Geodesic Distance on Gaussian Manifolds to Reduce the Statistical Errors in the Investigation of Complex Systems

Figure 4

Pictorial description of the procedure to find the sigma of the additive Gaussian noise in the data. The plots correspond to the case of data sampled from a log normal distribution and an additive normal noise of 20% of the log-normal mean. On the left a 3D view of the scan in the sigma used to calculate the GDGM and indicated . On the right end side, the zoomed projections on the plane are reported. As can be seen, the inflection point in the corresponds exactly to the 20% of additive Gaussian noise.

(a) 3D view of GD plane

(b) Zoom of 2D view:

(c) 2D view: