Or use scatterplots with points that have opacity < 100%.
C'mon there is still a bunch of cases where a scatterplot is much much clearer than that kind of 2d histogram, for example when there is a non linear relation with very high correlation.
opacity=35%: http://i.imgur.com/VB1E0.png
opacity=20%, and 2x bigger bins for the hexbin: http://i.imgur.com/yDR3j.png
Which image do you think better displays the image?
Just to make it interesting, I set it up so that the x values are not uniformly distributed. That's very easy to see in the hexbin, but still hard in the scatterplot.
The hexbin will always have a higher visual resolution than the scatterplot because the hexbin uses multiple colors to differentiate different densities. The scatterplot uses only one color.
This is an example of bad plotting practice, not a bad plotting method. That said, eyeballing a plot is a weak way to analyze data this dense. That's what statistics are for.
I disagree that the hexbin has lower resolution. The color dimension allows the human eye to easily differentiate regions having similar densities (e.g., 70 vs 50). The difference between deep red and orange is a lot bigger than the difference between dark blue and slightly less dark blue.
The hexbin has lower spatial resolution, it's true, but I'd argue that the spatial resolution you get in a scatterplot is illusory. It doesn't reflect the underlying probability distribution, only the particular sample.
That may be true, but is it better? Does the scatterplot underemphasize differen densities, or does the density plot overemphasize them? I think the scatterplot is more intuitive. There are 21 equal steps between 0 and 100% black. Two points are twice as dark as one, four points are twice as dark as two. Darker means more, lighter means less.
Compare that to shifting from blue to red. Does the shift from orange to red indicate the same density difference as the shift from blue to orange? To decide you need to consult the color scale. The scatterplot is intuitive, and requires no scale.
> The hexbin has lower spatial resolution, it's true, but I'd argue that the spatial resolution you get in a scatterplot is illusory. It doesn't reflect the underlying probability distribution, only the particular sample.
The spatial resolution of a scatterplot represents empirical reality. Each point corresponds to a single observation, with no probability distribution implied or imposed. The density plot, in contrast, imposes a probability distribution, which may or may not reflect the true distribution of the population. The larger the bins, the more likely the displayed pattern is 'illusory'.
tl;dr; I'm a Bayesian, you are a Frequentist (at least with regards to plotting).
Histograms tend to work best when the data is well understood, while scatterplots are better for samples from an unknown distribution (incl. lattices, multimodals or even double exponentials).
Try also small samples. When the piecewise uniform prior (on both the data and the intensity) is approximately accurate, histograms are far better, as they guide the eye away from nonexistent patterns. But the bandwidth needs to be judiciously set, and often the data transformed.
Clustering is hard to automate.
http://gvi.seas.harvard.edu/paper/evaluation-artery-visualiz...
http://www.jwave.vt.edu/~rkriz/Projects/create_color_table/c...
Colormap design is arguably as hard as visualization design. My favorite go-to place for them is http://colorbrewer2.org, but if you need to know only one thing about them, it's that varying hue continuously does not work nearly as well as you might think it does.
In addition, the fundamental reason scatterplots are bad, even with opacity, is essentially that opacity gives rise to an exponential relationship between overplotting and transparency.
There exists an alternative solution, which is to use additive blending and an adaptive linear colorscale, from zero to maximum-overdraw. Unfortunately, at present there exists no data visualization toolkits which support this.
But after reading that paper, I do agree that rainbow has some significant issues. One thing that might be worth trying: make a rainbow color map, but map values to colors in such a way that |x-y|=C x cielab_dist(color(x), color(y)).
Based on the names, it seems [1, 2] (along with all the other capitalized matplotlib colormaps) to be a ColorBrewer [3] colormap, which are all designed with these perceptual considerations in mind [4].
[1] https://github.com/gka/chroma.js/wiki/Predefined-Colors
[2] http://matplotlib.sourceforge.net/examples/pylab_examples/sh...
[4] http://vis4.net/blog/posts/avoid-equidistant-hsv-colors/
can you elaborate on this, I don't see why it would not be linear.
>There exists an alternative solution, which is to use additive blending and an adaptive linear colorscale, from zero to maximum-overdraw. Unfortunately, at present there exists no data visualization toolkits which support this.
I think this _might_ be done in Mathematica, since Graphics objects can be manipulated symbolically, but I might be wrong.
If you create a plot with opacity alpha, and which puts N points on top of each other, the remaining 'transparency', that is, the resulting opacity is
1 - (1 - alpha)^N
This is an exponential, which has the unfortunate feature that it's flat for most of the regime, and then spikes in a relatively short scale. The spike is where we get color differentiation (different opacities get different colors). That's bad: color differentiation should be uniform across the scale.
I'm pretty certain Mathematica doesn't do this right either, because it's a pixel-based technique that requires frame buffer manipulation. Instead of rendering with the usual blending operation, you do everything with additive blending, compute the maximum overdraw, and then color-scale linearly.