The Shape of dаta: Geometry-Based Machine Learning and Data Analysis in R

Cover
Praise for The Shape of Data
Title Page
Copyright
Dedication
About the Authors
Foreword
Acknowledgments
Introduction
   Who Is This Book For?
   About This Book
   Downloading and Installing R
   Installing R Packages
   Getting Help with R
   Support for Python Users
   Summary
Chapter 1: The Geometric Structure of Data
   Machine Learning Categories
      Supervised Learning
      Unsupervised Learning
      Matching Algorithms and Other Machine Learning
   Structured Data
      The Geometry of Dummy Variables
      The Geometry of Numerical Spreadsheets
      The Geometry of Supervised Learning
   Unstructured Data
      Network Data
      Image Data
      Text Data
   Summary
Chapter 2: The Geometric Structure of Networks
   The Basics of Network Theory
      Directed Networks
      Networks in R
      Paths and Distance in a Network
   Network Centrality Metrics
      The Degree of a Vertex
      The Closeness of a Vertex
      The Betweenness of a Vertex
      Eigenvector Centrality
      PageRank Centrality
      Katz Centrality
      Hub and Authority
   Measuring Centrality in an Example Social Network
   Additional Quantities of a Network
      The Diversity of a Vertex
      Triadic Closure
      The Efficiency and Eccentricity of a Vertex
      Forman–Ricci Curvature
   Global Network Metrics
      The Interconnectivity of a Network
      Spreading Processes on a Network
      Spectral Measures of a Network
   Network Models for Real-World Behavior
      Erdös–Renyi Graphs
      Scale-Free Graphs
      Watts–Strogatz Graphs
   Summary
Chapter 3: Network Analysis
   Using Network Data for Supervised Learning
      Making Predictions with Social Media Network Metrics
      Predicting Network Links in Social Media
   Using Network Data for Unsupervised Learning
      Applying Clustering to the Social Media Dataset
      Community Mining in a Network
   Comparing Networks
   Analyzing Spread Through Networks
      Tracking Disease Spread Between Towns
      Tracking Disease Spread Between Windsurfers
      Disrupting Communication and Disease Spread
   Summary
Chapter 4: Network Filtration
   Graph Filtration
   From Graphs to Simplicial Complexes
      Examples of Betti Numbers
      The Euler Characteristic
      Persistent Homology
   Comparison of Networks with Persistent Homology
   Summary
Chapter 5: Geometry in Data Science
   Common Distance Metrics
      Simulating a Small Dataset
      Using Norm-Based Distance Metrics
      Comparing Diagrams, Shapes, and Probability Distributions
   K-Nearest Neighbors with Metric Geometry
   Manifold Learning
      Using Multidimensional Scaling
      Extending Multidimensional Scaling with Isomap
      Capturing Local Properties with Locally Linear Embedding
      Visualizing with t-Distributed Stochastic Neighbor Embedding
   Fractals
   Summary
Chapter 6: Newer Applications of Geometry in Machine Learning
   Working with Nonlinear Spaces
      Introducing dgLARS
      Predicting Depression with dgLARS
      Predicting Credit Default with dgLARS
   Applying Discrete Exterior Derivatives
   Nonlinear Algebra in Machine Learning Algorithms
   Comparing Choice Rankings with HodgeRank
   Summary
Chapter 7: Tools for Topological Data Analysis
   Finding Distinctive Groups with Unique Behavior
   Validating Measurement Tools
   Using the Mapper Algorithm for Subgroup Mining
      Stepping Through the Mapper Algorithm
      Using TDAmapper to Find Cluster Structures in Data
   Summary
Chapter 8: Homotopy Algorithms
   Introducing Homotopy
   Introducing Homotopy-Based Regression
   Comparing Results on a Sample Dataset
   Summary
Chapter 9: Final Project: Analyzing Text Data
   Building a Natural Language Processing Pipeline
   The Project: Analyzing Language in Poetry
      Tokenizing Text Data
      Tagging Parts of Speech
      Normalizing Vectors
   Analyzing the Poem Dataset in R
   Using Topology-Based NLP Tools
   Summary
Chapter 10: Multicore and Quantum Computing
   Multicore Approaches to Topological Data Analysis
   Quantum Computing Approaches
      Using the Qubit-Based Model
      Using the Qumodes-Based Model
      Using Quantum Network Algorithms
      Speeding Up Algorithms with Quantum Computing
      Using Image Classifiers on Quantum Computers
   Summary
References
   Chapter 1
   Chapter 2
   Chapter 3
   Chapter 4
   Chapter 5
   Chapter 6
   Chapter 7
   Chapter 8
   Chapter 9
   Chapter 10
   Chapter 6 Datasets
   Chapter 9 Dataset Poems
Index