Extras

Sometimes I can find techniques that see usefull for my work, I will save them here

Dynamical Systems Analysis

Beyond PCA, AtractorsQGP.jl provides tools to analyze the system from the perspective of chaos theory and dynamical systems.

While I am doing my research sometimes I find out about interesting algorithms:

Measures the rate of separation of infinitesimally close trajectories. A negative LLE strongly indicates the presence of an attracting manifold.

u0 = [2.0, 5.0] # [T0 in fm⁻¹, A0]
lle = run_LLE(model_brsss, u0, (0.22, 5.0); perturbation=1e-6)
println("Local Lyapunov Exponent: ", lle)

Estimates the intrinsic geometric dimension of the data cloud at a given time using the participation ratio of the covariance matrix eigenvalues.

_, X_tau = get_tau_slice(dataset, 0.5)
dim = estimate_dimension(X_tau)

How distances Increse in higher dimensions? How to indentify which features are more significant/important/relevant

Shows how PCA and PCA-kernel got a little problems with holding the structure of data

How does it work? [!IMPORTANT] $\epsilon(W) = \sum_i = |\vec{X}_i - \sum_j W_{ij}\vec{Y}_j|^2$

Computing a set of weights that can be used for reconstructing a point