How to visualize a,b results of x,y variables

I have a bunch of experimental data points each of which has 2 variables (x,y) and 2 results (a,b). Each pair or x,y values produces a pair of a,b resultant values.
There is a single optimal pair of a,b values and I’d like to figure out a way to illustrate the data to show the relationship between each x,y pair and how close each a,b pair is to the ideal.

I’m thinking about a dual surface/contour plot with 2 different z-axes. Ideally I would center both z-axes at the ideal values. I don’t know if this is possible. Might be kinda messy.

Any other thoughts? I’m sure there must be other examples where this is a problem.

In the x,y plane, could you overlay contours of a with contours of b?
-Sterling

···

On Jul 8, 2015, at 8:19PM, Jonno <jonnojohnson@...287...> wrote:

I have a bunch of experimental data points each of which has 2 variables (x,y) and 2 results (a,b). Each pair or x,y values produces a pair of a,b resultant values.
There is a single optimal pair of a,b values and I'd like to figure out a way to illustrate the data to show the relationship between each x,y pair and how close each a,b pair is to the ideal.
I'm thinking about a dual surface/contour plot with 2 different z-axes. Ideally I would center both z-axes at the ideal values. I don't know if this is possible. Might be kinda messy.

Any other thoughts? I'm sure there must be other examples where this is a problem.
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I was thinking of doing that or having 2 surface plots but I think it would be visually quite confusing.
I was trying to think of an example since I’m sure someone has come up with a nice way to display this kind of data.

Imagine if the data was average temperature (a) and average rainfall (b) for a region in the world (lat/long = x,y). The goal is to display the data such that it’s obvious where the locations are that have closest to the ideal temp/rain combination.

How would you go about that?

···

On Thu, Jul 9, 2015 at 12:28 AM, Sterling Smith <smithsp@…3304…> wrote:

In the x,y plane, could you overlay contours of a with contours of b?

-Sterling

On Jul 8, 2015, at 8:19PM, Jonno <jonnojohnson@…287…> wrote:

I have a bunch of experimental data points each of which has 2 variables (x,y) and 2 results (a,b). Each pair or x,y values produces a pair of a,b resultant values.

There is a single optimal pair of a,b values and I’d like to figure out a way to illustrate the data to show the relationship between each x,y pair and how close each a,b pair is to the ideal.

I’m thinking about a dual surface/contour plot with 2 different z-axes. Ideally I would center both z-axes at the ideal values. I don’t know if this is possible. Might be kinda messy.

Any other thoughts? I’m sure there must be other examples where this is a problem.


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It might just have to be 2 separate contour/surface plots side by side, perhaps with a linked cursor between them.
The other thing I considered was combining the a,b data into a single value (combined % deviation from ideal?) but that reduces the data which I’d rather not do if possible.

···

On Thu, Jul 9, 2015 at 9:40 AM, Jonno <jonnojohnson@…287…> wrote:

I was thinking of doing that or having 2 surface plots but I think it would be visually quite confusing.
I was trying to think of an example since I’m sure someone has come up with a nice way to display this kind of data.

Imagine if the data was average temperature (a) and average rainfall (b) for a region in the world (lat/long = x,y). The goal is to display the data such that it’s obvious where the locations are that have closest to the ideal temp/rain combination.

How would you go about that?

On Thu, Jul 9, 2015 at 12:28 AM, Sterling Smith <smithsp@…3304…> wrote:

In the x,y plane, could you overlay contours of a with contours of b?

-Sterling

On Jul 8, 2015, at 8:19PM, Jonno <jonnojohnson@…287…> wrote:

I have a bunch of experimental data points each of which has 2 variables (x,y) and 2 results (a,b). Each pair or x,y values produces a pair of a,b resultant values.

There is a single optimal pair of a,b values and I’d like to figure out a way to illustrate the data to show the relationship between each x,y pair and how close each a,b pair is to the ideal.

I’m thinking about a dual surface/contour plot with 2 different z-axes. Ideally I would center both z-axes at the ideal values. I don’t know if this is possible. Might be kinda messy.

Any other thoughts? I’m sure there must be other examples where this is a problem.


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It's not an easy thing to visualize in general. You might want to look at approaches to visualizing complex functions (i.e., functions whose input and output are both complex variables). These essentially map pairs (a, b) to pairs (x, y) as in your situation, and mathematicians have come up with various ways to visualize them. Some are described at https://www.pacifict.com/ComplexFunctions.html and the wikipedia article at https://en.wikipedia.org/wiki/Complex_analysis has some links in the references to web pages for graphing such functions.

  If the data are measured at (or can be reasonably reduced to) discrete points (as temp/rainfall are likely to be), another possibility is a scatterplot using, say, the color and size of the markers as indicators of the two variables (e.g., red/blue for hot/cold temp, larger/smaller circles for higher/lower rainfall).

  In some cases, like your example with temperature and rainfall, you may instead be able to combine the two output dimensions into a single one that somehow captures the overall "distance" from the ideal point. That is, for a given point, if your goal is to show how close it is to the ideal *combination* of temp and rain, you may not need to display how close it is on each dimension separately, but just how close it is to the ideal overall. Exactly how to compute this would vary based on the data (e.g., standardizing the values and taking the euclidean distance from the ideal).

  Your temp/rainfall example caught my eye because a few years ago I did a blog post on a similar topic, considering temperature and humidity (http://iq.brenbarn.net/2011/11/18/good-days-mate/). There I decided to graph just a single variable, namely the number of days on which either temperature *or* humidity is outside a "comfortable" range. Obviously this approach may not make sense for every situation. But what I mean is that, in some cases, you can use domain-specific knowledge about what the dimensions mean to combine them into one dimension that approximates what it is you're trying to illustrate with the graph.

···

On 2015-07-09 07:40, Jonno wrote:

I was thinking of doing that or having 2 surface plots but I think it
would be visually quite confusing.
I was trying to think of an example since I'm sure someone has come up
with a nice way to display this kind of data.
Imagine if the data was average temperature (a) and average rainfall (b)
for a region in the world (lat/long = x,y). The goal is to display the
data such that it's obvious where the locations are that have closest to
the ideal temp/rain combination.
How would you go about that?

--
Brendan Barnwell
"Do not follow where the path may lead. Go, instead, where there is no path, and leave a trail."
    --author unknown

Maybe you could plot the ratio? That should give you rainfall per degree Celsius.

···

On Thu, Jul 9, 2015 at 12:28 AM, Sterling Smith <smithsp@…3304…> wrote:

In the x,y plane, could you overlay contours of a with contours of b?

-Sterling

On Jul 8, 2015, at 8:19PM, Jonno <jonnojohnson@…287…> wrote:

I have a bunch of experimental data points each of which has 2 variables (x,y) and 2 results (a,b). Each pair or x,y values produces a pair of a,b resultant values.

There is a single optimal pair of a,b values and I’d like to figure out a way to illustrate the data to show the relationship between each x,y pair and how close each a,b pair is to the ideal.

I’m thinking about a dual surface/contour plot with 2 different z-axes. Ideally I would center both z-axes at the ideal values. I don’t know if this is possible. Might be kinda messy.

Any other thoughts? I’m sure there must be other examples where this is a problem.


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Thanks for all the ideas.

···

On Thu, Jul 9, 2015 at 8:09 PM, Joy merwin monteiro <joy.merwin@…287…> wrote:

Maybe you could plot the ratio? That should give you rainfall per degree Celsius.

On 9 Jul 2015 20:11, “Jonno” <jonnojohnson@…985…> wrote:

I was thinking of doing that or having 2 surface plots but I think it would be visually quite confusing.
I was trying to think of an example since I’m sure someone has come up with a nice way to display this kind of data.

Imagine if the data was average temperature (a) and average rainfall (b) for a region in the world (lat/long = x,y). The goal is to display the data such that it’s obvious where the locations are that have closest to the ideal temp/rain combination.

How would you go about that?


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On Thu, Jul 9, 2015 at 12:28 AM, Sterling Smith <smithsp@…3304…> wrote:

In the x,y plane, could you overlay contours of a with contours of b?

-Sterling

On Jul 8, 2015, at 8:19PM, Jonno <jonnojohnson@…287…> wrote:

I have a bunch of experimental data points each of which has 2 variables (x,y) and 2 results (a,b). Each pair or x,y values produces a pair of a,b resultant values.

There is a single optimal pair of a,b values and I’d like to figure out a way to illustrate the data to show the relationship between each x,y pair and how close each a,b pair is to the ideal.

I’m thinking about a dual surface/contour plot with 2 different z-axes. Ideally I would center both z-axes at the ideal values. I don’t know if this is possible. Might be kinda messy.

Any other thoughts? I’m sure there must be other examples where this is a problem.


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