Normalization versus Percent Change

[Tone L]

TL;DR

Why doesn't normalized data represent percent change? How can I quantify normalized data?

I have been working with some time series data of spectral signals, each wavelength has a different signal, so I normalize the data so I can plot it effectively. However, I am struggling to quantify the new normalized data. I will give an example below.

Normalizing data often refers to re-scaling by the minimum and range of the variables, to make all the elements lie between 0 and 1 thus bringing all the values of numeric columns in the data set to a common scale.

The equation is defined as, $$x={x_i−x_{min}}{x_{max}−x_{min}}$$, now this will represent a new list of values from 0 to 1.

Now to illustrate my confusion I will present an example, of just one wavelength. At t0 the corresponding normalized value is 0.987 and at $t_{10}$ the value is 0.927.
At t0 the spectral value is 50482 and $t_{10}$ it is 50415. Using the spectral values, the percent difference between t0 and $t_{10}$ is: 0.13% and for the normalized data it is 6.07%.
When I plot the results they visually are identical... Normalizing doesn't re-scale the values, it completely changes them, but visually they look the same. Thus, my confusion. Why is the percent change not equal to one another, thanks a lot guys!

 

[jedishrfu]

When you normalize a dataset and plot it, the shape should look the same. Normalization either reduces a number or magnifies a number.

As an example, you may have two recordings of the same audio source. The first is from a mic close to the source and the other is from a mic far from the source. The first mic dataset would have relatively high db values while the faraway mic would have lower db values. Basically for sound when you double the distance the db value drops by 6db. Looking at the two plots it might not be obvious that they are recordings of the same audio source.

By normalizing both datasets you are then able to compare both datasets and discover that they are recordings from the same audio source as the peaks and valleys should closely line up. However, they may not exactly line up due to various acoustical properties of the space where the recordings occurred but you could reasonably determine that they are recordings of the same audio source.