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I have a data frame that has 3 values for each point in the form: (x, y, boolean). I'd like to find an area bounded by values of (x, y) where roughly half the points in the area are TRUE and half are FALSE.

I can scatterplot then data and color according to the 3rd value of each point and I get a general idea but I was wondering if there would be a better way. I understand that if you take a small enough area where there are only 2 points and one if TRUE and the other is FALSE then you have 50/50 so I was thinking there has to be a better way of deciding what size area to look for.

Visually I see this has drawing a square on the scatter plot and moving it around the x and y axis each time checking the number of TRUE and FALSE points in the area, but is there a way to determine what a good size for the area is based on the values?

Thanks

EDIT: G5W's answer is a step in the right direction but based on their scatterplot, I'm looking to create a square / rectangle idea in which ~ half the points are green and half are red. I understand that there is potentially an infinite amount of those areas but thinking there might be a good way to determine an optimal size for the area (maybe it should contain at least a certain percentage of the points or something)

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mast
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    When asking for help you should provide a [reproducible example](http://stackoverflow.com/questions/5963269/how-to-make-a-great-r-reproducible-example) to make it easier to help you. Based on your description there are likely infinitely many regions you could make so how are you defining "good size"? What makes one region "better" than another? Are you only considering square or rectangular regions? – MrFlick Mar 27 '17 at 15:27
  • So are you looking for regions where the density of TRUE is approximately equal to the density of FALSE? – G5W Mar 27 '17 at 17:48
  • @G5W Yes, that's a great way to put it. There are about twice as many FALSE than TRUE, also. – mast Mar 27 '17 at 17:51

1 Answers1

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Note update below

You do not provide any sample data, so I have created some bogus data like this:

TestData = data.frame(x = c(rnorm(100, -1, 1), rnorm(100, 1,1)),
y = c(rnorm(100, -1, 1), rnorm(100, 1,1)),
z = rep(c(TRUE,FALSE), each=100))

I think that what you want is how much area is taken up by each of the TRUE and FALSE points. A way to interpret that task is to find the convex hull for each group and take its area. That is, find the minimum convex polygon that contains a group. The function chull will compute the convex hull of a set of points. 

plot(TestData[,1:2], pch=20, col=as.numeric(TestData$z)+2)
CH1 = chull(TestData[TestData$z,1:2])
CH2 = chull(TestData[!TestData$z,1:2])
polygon(TestData[which(TestData$z)[CH1],1:2], lty=2, col="#00FF0011")
polygon(TestData[which(!TestData$z)[CH2],1:2], lty=2, col="#FF000011")

Convex hulls

Once you have the polygons, the polyarea function from the pracma package will compute the area. Note that it computes a "signed" area so you either need to be careful about which direction you traverse the polygon or take the absolute value of the area. 

library(pracma)
abs(polyarea(TestData[which(TestData$z)[CH1],1],
    TestData[which(TestData$z)[CH1],2]))
[1] 16.48692
abs(polyarea(TestData[which(!TestData$z)[CH2],1],
    TestData[which(!TestData$z)[CH2],2]))
[1] 15.17897

Update

This is a completely different answer based on the updated question. I am leaving the old answer because the question now refers to it.

The question now gives a little more information about the data ("There are about twice as many FALSE than TRUE") so I have made an updated bogus data set to reflect that. 

set.seed(2017)
TestData = data.frame(x = c(rnorm(100, -1, 1), rnorm(200, 1, 1)),
y = c(rnorm(100, 1, 1), rnorm(200, -1,1)),
z = rep(c(TRUE,FALSE), c(100,200)))

The problem is now to find regions where the density of TRUE and FALSE are approximately equal. The question asked for a rectangular region, but at least for this data, that will be difficult. We can get a good visualization to see why.

We can use the function kde2d from the MASS package to get the 2-dimensional density of the TRUE points and the FALSE points. If we take the difference of these two densities, we need only find the regions where the difference is near zero. Once we have this difference in density, we can visualize it with a contour plot. 

library(MASS)
Grid1 = kde2d(TestData$x[TestData$z], TestData$y[TestData$z],
    lims = c(c(-3,3), c(-3,3)))
Grid2 = kde2d(TestData$x[!TestData$z], TestData$y[!TestData$z],
    lims = c(c(-3,3), c(-3,3)))
GridDiff = Grid1
GridDiff$z = Grid1$z - Grid2$z
filled.contour(GridDiff, color = terrain.colors)

Contour plot

In the plot it is easy to see the place that there are far more TRUE than false near (-1,1) and where there are more FALSE than TRUE near (1,-1). We can also see that the places where the difference in density is near zero lie in a narrow band in the general area of the line y=x. You might be able to get a box where a region with more TRUEs is balanced by a region with more FALSEs, but the regions where the density is the same is small.

Of course, this is for my bogus data set which probably bears little relation to your real data. You could perform the same sort of analysis on your data and maybe you will be luckier with a bigger region of near equal densities.

G5W
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  • This is helpful but not quite what I was going for. I've edited your image (https://i.imgur.com/1C0RaUO.png) and added an area where (not exact in this image but estimate) half the points are green and half are red. I understand there's potentially an infinite amount of those areas (if you vary the size and move it around) but looking for suggestions on determining the area – mast Mar 27 '17 at 17:39
  • In _all_ of the data, are the number of TRUE and FALSE approximately equal? – G5W Mar 27 '17 at 17:44