Okay. Let me show you a few examples of trees. Tree visualizations are based on node link diagrams. The first one is visualization of a file system structure. As you can see, every single node represents one folder or one file, and it's represented by a single mark. Now, there is a connection between two marks when there is a containment relationship between these two. So say, if a file is contained within a folder then the two marks that represent the file in the folder are connected by a line. Very simple. So, in this case, we have a node link diagram, a tree node link diagram that is arranged horizontally. But a tree diagram can also be arranged vertically like this one. Exactly the same procedure. In this case, we have what is called the Sentence Parsing Tree. The idea here is that if you look at the leaves of the tree, the leaves are the nodes at the bottom that don't have any other children following. If you look at the leaves, the leaves is the actual sentence. The structure is the element of the syntax that describe the sentence from the lexical point of view. Another example, if a phylogenetic trees that's the kind of situation that I described in the previous videos. The phylogenetic trees are very, very common in biology especially to show the relationship between different animals and how they evolved over time. Another very interesting structure that is very similar to these ones, but also somewhat different is the structure that you sometimes see in user interfaces that is basically a list with indented elements to show the actual hierarchical structure. One thing that I really like about this solution, even though it's very simple is that it can be used, as we will see later on in the course, as an element in a user interface, and it's very versatile and very, very easy to interpret. People typically understand very quickly what it means and how to read it. Another option for node link diagrams that represent trees is to arrange the tree in a radial layout. So, the idea is that the root node is in the middle and then the children branch out in a radial direction, so following the direction of the radius, that's why I said radial. This is also very common in, again, in biology. If you look for phylogenetic trees you may find an arrangement like this one instead of the one that I've shown you before. I want to conclude here by highlighting some important issues with node link diagrams that are used when they are used for visualizing trees. The first one is the usual one, there is scalability. Scalability, as you may have noticed is always an issue in visualization. Of course, we have the same situation here. The higher the number of nodes and the harder it is to fit everything into one single visualization. So, that's a general problem. In particular here, we have a bigger problem. Imagine that the number of data points that are organized in a hierarchical structure grows. If you reflect on the solution that I've shown you so far, the data points would be at the leaf level of the hierarchy. Think about, say, the animals in a phylogenetic tree, they're all leaves of the tree. Now if the number of items grows, with this solution the growth has to be in one of the two possible directions either horizontally or vertically. This means that it doesn't scale very, very well. So, one little advantage of a radio layout is that it tends to scale slightly better than the other layouts. So, that's one important observation. But in general, trees don't scale very well with the number of nodes. Another important issue is labeling. So, labeling is very important because you want to be able to interpret the meaning of the nodes, but the more labels you have to attach to the nodes, the more clutter you have, and this also has an effect on scalability. Last thing that I want to say is that as you may have noticed, similarly to what we have seen with general networks, you can encode information on top of the markers and on top of the lines that connect the markers. So, as a general remark here, if you have in the dataset additional information that is important to visualize regarding the nodes, properties of the nodes or properties of the connections between the nodes, all the usual encoding methods are available to represent information with these marks.
