Tutorial - Higher-order characters

You can also download this tutorial as a Jupyter Notebook

• Higher-order character decomposition: char module
  • What are higher-order characters?
    • The general goal: find the dominant higher-order characters of a function
  • A simple example: identifying a single quadratic character
  • A first multi-character example
  • How the algorithm works
    • Why separation of eigenvalues is needed
      • A solution: random sampling and iteration
    • How the separation process works in higher orders
    • Refinements of the algorithm
      • Refining Step 1 (the initial regularization)
      • Refining Step 3: iterative refinement
      • The role of randomization
      • Convergence and termination
      • The random separator policy
    • The class hofa.char.RandomSeparator
      • Initial threshold calculation
      • Iteration threshold calculation
      • Separation gap calculation
      • Random number generator access
      • Maximum iterations
      • Iterative search flag
    • Standard implementation: StandardRandomSeparator
      • Constructor
      • Initial threshold calculation
      • Iteration threshold calculation
      • Separation gap calculation
      • Random number generator access
      • Maximum iterations
      • Iterative search flag
    • Result container: RandomizedSeparationResult
      • Fields
  • Example: three quadratic waves and cubic noise
    • Problem statement
    • Objective
    • Strategy
  • Example: locating quadratic behaviour in data analysis
    • Problem statement
    • Strategy
    • Results
    • Theoretical justification