Brilliant piece of innovation Luigi!

This may seem a really strange question but here goes anyway ...

Is it possible that this concept could be applied to extract some semantic meaning from a corpus of text on a particular topic? For example if there were a series of papers on a concept written in different English language styles over time which described alternate interpretations or meaning of a particular topic I wonder if the textual data sets also could be correlated in the manner you describe and somehow that correlation leads to semantic insights or at least the basis for further Computational experimentation to do so.

What triggered me to ask you this is your statement below:

“Results: We were able to develop a function which calculates mutual information between two sets of data, and relies on a distance function to do so. As any data can be considered to be embedded in a metric space, this implementation works in principle for any kind of data, whether it is images, videos or just time series.”

This is all very “AI’ish” and non-deterministic but I wonder if it makes any sense to you?

I would certainly like to play with this idea of yours on simple data sets like word definitions of complex words with lots of historical alternate descriptions just to see what emerges from relatively simple but possibly large enough number of alternate definitions of the same word.

Cheers ... Syd Geraghty

Hello Jim,

You're welcome, and sorry for the late answer. Yes, the code

KraskovI1[list, list+T, 4], with T ranged 0,20

is equivalent to ResourceFunction["MutualInformation"][list,20]. Also note that there's the alternative ResourceFunction["MutualInformation"][list,t,s]. Moreover, note that the 4 in your example is now an option, "KNeighbour", which is used when working with lists of samples.

When working on the project I needed some more flexibility and opted to work directly with the function KraskovI1. Later I wrapped it up in the function MutualInformation and submitted it to the repository, so that's the reason on the discrepancies you see.

As a side note, I'm slowly updating the function to make it better, I updated it to work on any multivariate distribution and added some more error checking. You can always find an updated version here, but hopefully it will be soon on the Wolfram Function Repository.

About your last question, I'm not sure what you mean. As you noticed, the first element is the zero-shift MI, which is not 0, but some of my plots are "clipped" to show the most interesing part, since a peak at position 1 isn't that interesting and was usually too high. Also, ListLinePlot will always plot any list starting from 1, if you need the plot to start from 0 you have to specify an x value along with the y value, e.g.

ListLinePlot[Thread[List[Range[0, 9], Range[10]]], PlotRange -> All]

If you need any further help, please feel free to contact me on linkedin (you can find it on my profile).

And good luck with your work!

Hi, thanks for the interest! My function is currently under review for submission in the Wolfram Function Repository, but you can find a preliminary (not reviewed) version here. It doesn't explicitely support timeseries yet, but I plan on adding that soon.

(Ignore the comment of the reviewer in the examples section, I just resubmitted it and couldn't delete that)