <- TDAstats::calculate_homology(TDAstats::circle2d[sample(1:100,50),],
                                     dim = 0,threshold = 2)
  D8 <- TDAstats::calculate_homology(TDAstats::circle2d[sample(1:100,50),],
                                     dim = 0,threshold = 2)
  g_new <- list(D7,D8)

  # calculate new embedding coordinates
  new_pca <- predict_diagram_kpca(new_diagrams = g_new,embedding = pca,num_workers = 2)
  
  # repeat with precomputed Gram matrix, gives same result but much faster
  K <- gram_matrix(diagrams = g_new,other_diagrams = pca$diagrams,dim = pca$dim,
                   t = pca$t,sigma = pca$sigma,num_workers = 2)
  new_pca <- predict_diagram_kpca(K = K,embedding = pca,num_workers = 2)
}