Humanities Intensive Learning + Teaching, Day 5, Maryland Institute for Technology in the Humanities, #hilt2014Posted: August 17, 2014
Sorry for the delay in completing this – it has been crazy and I prefer to write directly into the live blog, which means a network feed, as I just find it easier to put things together this way. (It’s only been a week (ish) anyway.)
Today (well, then), we looked at modularity and how we could break networks into separate communities. This is important because it helps us to be able to see structure. The human eye is a great tool but it often needs help and modularity is a good way to do this. We have strong ties between components in directed networks (unidirectional) because we have taken the time to say that the link goes this way. We have weak ties in undirected networks because there is no solidity to the association form one side to the other. The more connected something is, the more strongly tied it is to the things it connects to so, when we hunt for communities, we want to take away the least number of connections to produce the largest number of connected communities.
Let’s look at the Hamlet graph (after Moretti) with some colouring added for the various communities and all the connections left in.
Now let’s take out the intra-community links.
Now we can suddenly see, in terms of dialogue exchanges and interaction, how isolated Hamlet actually is. The members of the court are one community. The invaders are another. Horatio, the proxy for the Danish state, is deeply involved in statehood. Hamlet, however, is more heavily connected to the characters who help with his dawning realisation that something has gone awry. No wonder he goes mad, he’s the Nigel Nofriends of Medieval Denmark, with only the insane Clown Posse and a group of second-rate actors to keep him company.
After this we spent some extensive time working on producing prettier looking graphs with Gephi and using more advanced algorithms to help us to represent what’s going on. We looked at the Twitter data for the conference and came up with this:
This shows the separate groups of Twitter user communities who used the HILT2014 hashtag. My small cluster is the small purple arrow bottomish left. We’ve also ranked the size of the data labels based on the significance of that person in the Twitter information chain, using the PageRank algorithm. So, Jim McGrath wins Twitter for HILT 2014! We also look and how important certain links were in the network by looking at edge betweenness to determine which links are used by the most shortest paths and then use this to identify important connected components.
Lots of good hands-on stuff and a very interesting course! I learned a great deal and have already started using it elsewhere.
Humanities Intensive Learning + Teaching, Day 4, Maryland Institute for Technology in the Humanities, #hilt2014Posted: August 8, 2014
Or, the alternative title, “The Play Formerly Known as Hamlet”. Today had a lot of fascination discussion where the bipartite nature of our class network became apparent, in terms of the the majority of the class who were Digital Humanists and really understood a detailed close reading of Hamlet – and your humble narrator.
Today we talked about modularity, which allows you to break your network up into separate modules, which makes a lot more sense when you call those modules things like communities, groups or clusters. Can your network be split up into areas where some groups are more connected to each other than they are to adjacent nodes? By doing this, we are trying to expose structural features of the network and, in particular, unexpected aspects of network structure – is there some set of nodes that have a role in the network that we don’t understand? If we talk about this in terms of people, if our social network is made up of small communities with connections between the communities, then we would expect gossip to spread more rapidly inside a community than between the communities. Simple, eh? The approach we take depends upon comparing the structure we have with a model of a random network using the same number of links.
Once we’ve done this, we can use this in a tool, such as Gephi, to clearly illustrate the groups. Here’s a grumpy Dane in illustration.
I’ve coloured and tagged the network to show the key players in Hamlet, based on Moretti’s analysis of Hamlet, which attached unweighted connections between participants who had direct conversations. Now, we’ve made the size of the nodes reflect how relatively important (in terms of betweenness, the number of paths that must go through this person). If we did this in terms of PageRank, another measure of the relative importance of nodes, based on their connectivity, the nodes in green would jump up in size. But what you should note is that Hamlet and Horatio are roughly the same size and, while Hamlet is much more connected to everyone (quelle surprise, given the play’s named after him), the only thing that we lose if Hamlet disappears is that we no longer can hear from the Insane Clown Posse, Lucianus and the Lord. In purely connected terms he doesn’t appear to be that important. We’d obviously lose a lot of the text if he disappeared but how important is Hamlet in Hamlet?
This led to a lot of discussion in class as to the validity of the original Moretti pamphlet, much of which is core to the entire discussion of Digital Humanities. How valid is any conclusion from a network model such as this when the innate nature of the capture process (to provide the capta) may completely remove the ability to draw certain conclusions? The class discussed the impact on perceived and invisible observers, who strictly don’t have dialogue with each other but potentially have an impact upon other characters and their narrative interactions. (The Moretti pamphlet may be found here.) Moretti had a lot to say about Horatio as a proxy for the state and was very interested in the closeness of Hamlet to everyone else, but (later on) we ran some random network experiments and it turned out to be the type of connections in the network (the clustering coefficient) that was more interesting than the closeness.
We then moved on to a discussion of a number of useful metric for networks, including the clustering effects that tend to indicate intention in the system we’re studying (there’s no real reason for a random network to form a small number of unique clusters unless you tune for it.) We also discussed the Small Worlds of Watts and Strogatz (1998) where you have cliques of nodes (tightly connected clusters) linked together by a smaller number of links, characterised by a power law distribution and a higher clustering coefficient (very basically).
We generated some random graphs to see if we got the structure we saw in Hamlet as noted earlier. Why? Because looking at Hamlet and drawing out information from the structure only has validity if (1) the model is accurate and (2) the situation couldn’t have easily arisen by chance. As noted, we generated a random graph for the same number of nodes and it had a similar average path length and identical diameter – but very different clustering coefficients! So it turns out that Hamlet wasn’t written by a monkey after all.
The final part of the session was on dynamic networks. This is the study of networks that change over time and we worked with some data that showed people’s association with an area over time. We could look at this in terms of change in time or in terms of progress through a corpus (chapters are as useful as dates here). What you want is a start date and an end date for the feautres in your network – when should the feature be there and when should it not be there anymore? It turns out that Gephi is quite convenient here, because you can merge a start and end time and end up with a time interval. Not bad, Gephi, not bad. Now we can see when things are active – great if you’re looking to see when students are active in forums or activities, for example. Here’s an example of the difference in the test network between the first and second halves of 2009, with all nodes of zero degree (nodes with no links) removed.
We then played around a lot with a vide variety of animations over time, including ongoing calculations, colour and shape alterations. Basically, it was rather hallucinatory by the end but that may be the Dr Pepper talking. We even got to see the sparklines (Zelchenko/Tufte) for some extra visualisation goodness!
This is one of those classic separations between the things we visualise for ourselves to help us to work out what’s interesting about a dataset and what we would visualise for presentation, especially to non-discipline people. There’s a really big difference between what scientists want to see and what other people want to see – and if we don’t realise that, then we risk either having presentations that don’t communicate enough information or we kill people with minutiae. Look at this – how useful is it for you?
Another good day but I think there are some very full brains!
Humanities Intensive Learning + Teaching, Day 3, Maryland Institute for Technology in the Humanities, #hilt2014Posted: August 8, 2014
Today was going to be a short day because we had the afternoon off to go and do cultural things. (I took the afternoon to write papers and catch up on work. I tend to work in both timezones when travelling because otherwise work will eat my head.) Today we explored a lot of filtering in Gephi, which was … interesting and best done in practice. Which we did. So, hooray!
We looked at Multimodal Network Projection throughout the day but I’ll come back to that. We started looking at other ways of determining the important and dependant nodes in a network, starting with the HITS algorithm, which identifies Hubs and Authorities in your network.
Then we moved into the wonderful world of PageRank, Citation networks and how all of these things work. PageRank is, fundamentally, how Google works out which pages to give you. You won’t be able to find out the details of the way that Google runs PageRank because gaming PageRank to serve up pages that you probably didn’t want to see is very big business and highly irritating. Search Engine Optimisers (SEOs) spend a lot of time trying to reverse engineer the algorithm and Google spends a lot of time tweaking it. It’s good we’ve solved all the important problems in the world so we can spend time on this.
Back to PageRank. PageRank looks at the number of links going to a node and what the quality of these links is in order to work out which the most important nodes (pages in the case of Google search) are and, hence, which ones you want. In Digital Humanities, you can use this to identify the most significant element of your model – which, by the way, quickly establishes that Hamlet is not as important as you think. Take that, Hamlet! Want more detail on PageRank? Look here.
In Citations, we want to see how is citing which reference, which is straightforward. In Co-Citation networks, we want to measure how often two documents are cited together. There are many reasons for looking at this, but it helps to detect things like cronyism (someone citing a paper because they like someone rather than because the information is useful). As we discussed before, the Matthew Effect comes in quickly, where frequently cited papers get even more frequently cited because they must be good because they’re cited so frequently. (Tadahhh.)
We also looked at a rather complicated area of multimodal projection, which is going to need some set-up. If you have a set of authors and a set of publications, then you can associate authors with publications and vice versa. However, this means that the only way for two authors to be connected is by sharing a publication and similarly for two publications sharing an author. This is a bipartite network and is very common in this kind of modelling. Now, if we make it more complicated, by moving to a conference and having Authors, Papers and Presentation Sessions, we now have a tripartite network and this becomes very hard to visualise.
What we can do is clean up this network to make it easier to represent by hiding some of the complexity in the connections between nodes. Let’s say we want to look at Authors and Presentation Sessions. Then, while the real network is Authors connected to Papers connected to Presentation Sessions, we can hide the Papers with a network link that effectively says “connects this author via a presentation to this session” and suddenly our network looks like it’s only Authors and Sessions. This level of visual de-cluttering, which is dimensional reduction for those playing along at home, makes it easier for us to visually represent the key information and produce network statistics on these simpler graphs. It’s also a natural fit for triple-based representations like the Resource Description Framework (RDF) because the links in the network now map straight to predicates. (Don’t worry if you didn’t get that last bit, some people just got very excited.)
Finally, we looked at how we collect information. Is it stuff we just pick up from the environment (data) or is it something that we choose the way that we collect it (capta)? (Capta comes from the word for capture. Data is passive. Capta is active. Take that, Bembridge Scholars!) If you think about it, every time you put your data into a spreadsheet, you are imposing a structure upon it, even down to which column is which – it’s not technically data, it’s capta because your interpretation alters it before it even reaches the analysis stage. When it comes to the network that you draw, do you care about the Proximities of elements in your network (location, membership or attitude), the Relations in your network (role, affective, perceptual), the Interactions or the Flows? All of these are going to change what the nodes and edges (links) represent in the network.
The simple rule is that entities are connected by relationships (For those who think in tuples, think “subject, predicate, object” and get your predicate on!) However you do it, you have to pick what’s important in your data, find it, capture it, analyse it and present it in a way that either shows you cool things or supports the cool things that you already know.
A lot to cover today!
After the session, I did some work and then headed off for dinner and board games with some of the other people from the workshop. A nice relaxing night after a rather intense three days.
Humanities Intensive Learning + Teaching, Day 2, Maryland Institute for Technology in the Humanities, #hilt2014Posted: August 8, 2014
In Day 2, we looked at using the Gephi tool itself, along with the nature of how networks are tied together, looking at network degree and how we could calculate paths through the network. It’s probably important to talk about some of the key concepts of how we measure connectedness in a network, and the relevant importance of nodes.
The degree of a node is the number of links that connect to it. If we care about whether the links have some idea of direction associated with them then we might split this into in-degree and out-degree, being the number of links going in and the number of links going out. What do we mean by direction? Consider Facebook. If you and I are going to be Friends then we both have to agree to be Friends – I can’t be a friend unless you want to a friend to. This is an undirected arrangement and a connection between us implies that both us have an equal connection to each other. Now think about unrequited love: Duckie loves Andie but Andie loves Blane. In this case, the love is directed. Just because Duckie loves Andie, it doesn’t mean that Andie loves Duckie.
ALTHOUGH IT SHOULD, JOHN HUGHES!!!
(An amusing aside for network/maths people is that, sadly, love is not transitive or “Pretty in Pink” would have been way ahead of its time.)
One of the other things that we care about in networks is the relative importance of nodes in terms of how many other nodes they are connected to and what this means in terms of the paths we take through the network. When we talk about paths, we usually mean the shortest path, where we start somewhere and go through the minimum number of intermediate points until we get to the destination. We don’t run around in circles. We don’t go one way and then go another. This is important because the paths through a network can quickly identify the important nodes and, therefore, the links between them that are the most travelled thoroughfares.
In this world, we start to worry about the centrality of a node, which indicates how important it is by looking at how many other nodes it is connected to or how many other nodes have to use it to get to other places in the network. This means that we have to talk about betweenness, which measures how many times the shortest paths that traverse a network have to go through a node. By calculating the betweenness of every node, for every path, we can work out which of the elements in our network see the most traffic.
In the case of the Medicis, from yesterday, all roads in Florence lead to the Medicis, the family with the highest betweenness rather than the family with the most money or fame. The Medicis are an extreme case because they occupy their position of importance as the only bridge (broker) between certain families.
If a network is made of highly connected elements and all of the betweenness is the same then no-one has an advantage. If your network can be effectively split into two highly connected groups, with a smaller number of high-betweenness elements linking them, then you are seeing a separation that may mean something significant in your particular network domain. From a power perspective, the high betweenness brokers now have the potential to have much more influence if they charge for transit and transform information that traverses them.
One of the things about creating a network from data is that the network we create may not necessarily model reality in a way that answers the questions we’re interested in, but by looking at the network and trying to work out if it’s got some different structure at the macro, meso and micro scale, then that might give us hints as to how to analyse it, to further develop our understanding of the area that we’re modelling with this network.
I’ve written about the difference between the real world and the model before, but let’s just say that “the map is not the territory” and move on. In terms of the structure of networks, while many people assume that the distribution of nodes and links associated with them would end up in some sort of Normal distribution, the truth is that we tend to see a hub-spoke tendency, where there are lots of nodes with few links and fewer nodes with lots of links. When we start to look at the detailed structure rather than the average structure, we can even talk about uniform the structure is. If a network looks the same across itself, such as the same number of connections between nodes, then it’s what we call assortative. If we have small clusters of highly connected nodes joined to other clusters with sparse links, then we’d thinking of it as disassortative. Suddenly, we are moving beyond some overall statistics to look at what we can really say about the structure of a network.
There’s also a phenomenon known as the Matthew Effect, where links and nodes added to a network tend to connect to better connected nodes and, as the network grows, nodes with more connections just get more connected – just like life.
Apart from a lot of Gephi, we finished the day by looking at paths in more detail, which allow us to talk about the network diameter, the size of the largest shortest path in the network. (Remembering that a shortest path contains no loops or false starts, so the largest shortest path shows you the largest number of unique nodes you can visit in the network and gives you an idea of how much time you can waste in that network. 🙂 )
There are some key concepts here, where having redundant paths in a network allows us to survive parts of a network going away (whether computer or social) and having redundant paths of the same quality allows us to endure loss without seeing a significant change in the shortest paths in the network. These are all concepts that we’re familiar with in real life but, once we start to measure them in our network models, we find out the critical components in our data model. If we’re modelling student forums, is there one person who is brokering all of the communication? What happens if she gets sick or leaves the course? Now we have numbers to discuss this – for more, tune in to the next instalment!
Humanities Intensive Learning + Teaching, Day 1, Maryland Institute for Technology in the Humanities, #hilt2014Posted: August 6, 2014
I’m attending the Humanities Intensive Learning + Teaching courses at Maryland Institute for Technology in the Humanities, #hilt2014, for the second year running. Last year was Matt Jocker’s excellent course on R and this year I’m attending Elijah Meek’s course on Network Analysis and Visualisation. The first day we covered network basics and why you might want to actually carry out visualisation across graphs – and what the hell are graphs anyway?
Graphs, put simply, are a collection of things and connections between those things. Now that I’ve killed every mathematician reading this blog, let’s continue. I’ve done a lot of work on this before in the Internet Topology Zoo but it’s now looking like analysis of large-scale online education is something I have to get good at, so it seemed a great opportunity to come and see how the DH community do this and get access to some mature processes and tools.
Why is this important as a visualisation (or representation, thanks, Elijah) target? Because pictures tell stories well and we can use this to drive argument and make change.
Let’s consider the Medici, the family who dominated Florence from the 1400s to the 18th century. While not being the most wealthy and powerful families at the outset, they were (by marriage and arrangements) one of the most well connected families. In fact, the connections from some groups of families to other families had to go through the Medicis – which made them more important because of their role in the network.
The graph makes the relationship and the importance clear. (Insert toast about Boston, Lowells and Cabots here.)
In graphs of the Internet, everything is connected to the Internet by definition, so we don’t have any isolated elements. (We do have networks that don’t connect to the Internet, such as super-secret defence networks and some power stations – not as many as there used to be – but we’re interested in the Internet.) It is possible to analyse communities and show ways that some people/entities/organisations are not connected to each other. Sometimes they form disconnected clusters, sometimes they sit by themselves, and this is where my interest comes in, because we can use this to analyse student behaviour as a learning community.
A student who enrols in your course is notionally part of your community but this is an administrative view of the network. It’s only when they take part in any learning and teaching activity that they actually become part of the learning community. Suddenly all of the students in your network can have a range of different types of connection, which is a good start to finding categories to talk about behaviour in large on-line courses, because now we can easily separate enrolment from attendance, attendance from viewing, viewing from participation in discussion, and discussion from submission of work. I hope to have a good look into this to find some nice (convenient) mathematical descriptions of the now defunct cMOOC/xMOOC distinction and how we can encourage behaviour to get students to form robust learning networks.
As we can see from the Medicis, the Medicis used their position in order to gain power – it wasn’t in their interests to form additional connections to make the network resilient if they fell on hard times. However, learning networks don’t want a central point that can fail (central points of failure are to be avoided in most contexts!) and this is why a learning community is so important. If students are connected to many other students and their lecturing staff, then the chances of one relationship (connection) failing causing the whole network to fail is very low. Some people are, naturally, very important in a learning community: we’d hope that instructors would be, tutors would be, and key students who handle discussions or explanations also would be. However, if we have very few of these important people, then everyone else is depending upon this small number to stay connected and this puts a lot of stress on these people and makes it easy for your network to fall apart.
I’ll talk more about this tomorrow and hit you with you some definitions!