teaspoon: Topological Signal Processing in Python

The emerging field of topological signal processing brings methods from Topological Data Analysis (TDA) to create new tools for signal processing by incorporating aspects of shape. This python package, teaspoon for tsp or topological signal processing, brings together available software for computing persistent homology, the main workhorse of TDA, with modules that expand the functionality of teaspoon as a state-of-the-art topological signal processing tool. These modules include methods for incorporating tools from machine learning, complex networks, information, and parameter selection along with a dynamical systems library to streamline the creation and benchmarking of new methods. All code is open source with up to date documentation, making the code easy to use, in particular for signal processing experts with limited experience in topological methods.

Table of Contents

• 1. Getting Started
  • 1.1. Requirements
  • 1.2. Installation
  • 1.3. Spork!
• 2. Modules
  • 2.1. Parameter Selection Module
    • 2.1.1. Mutual Information (MI) for time delay (tau).
    • MI_DV()
    • MI_basic()
    • MI_for_delay()
    • MI_kraskov()
    • 2.1.2. Auto-correlation for time delay (tau).
    • autoCorrelation_tau()
    • 2.1.3. Statistical analysis of the Fourier spectrum for time delay (tau).
    • AbsFFT()
    • LMSforDelay()
    • MaximumFrequency()
    • 2.1.4. Permutation Auto Mutual Information (PAMI) for time delay (tau).
    • PAMI_for_delay()
    • mutualPerm()
    • 2.1.5. MsPE for time delay (tau) and dimension (n).
    • MsPE_n()
    • MsPE_tau()
    • 2.1.6. False Nearest Neighbors (FNN) for dimension (n).
    • FNN_n()
  • 2.2. Machine Learning (ML) Module
    • 2.2.1. Datasets
      • mnist()
      • mpeg7()
      • shrec14()
    • 2.2.2. Featurization
      • 2.2.2.1. Persistence Landscapes
      • 2.2.2.2. Persistence Images
      • 2.2.2.3. Carlsson Coordinates
      • 2.2.2.4. Template Functions
      • 2.2.2.5. Path Signatures
      • 2.2.2.6. Kernel Method
    • 2.2.3. Classification
      • getPercentScore()
      • 2.2.3.1. Persistence Landscapes
      • 2.2.3.2. Persistence Images
      • 2.2.3.3. Carlsson Coordinates
      • 2.2.3.4. Template Functions
      • 2.2.3.5. Path Signatures
      • 2.2.3.6. Kernel Method
    • 2.2.4. References
  • 2.3. Topological Data Analaysis (TDA) Module
    • 2.3.1. Persistent Homology of Networks (PHN) Module
      • DistanceMatrix()
      • PH_network()
      • point_summaries()
      • 2.3.1.1. Example
    • 2.3.2. Distances
      • bottleneckDist()
      • wassersteinDist()
      • 2.3.2.1. Computing Wasserstein and Bottleneck Distances
    • 2.3.3. Drawing
      • drawDgm()
      • drawPtCloud()
      • 2.3.3.1. Examples
    • 2.3.4. Persistence
      • BettiCurve()
      • CROCKER()
      • maxBirth()
      • maxBirthSeries()
      • maxPers()
      • maxPersistenceSeries()
      • minBirth()
      • minBirthSeries()
      • minPers()
      • minPersistenceSeries()
      • removeInfiniteClasses()
    • 2.3.5. Zero Dimensional Sublevel Set Persistence (SLSP) Module
      • Persistence0D()
      • cutoff()
    • 2.3.6. Magnitude
      • 2.3.6.1. Magnitude function
  • 2.4. Signal Processing (SP) Module
    • 2.4.1. Time Series Analysis (TSA) Tools
      • 2.4.1.1. Takens’ Embedding
      • 2.4.1.2. Permutation Sequence Generation
      • 2.4.1.3. k Nearest Neighbors
      • 2.4.1.4. Coarse grained state space binning
      • 2.4.1.5. Coarse grained state space state sequence
      • 2.4.1.6. Zero Detection Algorithm (ZeDA)
      • 2.4.1.7. First Zero Detection Algorithm
    • 2.4.2. Network Representation of Time Series
      • 2.4.2.1. k Nearest Neighbors Graph
      • 2.4.2.2. Ordinal Partition Graph
      • 2.4.2.3. Coarse Grained State Space (CGSS) Graph
      • 2.4.2.4. Network Tools
    • 2.4.3. Information Module
      • 2.4.3.1. Entropy
    • 2.4.4. Miscellaneous
      • 2.4.4.1. Adaptive Partitioning
    • 2.4.5. Texture Analysis
      • 2.4.5.1. Texture Analaysis Overview
  • 2.5. Make Data (MakeData) Module
    • 2.5.1. Point Cloud Data Generation (PointCloud) Module
      • Annulus()
      • Circle()
      • Clusters()
      • Cube()
      • Sphere()
      • Torus()
      • normalDiagram()
      • testSetClassification()
      • testSetManifolds()
      • testSetRegressionBall()
      • testSetRegressionLine()
      • 2.5.1.1. Examples
    • 2.5.2. Dynamic Systems Library (DynSysLib) Module
      • DynamicSystems()
      • 2.5.2.1. Available Dynamical Systems
      • 2.5.2.2. Examples
• 3. Contributing
  • 3.1. Contributing to Documentation
• 4. License
• 5. Citing

Collaborators

The code is a compilation of work done by Elizabeth Munch and Firas Khasawneh along with their students and collaborators. People who have contributed to teaspoon include:

• Audun Myers

• Melih Yesilli

• Sarah Tymochko

• Danielle Barnes

• Ismail Guzel

• Max Chumley

Contact Information

• Liz Munch: muncheli@msu.edu

• Firas Khasawneh: khasawn3@egr.msu.edu