This advanced machine learning book highlights many algorithms from a geometric perspective and introduces tools in network science, metric geometry, and topological data analysis through practical application.

Whether you’re a mathematician, seasoned data scientist, or marketing professional, you’ll find The Shape of Data to be the perfect introduction to the critical interplay between the geometry of data structures and machine learning.

This book’s extensive collection of case studies (drawn from medicine, education, sociology, linguistics, and more) and gentle explanations of the math behind dozens of algorithms provide a comprehensive yet accessible look at how geometry shapes the algorithms that drive data analysis.

In addition to gaining a deeper understanding of how to implement geometry-based algorithms with code, you’ll explore:

• Supervised and unsupervised learning algorithms and their application to network data analysis
• The way distance metrics and dimensionality reduction impact machine learning
• How to visualize, embed, and analyze survey and text data with topology-based algorithms
• New approaches to computational solutions, including distributed computing and quantum algorithms

Table of Contents

Chapter 1: The Geometric Structure of Data

Chapter 2: The Geometric Structure of Networks

Chapter 3: Network Analysis

Chapter 4: Network Filtration

Chapter 5: Geometry in Data Science

Chapter 6: Newer Applications of Geometry in Machine Learning

Chapter 7: Tools for Topological Data Analysis

Chapter 8: Homotopy Algorithms

Chapter 9: Final Project: Analyzing Text Data

Chapter 10: Multicore and Quantum Computing

About the Authors

Colleen M. Farrelly is a senior data scientist whose academic and industry research has focused on topological data analysis, quantum machine learning, geometry-based machine learning, network science, hierarchical modeling, and natural language processing. Since graduating from the University of Miami with an MS in biostatistics, Colleen has worked as a data scientist in a vari- ety of industries, including healthcare, consumer packaged goods, biotech, nuclear engineering, marketing, and education. Colleen often speaks at tech conferences, including PyData, SAS Global, WiDS, Data Science Africa, and DataScience SALON. When not working, Colleen can be found writing haibun/haiga or swimming.

Yaé Ulrich Gaba

 completed his doctoral studies at the University of Cape Town (UCT, South Africa) with a specialization in topology and is currently a research associate at Quantum Leap Africa (QLA, Rwanda). His research interests are computational geometry, applied algebraic topology (topologi- cal data analysis), and geometric machine learning (graph and point-cloud representation learning). His current focus lies in geometric methods in data analysis, and his work seeks to develop effective and theoretically justified algorithms for data and shape analysis using geometric and topological ideas and methods.