Utilities

Linear Manifold Clustering Algorithm relies on multiple search and optimization methods:

kittler(X, bins, tol)

A minimum error thresholding method for multimodal histograms [1].

otsu(X, bins)

A gray-level thresholding method for multimodal histograms [2].

mdl(M, X; Pm = 32, Pd = 16, T = :Empirical, ɛ = 1e-4)

Performs calculation of the minimum description length for the linear manifold cluster.

Parameters:
  • M – Linear manifold cluster description as Manifold type instance.
  • X – Linear manifold cluster data as Matrix with points as its columns.
  • Pm – Precision encoding constant for the model, i.e. number of bits required for encoding on element of the model description. Default value is 32 which corresponds to Float32.
  • Pd – Precision encoding constant for the data.
  • T – Type of a dataset encoding model as symbol: :Gausian, :Uniform, :Empirical.
  • ɛ – Error tolerance for bin quantization used in an empirical model encoding

Returns number of bits required to encode linear manifold cluster with the MDL schema.

References

[1]
  1. Kittler & J. Illingworth: “Minimum Error Thresholding”, Pattern Recognition, Vol 19, nr 1. 1986, pp. 41-47, DOI:10.1016/0031-3203(86)90030-0
[2]
  1. Otsu: “A threshold selection method from gray-level histograms”, Automatica, 1975, 11, 285-296, DOI:10.1109/TSMC.1979.4310076