Bianka Nn Model

Bianka Nn Model

Bianka Nn Model - https://blltly.com/2tdgNl

Next we recall a few technical details of the two state-of-the-art methods: The HyperMap algorithm40 is based on the minimisation of the principal curvature (PC) of the underlying spatial embedding, in our case a geodesic, performing a gradient descent approach. The Mercator algorithm41 restricts the embedding independence and minimises the PC of the tangent space of the embedding from an arbitrary value. In our case the original embedding is already geodesic, but for crossing optimisations the algorithm minimises PC as well.

In the remainder we start with the definition of the loss function and the embedding approach, followed by the description of the HyperMap and the Mercator algorithms. Finally, we use this approach to optimise the angular coordinates of the ncMCE embedding and compare these new results to the original embedding and to the results of HyperMap and Mercator.

The approach of minimising the logarithmic loss is based on the embedding as a function of the angular coordinates, θ_i, where a network G has to be mapped to a two-dimensional grid, whose size is equal to the dimension of the embedding. The advantage of this parametrisation is that the loss function is additive and does not depend on the network size n or the number N of nodes. In the following, we briefly describe the approach of optimising the angular coordinates.

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