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giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration (2004.02551v2)

Published 6 Apr 2020 in cs.LG, math.AT, and stat.ML

Abstract: We introduce giotto-tda, a Python library that integrates high-performance topological data analysis with machine learning via a scikit-learn-compatible API and state-of-the-art C++ implementations. The library's ability to handle various types of data is rooted in a wide range of preprocessing techniques, and its strong focus on data exploration and interpretability is aided by an intuitive plotting API. Source code, binaries, examples, and documentation can be found at https://github.com/giotto-ai/giotto-tda.

Citations (166)

Summary

  • The paper presents giotto-tda as a toolkit that bridges topological data analysis and machine learning with a scikit-learn-compatible API.
  • It details the implementation of persistent homology and the Mapper algorithm to extract multi-scale features and visualize high-dimensional data.
  • The paper underscores community-driven development and robust documentation, making TDA accessible for practical data science applications.

An Academic Review of "giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration"

The paper presents "giotto-tda," a Python library designed to integrate topological data analysis (TDA) with ML, leveraging a scikit-learn-compatible API and advanced C++ implementations. The authors aim to make TDA accessible and usable for the Python data science community, addressing a significant gap in current ML toolboxes where TDA techniques are often underutilized due to their complex implementations.

Introduction and Motivation

TDA is a set of mathematical techniques that extract features capturing data shape, notably using persistent homology to analyze data across multiple scales. Although TDA has proven effective in diverse domains—such as material science, brain structure analysis, and cancer research—its adoption in mainstream ML practices has been limited. The authors identify the need for a high-level language implementation, leading to the development of giotto-tda, which extends the functionalities of scikit-learn to encompass TDA capabilities.

Architectural Overview

The giotto-tda library is architected to maintain compatibility with widely-used ML frameworks, allowing users to design TDA pipelines through modular components. This integration facilitates seamless incorporation of topological features into ML workflows. The library offers plotting capabilities for the interactive exploration of topological characteristics, enhancing its usability for data exploration tasks.

Persistent Homology

Persistent homology is central to giotto-tda, summarizing data in persistence diagrams. The framework provides tools to transform diverse data types suitable for persistent homology computation and subsequently extract multi-scale topological features. Users can represent these diagrams as curves, images, or through kernel definitions, with extensive hyperparameter tuning supported via integration with scikit-learn.

Giotto-tda compares favorably with other libraries, as highlighted in Table 1 of the paper. Notably, it includes directed persistent homology, enabling the analysis of non-symmetric interactions prevalent in many real-world datasets.

Mapper Algorithm

In addition to persistent homology, giotto-tda incorporates the Mapper algorithm, facilitating high-dimensional data visualization by constructing unweighted graphs. This implementation follows a sequential approach within scikit-learn pipelines, supporting interoperability and computational efficiency. The interactive plotting API permits real-time hyperparameter tuning, distinguishing it from other available tools like KeplerMapper.

Project Management and Community Engagement

The giotto-tda project emphasizes ease of installation, robust code quality, and extensive documentation, making it approachable for both researchers and practitioners. The community-driven development model and comprehensive learning resources, including a theory glossary and numerous tutorials, support widespread adoption and foster continuous improvement.

Concluding Thoughts

Giotto-tda represents a significant step in making TDA techniques accessible for large-scale ML tasks, adhering to scikit-learn's code and documentation standards. Future directions include integrating novel TDA methodologies, such as persistence Steenrod diagrams, to expand the library's analytical capabilities.

Through detailed exposition and a comprehensive feature set, the paper positions giotto-tda as an essential tool for those wishing to incorporate topological insights into machine learning workflows. By bridging the gap between TDA research and practical implementation, giotto-tda stands as a valuable contribution to the arsenal of data scientists and researchers alike.

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