module ml.voronoi#

Inheritance diagram of mlstatpy.ml.voronoi

Short summary#

module mlstatpy.ml.voronoi

About Voronoi Diagram

source on GitHub

Classes#

class

truncated documentation

VoronoiEstimationError

Raised when the algorithm failed.

Functions#

function

truncated documentation

voronoi_estimation_from_lr

Determines a Voronoi diagram close to a convex partition defined by a logistic regression in n classes. M \in \mathbb{M}_{nd}

Documentation#

About Voronoi Diagram

source on GitHub

exception mlstatpy.ml.voronoi.VoronoiEstimationError#

Bases : Exception

Raised when the algorithm failed.

source on GitHub

mlstatpy.ml.voronoi.voronoi_estimation_from_lr(L, B, C=None, D=None, cl=0, qr=True, max_iter=None, verbose=False)#

Determines a Voronoi diagram close to a convex partition defined by a logistic regression in n classes. M \in \mathbb{M}_{nd} a row matrix (L_1, ..., L_n). Every border between two classes i and j is defined by: \scal{L_i}{X} + B = \scal{L_j}{X} + B.

The function looks for a set of points from which the Voronoi diagram can be inferred. It is done through a linear regression with norm L1. See Régression logistique, diagramme de Voronoï, k-Means.

Paramètres
  • L – matrix

  • B – vector

  • C – additional conditions (see below)

  • D – addition condictions (see below)

  • cl – class on which the additional conditions applies

  • qr – use quantile regression

  • max_iter – number of condition to remove until convergence

  • verbose – display information while training

Renvoie

matrix P \in \mathbb{M}_{nd}

The function solves the linear system:

\begin{array}{rcl}
& \Longrightarrow & \left\{\begin{array}{l}\scal{\frac{L_i-L_j}{\norm{L_i-L_j}}}{P_i + P_j} +
2 \frac{B_i - B_j}{\norm{L_i-L_j}} = 0 \\
\scal{P_i-  P_j}{u_{ij}} - \scal{P_i - P_j}{\frac{L_i-L_j}{\norm{L_i-L_j}}} \scal{\frac{L_i-L_j}{\norm{L_i-L_j}}}{u_{ij}}=0
\end{array} \right.
\end{array}

If the number of dimension is big and the number of classes small, the system has multiple solution. Addition condition must be added such as CP_i=D where i=cl, P_i is the Voronoï point attached to class cl. Quantile regression is not implemented in scikit-learn. We use QuantileLinearRegression.

After the first iteration, the function determines the furthest pair of points and removes it from the list of equations. If max_iter is None, the system goes until the number of equations is equal to the number of points * 2, otherwise it stops after max_iter removals. This is not the optimal pair to remove as they could still be neighbors but it should be a good heuristic.

source on GitHub