This is often referred to as a bubble chart, and most common graphing libraries support it. An alternative would be a scatter plot with three variables where the third variable, value in your case, is coded by color.
Nearest neighbor ordering algorithms (hierarchical clustering, dendrograms) are well suited for sorting the items in either or both axes. If either axis relates directly to a physical dimension then it might be best to maintain that order in the matrix. A lot of the fun is in working out how to measure distance between items based on their values as that drives the results of the nearest neighbor order.
The authors created Bertifier (project page [1], demo [2], paper [3]); the paper has comparisons to other tools.
There was a paper at IEEE VIS last year ("Guiro: User-Guided Matrix Reordering" [4]) about a tool that implemented > 70 matrix seriation/reordering methods, but I don't think the code is available. There was also a State of the Art Review on matrix re-ordering methods from 2016 [5, 6]: it is mostly about the algorithms rather than available implementations, but it mentions reorder.js [7].
This optimization problem is very similar to that of minimizing the diagonal bandwidth of a matrix, a common problem in large numerical computations [1].
It is also related to cluster finding in graphs and graph layouts by considering the adjacency matrix.
The difference is that in both those cases the values are boolean, but in this post the cost function is weighted.
I love the physical modelling and manipulation; but there has to be a better way than removing and replacing all those rods every time you want to switch dimensions, surely?
That could work, but it seems like part of the purpose of this form of matrix is to be able to rearrange rows or columns as a unit. (Hence why it says, "Reordering was clearly the most crucial.")
So for example, you might remove all the vertical rods, leave the horizontal ones, and use the horizontal ones to rearrange rows.
This means you'd have to be able to detach the rods from the comb, but that's probably doable. You could build the comb so that the connecting piece clamps onto the end of the rods, for example. Put balls on the ends of the roads and have corresponding voids in the connecting piece and a hinge to close the connecting piece around the balls.
I'm a mediocre woodworker, but it seems to me cutting the dominoes on a table saw would be faster than laser cutting. Setup a sled with a stop of the proper width to create strips. The strips could be run through using the sled with the stop set to a potentially different dimension. One can then use either a drill press or a hand drill with a template to guide hole placement. A drill press would be preferred, since getting exact placement and alignment is essential to getting the rods to work.
The footnotes lead to some fascinating context into the associated research field.
The World Values Survey, which started in 1981, is "the largest non-commercial, cross-national, time series investigation of human beliefs and values ever executed, currently including interviews with almost 400,000 respondents. Moreover the WVS is the only academic study covering the full range of global variations, from very poor to very rich countries, in all of the world’s major cultural zones".
"WVS consists of nationally representative surveys conducted in almost 100 countries which contain almost 90 percent of the world’s population, using a common questionnaire" .
Their latest research study examines "Values In a Time Of Crisis" & the effects of the Covid-19 pandemic on values.
"a natural experiment indeed—to study how people’s moral values behave during times of crises. In the face of lacking evidence, we cannot take it for granted that the glacial stability of values observed in normal times continues throughout the Corona crisis. This uncertainty opens new territory and raises several imminent research questions:
- Does the Corona pandemic impact on people’s values? In other words, do people change their values under the imprint of this crisis?
- If yes, how massive are these changes? And if these changes are massive, in what direction do they move?
- How enduring are these changes, once an end of the crisis is at sight and once its economic consequences are overcome: do people’s moral values revert back to their old setpoint or does the crisis leave a lasting impact?"
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[ 4.2 ms ] story [ 49.7 ms ] threadDoes anyone know of any library to visualise data this way?
[edit] and you can also now easily do this in MS Excel
There was a paper at IEEE VIS last year ("Guiro: User-Guided Matrix Reordering" [4]) about a tool that implemented > 70 matrix seriation/reordering methods, but I don't think the code is available. There was also a State of the Art Review on matrix re-ordering methods from 2016 [5, 6]: it is mostly about the algorithms rather than available implementations, but it mentions reorder.js [7].
[1]: https://aviz.fr/bertifier
[2]: https://aviz.fr/bertifier_app/
[3]: https://aviz.fr/wiki/uploads/Bertifier/bertifier-authorversi...
[4]: https://vcg.seas.harvard.edu/publications/guiro-user-guided-...
[5]: https://onlinelibrary.wiley.com/doi/full/10.1111/cgf.12935
[6]: https://bib.dbvis.de/uploadedFiles/MatrixReorderingSTAR.pdf
[7]: https://github.com/jdfekete/reorder.js
The difference is that in both those cases the values are boolean, but in this post the cost function is weighted.
[1] https://en.wikipedia.org/wiki/Cuthill%E2%80%93McKee_algorith...
So for example, you might remove all the vertical rods, leave the horizontal ones, and use the horizontal ones to rearrange rows.
This means you'd have to be able to detach the rods from the comb, but that's probably doable. You could build the comb so that the connecting piece clamps onto the end of the rods, for example. Put balls on the ends of the roads and have corresponding voids in the connecting piece and a hinge to close the connecting piece around the balls.
The World Values Survey, which started in 1981, is "the largest non-commercial, cross-national, time series investigation of human beliefs and values ever executed, currently including interviews with almost 400,000 respondents. Moreover the WVS is the only academic study covering the full range of global variations, from very poor to very rich countries, in all of the world’s major cultural zones".
"WVS consists of nationally representative surveys conducted in almost 100 countries which contain almost 90 percent of the world’s population, using a common questionnaire" .
Their latest research study examines "Values In a Time Of Crisis" & the effects of the Covid-19 pandemic on values.
"a natural experiment indeed—to study how people’s moral values behave during times of crises. In the face of lacking evidence, we cannot take it for granted that the glacial stability of values observed in normal times continues throughout the Corona crisis. This uncertainty opens new territory and raises several imminent research questions:
http://www.worldvaluessurvey.org/WVSEventsShow.jsp?ID=416