book

The Shape of Data

by Colleen M. Farrelly, Yaé Ulrich Gaba

September 2023

Intermediate to advanced

264 pages

7h 27m

English

No Starch Press

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Praise for The Shape of Data
Title Page
Copyright
Dedication
About the Authors
Foreword
Acknowledgments
Introduction
Who Is This Book For?About This BookDownloading and Installing RInstalling R PackagesGetting Help with RSupport for Python UsersSummary
Chapter 1: The Geometric Structure of Data
Machine Learning CategoriesSupervised LearningUnsupervised LearningMatching Algorithms and Other Machine LearningStructured DataThe Geometry of Dummy VariablesThe Geometry of Numerical SpreadsheetsThe Geometry of Supervised LearningUnstructured DataNetwork DataImage DataText DataSummary
Chapter 2: The Geometric Structure of Networks
The Basics of Network TheoryDirected NetworksNetworks in RPaths and Distance in a NetworkNetwork Centrality MetricsThe Degree of a VertexThe Closeness of a VertexThe Betweenness of a VertexEigenvector CentralityPageRank CentralityKatz CentralityHub and AuthorityMeasuring Centrality in an Example Social NetworkAdditional Quantities of a NetworkThe Diversity of a VertexTriadic ClosureThe Efficiency and Eccentricity of a VertexForman–Ricci CurvatureGlobal Network MetricsThe Interconnectivity of a NetworkSpreading Processes on a NetworkSpectral Measures of a NetworkNetwork Models for Real-World BehaviorErdös–Renyi GraphsScale-Free GraphsWatts–Strogatz GraphsSummary

Chapter 3: Network Analysis
Using Network Data for Supervised LearningMaking Predictions with Social Media Network MetricsPredicting Network Links in Social MediaUsing Network Data for Unsupervised LearningApplying Clustering to the Social Media DatasetCommunity Mining in a NetworkComparing NetworksAnalyzing Spread Through NetworksTracking Disease Spread Between TownsTracking Disease Spread Between WindsurfersDisrupting Communication and Disease SpreadSummary
Chapter 4: Network Filtration
Graph FiltrationFrom Graphs to Simplicial ComplexesExamples of Betti NumbersThe Euler CharacteristicPersistent HomologyComparison of Networks with Persistent HomologySummary
Chapter 5: Geometry in Data Science
Common Distance MetricsSimulating a Small DatasetUsing Norm-Based Distance MetricsComparing Diagrams, Shapes, and Probability DistributionsK-Nearest Neighbors with Metric GeometryManifold LearningUsing Multidimensional ScalingExtending Multidimensional Scaling with IsomapCapturing Local Properties with Locally Linear EmbeddingVisualizing with t-Distributed Stochastic Neighbor EmbeddingFractalsSummary
Chapter 6: Newer Applications of Geometry in Machine Learning
Working with Nonlinear SpacesIntroducing dgLARSPredicting Depression with dgLARSPredicting Credit Default with dgLARSApplying Discrete Exterior DerivativesNonlinear Algebra in Machine Learning AlgorithmsComparing Choice Rankings with HodgeRankSummary
Chapter 7: Tools for Topological Data Analysis
Finding Distinctive Groups with Unique BehaviorValidating Measurement ToolsUsing the Mapper Algorithm for Subgroup MiningStepping Through the Mapper AlgorithmUsing TDAmapper to Find Cluster Structures in DataSummary
Chapter 8: Homotopy Algorithms
Introducing HomotopyIntroducing Homotopy-Based RegressionComparing Results on a Sample DatasetSummary
Chapter 9: Final Project: Analyzing Text Data
Building a Natural Language Processing PipelineThe Project: Analyzing Language in PoetryTokenizing Text DataTagging Parts of SpeechNormalizing VectorsAnalyzing the Poem Dataset in RUsing Topology-Based NLP ToolsSummary
Chapter 10: Multicore and Quantum Computing
Multicore Approaches to Topological Data AnalysisQuantum Computing ApproachesUsing the Qubit-Based ModelUsing the Qumodes-Based ModelUsing Quantum Network AlgorithmsSpeeding Up Algorithms with Quantum ComputingUsing Image Classifiers on Quantum ComputersSummary
References
Index

Content preview from The Shape of Data

4 Network Filtration

We’ve explored many ways to analyze network data by measuring geometric properties. In this chapter, we’ll introduce network filtration for weighted networks, which tracks geometric properties and network metrics over threshold values imposed on the network. Then we’ll examine how network data can be transformed into a higher-dimensional topological object called a simplicial complex, and we’ll explore higher-dimensional versions of the network metrics we’ve previously considered. From there, we’ll return to graph comparisons using a tool from topology related to filtrations.

Graph Filtration

In the previous chapters, ...

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The Shape of Data

by Colleen M. Farrelly, Yaé Ulrich Gaba

4 Network Filtration

Graph Filtration

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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