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Robust principal graphs

Andrei Zinovyev edited this page Nov 3, 2017 · 12 revisions

Introduction

Robust elastic principal graphs can resist certain amount of background noise added to the data distribution. In order to achive this, we suggested two approaches:

  1. Trimming the data approximation energy term by a certain robustness radius

See example of using robust version of ElPiGraph here

  1. Exploiting the properties of piece-wise quadratic potentials (PQSQ)

Information on the parameter values used in 'Robust principal graphs for data approximation' paper by Gorban A.N., Mirkers E., Zinovyev A. to construct 2D examples of complex data distributions and their graph-based approximations.

These parameters can be set in the Java applet for constructing non-linear approximations of 2D data, using various algorithm. See detailed description of the meaning of the method parameters at this page.

<a href="https://en.wikipedia.org/wiki/Neural_gas>Growing_neural_gas>Growing Neural Gas (GNG): ripening period is 300, edge lifetime is 88, step of winner learning is 0.05, step of neighbours learning is 0.0006, error decreasing after bisection %is 0.5,error forgetting ratio is 0.0005, maximal number of neurons is 100.

Growing SOM (GSOM): new node is added with the same curvature, maximal number of nodes is 500, half of neighbour B-spline width is 3.

Robust Growing SOM (RGSOM): new node is added with the same curvature, maximal number of nodes is 500, half of neighbour B-spline width is 3, robustness radius is 30.

EM (Elastic Map): stretching module is 0.01, bending module is 0.05, new node is added with the same curvature, maximal number of nodes is 500.

Robust EM (REM): stretching module is 0.01, bending module is 0.05, new node is added with the same curvature, maximal number of nodes is 500, robust radius is 30.

Elastic principal graph (PG): stretching module is 0.001, bending module is 0.01, scaling exponent is 0, growing grammars "Add node and edge" and "Add node by edge bisection" applied twice and shrinking grammars "Delete leaf node" and "Delete edge by nodes union" applied once in each cycle, as described in this paper, maximal number of nodes is 500.

Robust principal graph (RPG): stretching module is 0.001, bending module is 0.01, scaling exponent is 0, growing grammars "Add node and edge" and "Add node by edge bisection" applied twice and shrinking grammars "Delete leaf node" and "Delete edge by merging nodes" applied once in each cycle, maximal number of nodes is 500, the robustness radius is 20.