Estimate of the Neural Network Dimension Using Algebraic Topology and Lie Theory

1 code implementation • 6 Apr 2020 • Luciano Melodia, Richard Lenz

In this paper we present an approach to determine the smallest possible number of neurons in a layer of a neural network in such a way that the topology of the input space can be learned sufficiently well.

Homological Time Series Analysis of Sensor Signals from Power Plants

1 code implementation • 3 Jun 2021 • Luciano Melodia, Richard Lenz

In this paper, we use topological data analysis techniques to construct a suitable neural network classifier for the task of learning sensor signals of entire power plants according to their reference designation system.

Time Series Time Series Analysis +1

Persistent Homology as Stopping-Criterion for Voronoi Interpolation

1 code implementation • 8 Nov 2019 • Luciano Melodia, Richard Lenz

In this study the Voronoi interpolation is used to interpolate a set of points drawn from a topological space with higher homology groups on its filtration.