Package index • tdarec

‘tdarec’ package

A ‘recipes’ and ‘dials’ extension for persistent homology and its vectorizations.

tdarec-package tdarec: A recipes and dials Extension for Persistent Homology

Data sets

Data sets provided to illustrate pre-processing steps.

mnist_train mnist_test: MNIST handwritten digits

Recipe steps to precede persistent homology

Functions that specify pre-processing steps to prepare data sets for persistent homology.

step_blur(): Blur raster data

Recipe steps to compute persistent homology

Functions that specify pre-processing steps to compute persistent homology of data sets.

step_pd_degree(): Separate persistent pairs by homological degree

step_pd_point_cloud(): Persistent homology of point clouds

step_pd_raster(): Persistent homology of raster data (images)

Recipe steps to vectorize persistent homology

Functions that specify pre-processing steps to vectorize persistent homology.

step_vpd_algebraic_functions(): Algebraic Functions Vectorization of Persistent Homology

step_vpd_betti_curve(): Betti Curve Vectorization of Persistent Homology

step_vpd_complex_polynomial(): Complex Polynomial Vectorization of Persistent Homology

step_vpd_descriptive_statistics(): Descriptive Statistics Vectorization of Persistent Homology

step_vpd_euler_characteristic_curve(): Euler Characteristic Curve Vectorization of Persistent Homology

step_vpd_normalized_life_curve(): Normalized Life Curve Vectorization of Persistent Homology

step_vpd_persistence_block(): Persistence Block Vectorization of Persistent Homology

step_vpd_persistence_image(): Persistence Image Vectorization of Persistent Homology

step_vpd_persistence_landscape(): Persistence Landscape Vectorization of Persistent Homology

step_vpd_persistence_silhouette(): Persistence Silhouette Vectorization of Persistent Homology

step_vpd_persistent_entropy_summary(): Persistent Entropy Summary Vectorization of Persistent Homology

step_vpd_tent_template_functions(): Tent Template Functions Vectorization of Persistent Homology

step_vpd_tropical_coordinates(): Tropical Coordinates Vectorization of Persistent Homology

Dials for the recipe steps

Dials to control the tunable parameters of pre-processing steps.

blur_sigmas(): Standard deviation of Gaussian blur

num_coef() poly_type() img_sigma() num_levels() weight_func_pl() bandwidth() weight_power() num_bars() num_bins() tent_shift(): Tune Vectorizations of Persistent Homology

Summarize data and finalize parameters

Helper functions to summarize topological data and finalizers for topological transformation parameters.

blur(): Gaussian blur of an array

ph_dim() pairs_min() pairs_max() birth_range() pers_max() pers_min() pers_range() life_support(): Summarize topological data

get_blur_range() hom_degree() max_hom_degree() get_hom_range(): (Maximum) topological dimension or homological degree

get_pairs_max() get_pers_max_frac() get_pers_min_mult(): Finalizers for persistent homology vectorizations