# Overview¶

A high-performance topological machine learning toolbox in Python

giotto-tda is a high performance topological machine learning toolbox in Python built on top of scikit-learn and is distributed under the GNU AGPLv3 license. It is part of the Giotto family of open-source projects.

## Guiding principles¶

• Seamless integration with scikit-learn
Strictly adhere to the scikit-learn API and development guidelines, inherit the strengths of that framework.
• Code modularity
Topological feature creation steps as transformers. Allow for the creation of a large number of topologically-powered machine learning pipelines.
• Standardisation
Implement the most successful techniques from the literature into a generic framework with a consistent API.
• Innovation
Improve on existing algorithms, and make new ones available in open source.
• Performance
For the most demanding computations, fall back to state-of-the-art C++ implementations, bound efficiently to Python. Vectorized code and implements multi-core parallelism (with joblib).
• Data structures
Support for tabular data, time series, graphs, and images.

## 30s guide to giotto-tda¶

For installation instructions, see the installation instructions.

The functionalities of giotto-tda are provided in scikit-learn–style transformers. This allows you to generate topological features from your data in a familiar way. Here is an example with the VietorisRipsPersistence transformer:

from gtda.homology import VietorisRipsPersistence
VR = VietorisRipsPersistence()


which computes topological summaries, called persistence diagrams, from collections of point clouds or weighted graphs, as follows:

diagrams = VR.fit_transform(point_clouds)


A plotting API allows for quick visual inspection of the outputs of many of giotto-tda’s transformers. To visualize the i-th output sample, run

diagrams = VR.plot(diagrams, sample=i)


You can create scalar or vector features from persistence diagrams using giotto-tda’s dedicated transformers. Here is an example with the PersistenceEntropy transformer:

from gtda.diagrams import PersistenceEntropy
PE = PersistenceEntropy()
features = PE.fit_transform(diagrams)


features is a two-dimensional numpy array. This is important to making this type of topological feature generation fit into a typical machine learning workflow from scikit-learn. In particular, topological feature creation steps can be fed to or used alongside models from scikit-learn, creating end-to-end pipelines which can be evaluated in cross-validation, optimised via grid-searches, etc.:

from sklearn.ensemble import RandomForestClassifier
from gtda.pipeline import make_pipeline
from sklearn.model_selection import train_test_split

X_train, X_valid, y_train, y_valid = train_test_split(point_clouds, labels)
RFC = RandomForestClassifier()
model = make_pipeline(VR, PE, RFC)
model.fit(X_train, y_train)
model.score(X_valid, y_valid)


giotto-tda also implements the Mapper algorithm as a highly customisable scikit-learn Pipeline, and provides simple plotting functions for visualizing output Mapper graphs and have real-time interaction with the pipeline parameters:

from gtda.mapper import make_mapper_pipeline
from sklearn.decomposition import PCA
from sklearn.cluster import DBSCAN

pipe = make_mapper_pipeline(filter_func=PCA(), clusterer=DBSCAN())
plot_interactive_mapper_graph(pipe, data)


## Resources¶

### Tutorials and examples¶

We provide a number of tutorials and examples, which offer:

• quick start guides to the API;

• in-depth examples showcasing more of the library’s features;

• intuitive explanations of topological techniques.

### Use cases¶

A selection of use cases for giotto-tda is collected at this page. Please note, however, that some of these were written for past versions of giotto-tda. In some cases, only small modifications are needed to run them on recent versions, while in others it is best to install the relevant past version of giotto-tda (preferably in a fresh environmnent). In a couple of cases, the legacy giotto-learn or giotto-learn-nightly will be needed.

## What’s new¶

### Major Features and Improvements¶

• An object-oriented API for interactive plotting of Mapper graphs has been added with the MapperInteractivePlotter (#586). This is intended to supersede plot_interactive_mapper graph as it allows for inspection of the current state of the objects change by interactivity. See also “Backwards-Incompatible Changes” below.

• Further citations have been added to the mathematical glossary (#564).

### Bug Fixes¶

• A bug preventing EuclideanCechPersistence from working correctly on point clouds in more than 2 dimensions has been fixed (#588).

• A validation bug preventing VietorisRipsPersistence and WeightedRipsPersistence from accepting non-empty dictionaries as metric_params has been fixed (#590).

• A bug causing an exception to be raised when node_color_statistic was passed as a numpy array in plot_static_mapper_graph has been fixed (#576).

### Backwards-Incompatible Changes¶

• A major change to the behaviour of the (static and interactive) Mapper plotting functions plot_static_mapper_graph and plot_interactive_mapper_graph was introduced in #584. The new MapperInteractivePlotter class (see “Major Features and Improvements” above) also follows this new API. The main changes are as follows:

• color_by_columns_dropdown has been eliminated.

• color_variable has been renamed to color_features (but cannot be an array).

• An additional keyword argument color_data has been added to more clearly separate the input data to the Mapper pipeline from the data to be used for coloring.

• node_color_statistic is now applied column by column – previously it could end up being applied to 2d arrays as a whole.

• The defaults for color-related arguments lead to index values instead of the mean of the data.

• The default for weight_params in WeightedRipsPersistence is now the empty dictionary, and None is no longer allowed (#595).

### Thanks to our Contributors¶

This release contains contributions from many people:

Umberto Lupo, Wojciech Reise, Julian Burella Pérez, Sean Law, Anibal Medina-Mardones, and Lewis Tunstall

We are also grateful to all who filed issues or helped resolve them, asked and answered questions, and were part of inspiring discussions.