signal to noise ratio

Created	Last Edited	Edits
2025-02-10	2025-05-13	3

Data

subject:: Data Science Methods for Large Scale Graphs
parent:: Graph Signals and Graph Signal Processing
theme:: math notes

signal-to-noise ration (snr)

The signal to noise ratio is the ratio of the power of signal (the thing we want to measure) to the power of the extraneous noise. This is given as:

S N R = \frac{P_{signal}}{P_{noise}}

Where $P_{_}$ is the average power, or second moment. When the signal and noise are Random Variables, then we have

S N R = \frac{E [X_{signal}^{2}]}{E [X_{noise}^{2}]}

Example

In our SBM example with $c = 2$ , with $B = {\begin{cases} p if c_{1} = c_{2} \\ q otherwise \end{cases}$ , then

S N R = \frac{(p - q)^{2}}{2 (p + q)}

numerator is the signal: degree discrepancy in nonequal subgraphs
denominator is noise: the average degree for all nodes in the graph

Mentions

File
almost exact recovery is impossible when the signal to noise ratio is less than the threshold
information theoretic threshold
2025-02-10 graphs lecture 6
2025-02-12 graphs lecture 7