by user50313
Last Updated June 30, 2020 03:19 AM

Does anybody have suggestions on how to de-normalize Google Trends data? The site says that their trends are made with the following metric:

The numbers on the graph reflect how many searches have been done for a particular term, relative to the total number of searches done on Google over time. They don't represent absolute search volume numbers, because the data is normalized and presented on a scale from 0-100. Each point on the graph is divided by the highest point and multiplied by 100. When we don't have enough data, 0 is shown

I've been trying to work backwards from there but realized I need the peak value for each search query, which I don't have. Any thoughts appreciated.

Here's an example Google Trends search: http://www.google.com/trends/explore#q=stack%20exchange&cmpt=q&tz=

Since the normalization consists in $$ \mathbf{z} = \frac{\mathbf{x}}{\max(\mathbf{x})}, $$ where $\mathbf{x}$ is the vector of search volumes, and $\max(\mathbf{x})$ is the maximal element of $\mathbf{x}$, if you want de-normalized data, you should multiply each element of the normalized vector times the maximal element of $\mathbf{x}$:

$$ \mathbf{x} = \mathbf{z} \times \max(\mathbf{x}). $$

Unfortunately, if you don't know the value of $\max(\mathbf{x})$ you can't de-normalize your data.

I have a paper related to denormalization of Google Trends' indices here: https://www.jmir.org/2020/1/e13347/

The short tutorial on denormalization is here: https://www.slideshare.net/ShahanAliMemon/google-trends-denormalized-175072435

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