giotto.diagrams
.HeatKernel¶

class
giotto.diagrams.
HeatKernel
(sigma, n_values=100, n_jobs=None)¶ Convolution of persistence diagrams with a Gaussian kernel.
Based on ideas in [1]. Given a persistence diagram consisting of birthdeathdimension triples [b, d, q], subdiagrams corresponding to distinct homology dimensions are considered separately and regarded as sums of Dirac deltas. Then, the convolution with a Gaussian kernel is computed over a rectangular grid of locations evenly sampled from appropriate ranges of the filtration parameter. The same is done with the reflected images of the subdiagrams about the diagonal, and the difference between the results of the two convolutions is computed. The result can be thought of as a raster image.
 Parameters
 sigmafloat
Standard deviation for Gaussian kernel.
 n_valuesint, optional, default:
100
The number of filtration parameter values, per available homology dimension, to sample during
fit
. n_jobsint or None, optional, default:
None
The number of jobs to use for the computation.
None
means 1 unless in ajoblib.parallel_backend
context.1
means using all processors.
 Attributes
See also
Notes
The samplings in
samplings_
are in general different between different homology dimensions. This means that the (i, j)th pixel of a persistence image in homology dimension q typically arises from a different pair of parameter values to the (i, j)th pixel of a persistence image in dimension q’.References
 1
J. Reininghaus, S. Huber, U. Bauer, and R. Kwitt, “A Stable MultiScale Kernel for Topological Machine Learning”; 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 4741–4748, 2015; doi: 10.1109/CVPR.2015.7299106.
Methods
fit
(self, X[, y])Store all observed homology dimensions in
homology_dimensions_
and, for each dimension separately, store evenly sample filtration parameter values insamplings_
.fit_transform
(self, X[, y])Fit to data, then transform it.
get_params
(self[, deep])Get parameters for this estimator.
set_params
(self, \*\*params)Set the parameters of this estimator.
transform
(self, X[, y])Compute raster images obtained from diagrams in X by convolution with a Gaussian kernel.

__init__
(self, sigma, n_values=100, n_jobs=None)¶ Initialize self. See help(type(self)) for accurate signature.

fit
(self, X, y=None)¶ Store all observed homology dimensions in
homology_dimensions_
and, for each dimension separately, store evenly sample filtration parameter values insamplings_
. Then, return the estimator.This method is there to implement the usual scikitlearn API and hence work in pipelines.
 Parameters
 Xndarray, shape (n_samples, n_features, 3)
Input data. Array of persistence diagrams, each a collection of triples [b, d, q] representing persistent topological features through their birth (b), death (d) and homology dimension (q).
 yNone
There is no need for a target in a transformer, yet the pipeline API requires this parameter.
 Returns
 selfobject

fit_transform
(self, X, y=None, **fit_params)¶ Fit to data, then transform it.
Fits transformer to X and y with optional parameters fit_params and returns a transformed version of X.
 Parameters
 Xnumpy array of shape [n_samples, n_features]
Training set.
 ynumpy array of shape [n_samples]
Target values.
 Returns
 X_newnumpy array of shape [n_samples, n_features_new]
Transformed array.

get_params
(self, deep=True)¶ Get parameters for this estimator.
 Parameters
 deepboolean, optional
If True, will return the parameters for this estimator and contained subobjects that are estimators.
 Returns
 paramsmapping of string to any
Parameter names mapped to their values.

set_params
(self, **params)¶ Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form
<component>__<parameter>
so that it’s possible to update each component of a nested object. Returns
 self

transform
(self, X, y=None)¶ Compute raster images obtained from diagrams in X by convolution with a Gaussian kernel.
 Parameters
 Xndarray, shape (n_samples, n_features, 3)
Input data. Array of persistence diagrams, each a collection of triples [b, d, q] representing persistent topological features through their birth (b), death (d) and homology dimension (q).
 yNone
There is no need for a target in a transformer, yet the pipeline API requires this parameter.
 Returns
 Xtndarray, shape (n_samples, n_homology_dimensions, n_values, n_values)
Raster images: one image per sample and per homology dimension seen in
fit
. Index i along axis 1 corresponds to the ith homology dimension inhomology_dimensions_
.