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I don't understand how Voronoi diagrams are an improvement over a stacked bar chart.

ajross 8y ago
Heh. The obvious answer is "because Voronoi tesselations can convey a 2D location in addition to the data set size". But this doesn't use that. So... yeah, they're not.
- 3pt14159 8y ago
  I thought it did though. The centroid of the space relates the relative relatedness of the subsegment. I.e., animals are closer to plants than viruses.
Gatsky 8y ago
Actually, just a table would be sufficient.
- larkeith 8y ago
  They provided a table: http://www.pnas.org/highwire/markup/814728/expansion http://www.pnas.org/highwire/markup/814728/expansion
Isamu 8y ago
I agree ... they explain "This type of visualization is similar to pie charts but has a much higher dynamic range". So it's true that it is better than pie charts, which are horrible and inexplicably popular. All they emphasize is that the total adds up to 100%. But it is still hard to compare relative areas even with the Voronoi. Comparing bar height is easier, but not sexy.
- rcoveson 8y ago
  I disagree. Comparing bar heights with large dynamic range requires vanishingly small bars or a graph that doesn't fit on one screen, both of which inhibit intuition about relative size. I don't know that that would be the case with this particular data, but I can certainly imagine a dataset whose data would fit easily when expressed as two dimensional areas but would become too large for a screen or too small for a pixel when rendered as one dimensional objects.
  - Isamu 8y ago
    >Comparing bar heights with large dynamic range requires vanishingly small bars True. It is nice that the smallest parts don't have to all appear as similarly tiny slivers. Comparing areas, though, is not a strength of human perception. It would be interesting to test a population of users, given a Voronoi diagram, to estimate the apparent percentage of each area. And it is instructive that in the paper they still resort to a second, zoomed-in view that breaks down the smallest subsets. You'd want to do the same no matter the representation.
venning 8y ago
As a counterpoint, I found it to be very helpful in understanding the information presented. The animals breakdown (Chart B) contains 10 values, ranging from 1 Gt to 0.002 Gt. That's a difference of 500x. That's a bit hard to perceive in a one-dimensional chart. The two-dimensionality of a Voronoi makes it easier to perceive, particularly in a small image (as is presented on a phone's screen), at least to me. I imagine this is mostly due to a 2D chart consuming far more physical pixels to convey the same information. A stacked bar chart of the same information: [1]. Admittedly, I didn't take time sprucing up that chart, but I find it extremely hard to intuit from and can't even see the value for "wild birds". [1] https://www.meta-chart.com/share/untitled-23893 https://www.meta-chart.com/share/untitled-23893
rcoveson 8y ago
When differences are vast, a linear bar chart becomes unreadable, and logarithmic bar charts make intuition about sizes difficult. Two dimensional spatial comparisons are intuitive and compact.
rcoveson 8y ago
I've rendered the data as a stacked bar chart; I think the reason a bar chart is ineffective here is clear. It would have to be logarithmic to deal with the wide range of values, and logarithmic charts make it extremely difficult to quickly compare values. Stacked bar: https://i.imgur.com/TfjDJyA.png https://i.imgur.com/TfjDJyA.png
- psychometry 8y ago
  I was thinking it should be a stacked bar chart for the top-level categorization (e.g. plants, animals, fungi, etc.) with a separate stacked bar chart for proportions within each group of interest (e.g. humans, insects, etc.).
  - rcoveson 8y ago
    Not sure I understand. What would be stacked in the first chart you describe? If it's the sub-categories that are stacked, I believe that's what I've rendered here. If it's the top-level categories that are stacked, it's not really a bar chart at all; there'd be only one bar. Either way, you'd still be comparing animals to viruses to plants with one-variable-dimension objects, and you'd have the same problem. The topmost categories simply vary too much in size.
simonh 8y ago
I think it’s at least partly about space efficiency. A bar chart with a few tall bars and many much shorter ones ends up wasting a large amount of space, while a Voronoi makes effective use of the whole graph area to represent data. This allows the area representing small ‘bars’ to be larger given constant graph size, and therefore more clearly represents them.

Heh. The obvious answer is "because Voronoi tesselations can convey a 2D location in addition to the data set size". But this doesn't use that. So... yeah, they're not.

3pt14159 8y ago
I thought it did though. The centroid of the space relates the relative relatedness of the subsegment. I.e., animals are closer to plants than viruses.

Gatsky 8y ago

Actually, just a table would be sufficient.

larkeith 8y ago
They provided a table: http://www.pnas.org/highwire/markup/814728/expansion http://www.pnas.org/highwire/markup/814728/expansion

Isamu 8y ago

I agree ... they explain "This type of visualization is similar to pie charts but has a much higher dynamic range". So it's true that it is better than pie charts, which are horrible and inexplicably popular. All they emphasize is that the total adds up to 100%. But it is still hard to compare relative areas even with the Voronoi. Comparing bar height is easier, but not sexy.

rcoveson 8y ago
I disagree. Comparing bar heights with large dynamic range requires vanishingly small bars or a graph that doesn't fit on one screen, both of which inhibit intuition about relative size. I don't know that that would be the case with this particular data, but I can certainly imagine a dataset whose data would fit easily when expressed as two dimensional areas but would become too large for a screen or too small for a pixel when rendered as one dimensional objects.
- Isamu 8y ago
  >Comparing bar heights with large dynamic range requires vanishingly small bars True. It is nice that the smallest parts don't have to all appear as similarly tiny slivers. Comparing areas, though, is not a strength of human perception. It would be interesting to test a population of users, given a Voronoi diagram, to estimate the apparent percentage of each area. And it is instructive that in the paper they still resort to a second, zoomed-in view that breaks down the smallest subsets. You'd want to do the same no matter the representation.

venning 8y ago

As a counterpoint, I found it to be very helpful in understanding the information presented. The animals breakdown (Chart B) contains 10 values, ranging from 1 Gt to 0.002 Gt. That's a difference of 500x. That's a bit hard to perceive in a one-dimensional chart. The two-dimensionality of a Voronoi makes it easier to perceive, particularly in a small image (as is presented on a phone's screen), at least to me. I imagine this is mostly due to a 2D chart consuming far more physical pixels to convey the same information. A stacked bar chart of the same information: [1]. Admittedly, I didn't take time sprucing up that chart, but I find it extremely hard to intuit from and can't even see the value for "wild birds". [1] https://www.meta-chart.com/share/untitled-23893 https://www.meta-chart.com/share/untitled-23893

rcoveson 8y ago

When differences are vast, a linear bar chart becomes unreadable, and logarithmic bar charts make intuition about sizes difficult. Two dimensional spatial comparisons are intuitive and compact.

rcoveson 8y ago

I've rendered the data as a stacked bar chart; I think the reason a bar chart is ineffective here is clear. It would have to be logarithmic to deal with the wide range of values, and logarithmic charts make it extremely difficult to quickly compare values. Stacked bar: https://i.imgur.com/TfjDJyA.png https://i.imgur.com/TfjDJyA.png

psychometry 8y ago
I was thinking it should be a stacked bar chart for the top-level categorization (e.g. plants, animals, fungi, etc.) with a separate stacked bar chart for proportions within each group of interest (e.g. humans, insects, etc.).
- rcoveson 8y ago
  Not sure I understand. What would be stacked in the first chart you describe? If it's the sub-categories that are stacked, I believe that's what I've rendered here. If it's the top-level categories that are stacked, it's not really a bar chart at all; there'd be only one bar. Either way, you'd still be comparing animals to viruses to plants with one-variable-dimension objects, and you'd have the same problem. The topmost categories simply vary too much in size.

simonh 8y ago

I think it’s at least partly about space efficiency. A bar chart with a few tall bars and many much shorter ones ends up wasting a large amount of space, while a Voronoi makes effective use of the whole graph area to represent data. This allows the area representing small ‘bars’ to be larger given constant graph size, and therefore more clearly represents them.