Papers › An Expectation-Maximization Algorithm for the Fractal Inverse Problem
An Expectation-Maximization Algorithm for the Fractal Inverse Problem
Peter Bloem, Steven de Rooij
We present an Expectation-Maximization algorithm for the fractal inverse problem: the problem of fitting a fractal model to data. In our setting the fractals are Iterated Function Systems (IFS), with similitudes as the family of transformations. The data is a point cloud in ℝᴴ with arbitrary dimension H. Each IFS defines a probability distribution on ℝᴴ, so that the fractal inverse problem can be cast as a problem of parameter estimation. We show that the algorithm reconstructs well-known fractals from data, with the model converging to high precision parameters. We also show the utility of the model as an approximation for datasources outside the IFS model class.
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