I’ve spent much of the past two weeks messing about with different ways to reduce down over 200,000 bubbles (now almost 220,000) into a sensible catalogue. This gets very messy so I will try and explain what I’ve been up to in stages. This is a process called data reduction and for a citizen science, crowd-sourced project like the MWP, it can get complicated. I thought it may interested some of you to see where we currently are in the process of turning your clicks into results.
The key part of the data reduction problem is that we have a very large set of data – the massive number of bubbles that have been drawn – and need to decide which among them are ‘similar’ to each other. We need to keep some flexibility of our definition of similarity because right now, I’m not sure what ‘similar’ means.
Essentially, bubbles are ‘similar’ when two people draw a similarly sized bubble in a similar location. This is something that sounds remarkably easy to say but was hard to do well in code. Comparing 200,000 bubbles to each other is obviously computationally intensive.
In the end I decided that since the size of bubbles was a consideration then I would move across the galaxy, looking on ever-decreasing orders of size. To do this I split the galaxy into 2×2 degree boxes and take each box in turn. In each box I see if there are bubbles here that are of the order of the size of the box (meaning they have a maximum diameter that is between a half- and a whole-box). If there are bubbles on that scale I run a clustering algorithm and pick out groups of these bubbles with central positions clustered to within one quarter of the box size. If a cluster is found, those bubbles are then saved and removed from the whole list. I then divide the box into four and repeat until no bubble are found.
This method means that when a box contains no bubbles, we need not continue down in size scale, but when it does contain bubbles we always split and inspect the four child boxes. In this way we move through the galaxy, in ever-decreasing boxes, but in a fairly efficient manner.
We also have to perform the same analysis with an offset grid. This is exactly the same but making sure we catch bubbles that had fallen on the borders of boxes.
Once we have passed across the galaxy on all size scales, we need to make sure we’ve cleaned up the duplicates created by the offset grid. We do this by considering our newly created list of ‘clean’ bubbles and running through them in order of size. When we find bubbles of a similar size and location they are combined, according to the number of users that drew that bubble. This can be done more easily now that there are far fewer bubbles (in my tests we have dropped to around 5% of the initial number by this stage).
My initial run only looked at bubbles in the longitude range 0-30 degrees. Below are three images, showing one image from the MWP set (one of my favourites as lots of people see it differently). You can the the image, as it is shown to MWP users. Below that you see, overlaid in blue, the original bubbles as drawn by the users. In the third image you can see the same, but this time displaying the ‘cleaned’ results. In the original set the bubbles all have the same opacity, such that when they pile up you can see the similarities. The cleaned set gives the bubbles opacities according to their scores (think more opaque bubbles mean more users drew them).
It should be noted that the cleaned image does not yet display arcs, but rather always shows an entire ellipse. This is because I am not yet including the bubble cut-outs (which you can make out in the middle image) in the data reduction. These will be included at a later time.
You can see that I’m still getting some duplication at the end of the process – I may need to sweep across the final catalogue looking for similar bubbles until I reach a convergence when all bubbles are ‘unique’. I have been experimenting with this with mixed results but will continue my efforts.
If you’re still reading, I look forward to reading your comments. As I continue to make adjustments and progress with this reduction, I shall blog the results again. Many members of the science team are also having a go at this problem and so the final result may be quite different in the end as we improve things. I hope that this is an interesting insight into some of what goes on behind the scenes of the MWP.