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  • Overview
    • Guiding principles
    • 30s guide to giotto-tda
    • Resources
      • Tutorials and examples
      • Use cases
    • What’s new
      • Major Features and Improvements
      • Bug Fixes
      • Backwards-Incompatible Changes
      • Thanks to our Contributors
  • Installation
    • Dependencies
    • User installation
    • Developer installation
      • Linux
      • macOS
      • Windows
        • Boost
        • Pre-built binaries
        • Source code
        • Already installed Boost version
        • Troubleshooting
      • Source code
      • To install:
      • Testing
  • API reference
    • gtda.mapper: Mapper
      • Filters
        • Projection
        • Eccentricity
        • Entropy
      • Covers
        • OneDimensionalCover
        • CubicalCover
      • Clustering
        • FirstSimpleGap
        • FirstHistogramGap
        • ParallelClustering
      • Nerve (graph construction)
        • Nerve
      • Pipeline
        • make_mapper_pipeline
        • MapperPipeline
      • Visualization
        • plot_static_mapper_graph
        • plot_interactive_mapper_graph
        • MapperInteractivePlotter
      • Utilities
        • method_to_transform
        • transformer_from_callable_on_rows
    • gtda.homology: Persistent homology
      • Undirected simplicial homology
        • VietorisRipsPersistence
        • WeightedRipsPersistence
        • SparseRipsPersistence
        • WeakAlphaPersistence
        • EuclideanCechPersistence
      • Directed simplicial homology
        • FlagserPersistence
      • Cubical homology
        • CubicalPersistence
    • gtda.diagrams: Persistence diagrams
      • Preprocessing
        • ForgetDimension
        • Scaler
        • Filtering
      • Distances
        • PairwiseDistance
      • Representations
        • PersistenceLandscape
        • BettiCurve
        • HeatKernel
        • PersistenceImage
        • Silhouette
      • Features
        • Amplitude
        • PersistenceEntropy
        • NumberOfPoints
        • ComplexPolynomial
    • gtda.curves: Curves
      • Preprocessing
        • Derivative
      • Feature extraction
        • StandardFeatures
    • gtda.point_clouds: Point clouds
      • ConsistentRescaling
      • ConsecutiveRescaling
    • gtda.time_series: Time series
      • Preprocessing
        • SlidingWindow
        • Resampler
        • Stationarizer
      • Time-delay embedding
        • TakensEmbedding
        • SingleTakensEmbedding
        • takens_embedding_optimal_parameters
      • Target preparation
        • Labeller
      • Dynamical systems
        • PermutationEntropy
      • Multivariate
        • PearsonDissimilarity
    • gtda.graphs: Graphs
      • Graph creation
        • TransitionGraph
        • KNeighborsGraph
      • Graph processing
        • GraphGeodesicDistance
    • gtda.images: Images
      • Preprocessing
        • Binarizer
        • Inverter
        • Padder
        • ImageToPointCloud
      • Filtrations
        • HeightFiltration
        • RadialFiltration
        • DilationFiltration
        • ErosionFiltration
        • SignedDistanceFiltration
        • DensityFiltration
    • gtda.plotting: Plotting functions
      • plot_point_cloud
      • plot_heatmap
      • plot_diagram
      • plot_betti_curves
      • plot_betti_surfaces
    • gtda.base: Base
      • TransformerResamplerMixin
      • PlotterMixin
    • gtda.pipeline: Pipeline
      • Pipeline
      • make_pipeline
    • gtda.metaestimators: Meta-estimators
      • CollectionTransformer
    • gtda.utils: Utilities
      • check_collection
      • check_point_clouds
      • check_diagrams
      • validate_params
  • Tutorials and examples
    • Tutorials
      • Topological feature extraction using VietorisRipsPersistence and PersistenceEntropy
        • Generate data
        • Calculate persistent homology
        • Extract features
        • Use the new features in a standard classifier
        • Encapsulate the steps above in a pipeline
      • Plotting in giotto-tda
        • 1. Basic philosophy and plot methods
        • 2 Derived convenience methods: transform_plot and fit_transform_plot
      • Getting started with Mapper
        • Useful references
        • Import libraries
        • Generate and visualise data
        • Configure the Mapper pipeline
        • Visualise the Mapper graph
        • Run the Mapper pipeline
        • Creating custom filter functions
        • Visualise the Mapper graph interactively (Live Jupyter session needed)
      • Topology of time series
        • Useful references
        • See also
        • From time series to time delay embeddings
        • A periodic example
        • A non-periodic example
        • From time delay embeddings to persistence diagrams
        • Picking the embedding dimension and time delay
      • Topology in time series forecasting
        • See also
        • SlidingWindow
        • Multivariate time series example: Sliding window + topology Pipeline
        • Univariate time series – TakensEmbedding and SingleTakensEmbedding
        • Endogeneous target preparation with Labeller
        • Where to next?
      • Topological feature extraction from graphs
        • See also
        • Import libraries
        • Undirected graphs – VietorisRipsPersistence and SparseRipsPersistence
        • Directed graphs – FlagserPersistence
        • Where to next?
    • Examples
      • Gravitational wave detection
        • Useful references
        • See also
        • Motivation
        • Generate the data
        • Constant signal-to-noise ratio
      • Classifying 3D shapes
        • Generate simple shapes
        • From data to persistence diagrams
        • Train a classifier
        • Putting it all together
        • A more realistic example
        • Improving our model
      • The Lorenz attractor
        • See also
        • Import libraries
        • Setting up the Lorenz attractor simulation
        • Resampling the time series
        • Takens Embedding
        • Persistence diagram
        • Scikit-learn–style pipeline
        • Rescaling the diagram
        • Filtering diagrams
        • Persistence entropy
        • Betti Curves
        • Distances among diagrams
        • New distances in the embedding space: kNN graphs and geodesic distances
      • Classifying handwritten digits
        • Useful references
        • Load the MNIST dataset
        • From pixels to topological features
        • Building a full-blown feature extraction pipeline
        • Training a classifier
        • Using hyperparameter search with topological pipelines
      • Can two-dimensional topological voids exist in two dimensions?
        • Import libraries
  • Theory Glossary
    • Symbols
    • Analysis
      • Metric space
      • Normed space
      • Inner product space
      • Vectorization, amplitude and kernel
      • Euclidean distance and \(l^p\)-norms
      • Distance matrices and point clouds
      • \(L^p\)-norms
    • Homology
      • Cubical complex
        • Reference:
      • Simplicial complex
      • Abstract simplicial complex
      • Ordered simplicial complex
      • Directed simplicial complex
      • Chain complex
      • Homology and cohomology
      • Simplicial chains and simplicial homology
      • Cubical chains and cubical homology
    • Persistence
      • Filtered complex
      • Cellwise filtration
      • Clique and flag complexes
      • Persistence module
      • Persistent simplicial (co)homology
      • Vietoris-Rips complex and Vietoris-Rips persistence
      • Čech complex and Čech persistence
      • Multiset
      • Persistence diagram
        • Reference:
        • Earlier work:
      • Wasserstein and bottleneck distance
        • Reference:
      • Persistence landscape
        • References:
      • Weighted silhouette
        • References:
      • Heat vectorizations
        • References:
      • Persistence entropy
        • References:
      • Betti curve
    • Time series
      • Time series
      • Takens embedding
        • Reference:
      • Manifold
        • References:
      • Compact subset
    • Bibliography
  • Contributing
    • Guidelines
      • Essentials for contributing
        • Contributor License Agreement
        • Pull requests
        • Issues
      • Contribution guidelines and standards
        • General guidelines and philosophy for contribution
        • C++ coding style
        • Python coding style
        • Git pre-commit hook
        • Running unit tests
  • Release Notes
    • Release 0.5.0
      • Major Features and Improvements
      • Bug Fixes
      • Backwards-Incompatible Changes
      • Thanks to our Contributors
    • Release 0.4.0
      • Major Features and Improvements
      • Bug Fixes
      • Backwards-Incompatible Changes
      • Thanks to our Contributors
    • Release 0.3.1
      • Major Features and Improvements
      • Bug Fixes
      • Backwards-Incompatible Changes
      • Thanks to our Contributors
    • Release 0.3.0
      • Major Features and Improvements
        • Persistent homology of directed flag complexes via pyflagser
        • Edge collapsing and performance improvements for persistent homology
        • New transformers and functionality in gtda.homology
        • Persistence diagrams
        • New curves subpackage
        • New metaestimators subpackage
        • Images
        • Time series
        • Graphs
        • Mapper
        • Plotting
        • New tutorials and examples
        • Utils
        • Installation improvements
      • Bug Fixes
      • Backwards-Incompatible Changes
      • Thanks to our Contributors
    • Release 0.2.2
      • Major Features and Improvements
      • Bug Fixes
      • Backwards-Incompatible Changes
      • Thanks to our Contributors
    • Release 0.2.1
      • Major Features and Improvements
      • Bug Fixes
      • Backwards-Incompatible Changes
      • Thanks to our Contributors
    • Release 0.2.0
      • Major Features and Improvements
        • Plotting functions and plotting API
        • Changes and additions to gtda.homology
        • New images subpackage
        • New point_clouds subpackage
        • List of point cloud input
        • Changes and additions to gtda.diagrams
        • Changes and additions to gtda.utils
        • External modules and HPC improvements
      • Bug Fixes
      • Backwards-Incompatible Changes
      • Thanks to our Contributors
    • Release 0.1.4
      • Library name change
      • Change of license
      • Major Features and Improvements
      • Bug Fixes
      • Backwards-Incompatible Changes
      • Thanks to our Contributors
    • Release 0.1.3
      • Major Features and Improvements
      • Bug Fixes
      • Backwards-Incompatible Changes
      • Thanks to our Contributors
      • Major Features and Improvements
      • Bug Fixes
      • Backwards-Incompatible Changes
      • Thanks to our Contributors
    • Release 0.1.1
      • Major Features and Improvements
      • Bug Fixes
      • Backwards-Incompatible Changes
      • Thanks to our Contributors
    • Release 0.1.0
      • Major Features and Improvements
      • Bug Fixes
      • Backwards-Incompatible Changes
      • Thanks to our Contributors
    • Release 0.1a.0
  • FAQ
    • I am a researcher. Can I use giotto-tda in my project?
    • How do I cite giotto-tda?
    • I cannot install giotto-tda
    • There are many TDA libraries available. How is giotto-tda different?
giotto-tda
  • »
  • Giotto-TDA documentation
  • View page source

Giotto-TDA documentation¶

Contents¶

  • Overview
    • Guiding principles
    • 30s guide to giotto-tda
    • Resources
    • What’s new
  • Installation
    • Dependencies
    • User installation
    • Developer installation
  • API reference
    • gtda.mapper: Mapper
    • gtda.homology: Persistent homology
    • gtda.diagrams: Persistence diagrams
    • gtda.curves: Curves
    • gtda.point_clouds: Point clouds
    • gtda.time_series: Time series
    • gtda.graphs: Graphs
    • gtda.images: Images
    • gtda.plotting: Plotting functions
    • gtda.base: Base
    • gtda.pipeline: Pipeline
    • gtda.metaestimators: Meta-estimators
    • gtda.utils: Utilities
  • Tutorials and examples
    • Tutorials
    • Examples
  • Theory Glossary
    • Symbols
    • Analysis
    • Homology
    • Persistence
    • Time series
    • Bibliography
  • Contributing
    • Guidelines
  • Release Notes
    • Release 0.5.0
    • Release 0.4.0
    • Release 0.3.1
    • Release 0.3.0
    • Release 0.2.2
    • Release 0.2.1
    • Release 0.2.0
    • Release 0.1.4
    • Release 0.1.3
    • Release 0.1.1
    • Release 0.1.0
    • Release 0.1a.0
  • FAQ
    • I am a researcher. Can I use giotto-tda in my project?
    • How do I cite giotto-tda?
    • I cannot install giotto-tda
    • There are many TDA libraries available. How is giotto-tda different?
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