Skip to 0 minutes and 9 seconds Now that you know how self-organizing maps work, I would like to tell you a few small tricks, simple to apply, that will make sure you get far more out of them. The example I’ve shown you already was based on a data organization like this. Now the first trick is actually that by organizing your data in different ways, you can get far more out of self-organizing maps. This is data organization was based on vertically the medical districts, so these are your spatial units. Horizontally, you see the time series. That was ranging from 1946 all the way to 1970. Now if we have such a data set, we can organize it in different ways.
Skip to 1 minute and 0 seconds What we can do is we can cut it wave by wave, and then vertically append these so you can create a data set organized as you see in example two, where every medical district will appear several times, once for every wave. You should make sure, though, that the length of your waves is equal. You also see that we can transpose the data set so that it is organized not with vertically the spatial units, but the time, in this case, the waves. Horizontally, you see the medical districts. Let me show you a little bit more. So when we organize our data set in the original way, what we can do is we can identify medical districts with similar patterns.
Skip to 2 minutes and 3 seconds We go for the middle, for the second organization. We can easily compare different waves. And when we organize in time rather than in space, what we can do is we can characterize and compare spatial temporal diffusion patterns. So this was our first example with our first data organization. And what we’ve seen is that in this way, we saw that this purple spot was Reykjavik. And we revealed a spatial pattern similarity between these medical districts that all were grouped to or mapped to the neurons eight, nine, and 11, similar to the pattern observed in Reykjavik. So we revealed a spatial temporal pattern. Now take the second data organization. So in this case we have organized this data set per wave.
Skip to 3 minutes and 11 seconds So this is the length of one outbreak, one wave. We train to SOM with the complete data set, and this allows us to map back a single wave so I can compare them. And what you see here is actually such a mapping. This is mapping back of the complete data set containing all waves. This is only wave eight, only wave nine, and only wave 11. And what you see is that the pattern we observe for wave eight, mainly here in the top part, and over here, is not very similar to the pattern of wave number nine. It is more similar, however, to wave 11.
Skip to 4 minutes and 4 seconds It also allows us to inspect the position of a single health unit, medical district, in different ways to see how stable it is. Does it always end up roughly in the same position?
Skip to 4 minutes and 24 seconds Now this is the last example with data organization that was transposed. So in this case, the individual factor represents all of my spatial units, and only one moment in time. Let’s have a look at a small animation of wave eight and nine.
Skip to 4 minutes and 53 seconds So this was the spatial temporal diffusion pattern. Was it very similar? Perhaps you didn’t see it correctly. So let me play it again.
Skip to 5 minutes and 10 seconds Even if I warn you in advance, it is difficult to tell if two spatial diffusion patterns are alike. That’s why we use our self-organizing map again.
Skip to 5 minutes and 27 seconds This is the trained lattice that we talked about before. You see all the neurons and you see the factors of weight. Now if we present the lattice in this way, what we can easily identify is the similarity between the weight factors or adjacent neurons. That is the topological relationship that is preserved. However, we cannot see what the distance is between the different neurons. How alike or not alike two adjacent factors actually are. Now what we can do is we can project exactly this representation again, but now using a Sammon’s projection that is showing the distance between the factors of weight. And that looks like this.
Skip to 6 minutes and 28 seconds So we already discussed that every neuron has a number, and what you see here is that we have mapped all these numbers in this projection, but now the distance between them varies. Some adjacent neurons are more alike and others are less alike. For example, our neuron here is now located right over here.
Skip to 7 minutes and 0 seconds OK, now what I have is I have organized my data in time, and I am showing it now, projecting it onto to Sammon projection. Let’s play another animation of exactly the same data.
Skip to 7 minutes and 27 seconds What you see now is that besides the animation itself, you saw that I was, at the same time, projecting the trajectory of diffusion onto this Sammon projection, and I can characterize the complete diffusion pattern in this single line, or I should say this collection of lines, lines of transition stages. And I can do this for all the different waves. And now we can easily see that wave number eight, for example, the spatial temporal diffusion pattern, is very similar to wave number 14, but very different from wave number nine.
How to get more out of Self-Organizing Maps
Now that you know how self-organizing maps work, we dive deeper to make sure you get more out of them.
The first thing you can do is organize your data in different ways. Then you can get far more out of self-organizing maps. In the video you will see much more, such as data organization that is transposed.
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