Find dependence between similarity metrics and plot them on a map

[pawelbielski]

As suggested by Peter in our meeting, we could plot the dependence between pairs of similarity metrics on a scatter plot and on a map.

• [x] Create a function that takes data_map, reference series (e.g. qbo), two similarity metrics. Plot the scatter plot of values for two metrics (one metric on x axis, another on y axis, point represents a geolocation)

• [x] Create a function (or extend) to plot plot the regions that show high values for both similarity metrics on the map. Similarly, plot regions in which one value is high, and other low, and vice versa; both values are low. Maybe some of these variants we could plot on the same map.

• [x] Show their functionality in a separate jupyter notebook

[pawelbielski]

@pierretoussing

• [x] The scatterplots are very interesting. How about plotting a whole matrix of them next to each other for better comparability?

• [x] The plots are not as informative as we all expected... Just yellow regions in the equatorial region. Why is the yellow region moved to the south in the Cosine-Manhattan plot? Also here I would suggest plotting all the combinations (but remembering that cosine-manhattan = manhattan-cosine), for the better interpretability.

• [x] When it comes to color ranges... Hmm.. We see only violet and yellow--and nothing in between. How about the approach to equalize the values to scale/bin them by top 10%, next 10%, ... , last 10% for the better comparability? For the similarity metrics that are inverted (like transfer entropy), you could use the adjusted one (e.g. 1 - transfer_entropy).