# Sprague-Geers Metric for Data Similarity

This section defines and provides examples of the Sprague-Geers Metric for Data Similarity.

## Definition

Consider two signals a(x

_{k}) and b(x_{k}), k=1…N. You are interested in computing a metric that shows the similarity of these signals. Use the following steps to compute the Sprague-Geers metric:- Calculate the metric M for magnitude difference and P for phase difference as follows:
- Calculate the combined metric C as follows:
$C=1-\sqrt{{M}^{2}+{P}^{2}}$

C=1 is a perfect match. Metric C is what we want to show.Note: $\sqrt{{M}^{2}+{P}^{2}}$ is known as the Sprague-Geers Combined Metric.

## Example 1: Signals with the same overall magnitude, but drastically different slopes

Ψ_{aa}=143.50, Ψ_{bb}=143.50, Ψ_{ab}=77.00, M+0.00,
P=0.319714, C=0.680286

## Example 2: Two very similar signals displaced in the y direction by 5%

Ψ_{aa}=0.50, Ψ_{bb}=0.51, Ψ_{ab}=0.50, M=0.009852,
P=0.044719, C=0.954208

## Example 3: A synthesized MIT example for Dynamic Stiffness

Ψ_{aa}=3.39E+5, Ψ_{bb}=3.77E+5, Ψ_{ab}=3.57E+5, M=0.051164,
P=0.026831, C=0.942227

## Example 4: A synthesized MIT example for Loss Angle

Ψ_{aa}=1.39628E+1, Ψ_{bb}=6.67958, Ψ_{ab}=9.59216,
M=0.445811, P=0.037025, C=0.552654