Silhouette¶
-
class
gtda.diagrams.
Silhouette
(power=1.0, n_bins=100, n_jobs=None)[source]¶ Power-weighted silhouettes of persistence diagrams.
Based on ideas in 1. Given a persistence diagram consisting of birth-death-dimension triples [b, d, q], subdiagrams corresponding to distinct homology dimensions are considered separately, and their respective silhouette by sampling the silhouette function over evenly spaced locations from appropriate ranges of the filtration parameter.
- Parameters
power (float, optional, default:
1.
) – The power to which persistence values are raised to define the power-weighted silhouettes.n_bins (int, optional, default:
100
) – The number of filtration parameter values, per available homology dimension, to sample duringfit
.n_jobs (int 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.
-
homology_dimensions\_
Homology dimensions seen in
fit
, sorted in ascending order.- Type
list
-
samplings\_
For each number in homology_dimensions_, a discrete sampling of filtration parameters, calculated during
fit
according to the minimum birth and maximum death values observed across all samples.- Type
dict
See also
PersistenceLandscape
,PersistenceEntropy
,HeatKernel
,Amplitude
,PairwiseDistance
,BettiCurve
,gtda.homology.VietorisRipsPersistence
Notes
The samplings in
samplings_
are in general different between different homology dimensions. This means that the j-th entry of a silhouette in homology dimension q typically arises from a different parameter values to the j-th entry of a curve in dimension q’.References
- 1
F. Chazal, B. T. Fasy, F. Lecci, A. Rinaldo, and L. Wasserman, “Stochastic Convergence of Persistence Landscapes and Silhouettes”; In Proceedings of the thirtieth annual symposium on Computational Geometry, Kyoto, Japan, 2014, pp. 474–483; doi: 10.1145/2582112.2582128.
-
__init__
(power=1.0, n_bins=100, n_jobs=None)[source]¶ Initialize self. See help(type(self)) for accurate signature.
-
fit
(X, y=None)[source]¶ 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 here to implement the usual scikit-learn API and hence work in pipelines.
- Parameters
X (ndarray of 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).
y (None) – There is no need for a target in a transformer, yet the pipeline API requires this parameter.
- Returns
self
- Return type
object
-
fit_transform
(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
X (ndarray of 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).
y (None) – There is no need for a target in a transformer, yet the pipeline API requires this parameter.
- Returns
Xt – One silhouette (represented as a one-dimensional array) per sample and per homology dimension seen in
fit
. Index i along axis 1 corresponds to the i-th homology dimension inhomology_dimensions_
.- Return type
ndarray of shape (n_samples, n_homology_dimensions, n_bins)
-
fit_transform_plot
(X, y=None, sample=0, **plot_params)¶ Fit to data, then apply
transform_plot
.- Parameters
X (ndarray of shape (n_samples, ..)) – Input data.
y (ndarray of shape (n_samples,) or None) – Target values for supervised problems.
sample (int) – Sample to be plotted.
**plot_params – Optional plotting parameters.
- Returns
Xt – Transformed one-sample slice from the input.
- Return type
ndarray of shape (1, ..)
-
get_params
(deep=True)¶ Get parameters for this estimator.
- Parameters
deep (bool, default=True) – If True, will return the parameters for this estimator and contained subobjects that are estimators.
- Returns
params – Parameter names mapped to their values.
- Return type
mapping of string to any
-
plot
(Xt, sample=0, homology_dimensions=None)[source]¶ Plot a sample from a collection of silhouettes arranged as in the output of
transform
. Include homology in multiple dimensions.- Parameters
Xt (ndarray of shape (n_samples, n_homology_dimensions, n_bins)) – Collection of silhouettes, such as returned by
transform
.sample (int, optional, default:
0
) – Index of the sample in Xt to be plotted.homology_dimensions (list, tuple or None, optional, default:
None
) – Which homology dimensions to include in the plot.None
means plotting all dimensions present inhomology_dimensions_
.
-
set_params
(**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.- Parameters
**params (dict) – Estimator parameters.
- Returns
self – Estimator instance.
- Return type
object
-
transform
(X, y=None)[source]¶ Compute silhouettes of diagrams in X.
- Parameters
X (ndarray of 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).
y (None) – There is no need for a target in a transformer, yet the pipeline API requires this parameter.
- Returns
Xt – One silhouette (represented as a one-dimensional array) per sample and per homology dimension seen in
fit
. Index i along axis 1 corresponds to the i-th homology dimension inhomology_dimensions_
.- Return type
ndarray of shape (n_samples, n_homology_dimensions, n_bins)
-
transform_plot
(X, sample=0, **plot_params)¶ Take a one-sample slice from the input collection and transform it. Before returning the transformed object, plot the transformed sample.
- Parameters
X (ndarray of shape (n_samples, ..)) – Input data.
sample (int) – Sample to be plotted.
plot_params (dict) – Optional plotting parameters.
- Returns
Xt – Transformed one-sample slice from the input.
- Return type
ndarray of shape (1, ..)