The group of circles in the area above is a graph representing semantic clusters. You can think of semantic clusters as groups of documents that share common subject matter. The sizes of the clusters show the number of documents in that cluster relative to other clusters. The cluster labels detail the subject matter of each cluster.
The clusters are moving around (or not moving around) because they are part of a physical simulation. All clusters are considered bodies in space. All clusters exhibit anti-gravity, pushing each other apart. Related clusters have a spring pulling them together. Why would we do this weird stuff? This is because the end result of the simulation creates an interesting and readable (usually) arrangement of the clusters. Typically, semantically related clusters are found close together.
The color of a cluster is determined by a mathematical technique called PCA (or Principal Components Analysis) which is used to find general trends in the data. While the placement of the clusters tells you one thing (the "distance" to the center cluster), PCA tries to tell you something a little more subtle. Distinct colors don't have any exact meaning, but provide a signal of a strong relationship between two documents. Its result is that clusters with similarities have similar colors.
Preliminary: To understand the exact criteria for placing the clusters, you will need to understand what Euclidean distance means and what a node-and-edge graph and vector are.
Internally, each semantic cluster represents a vector in high-dimensional space (over 30,000 dimensions). First, every semantic cluster becomes a graph node which we add to our graph. Then for every pair of graph nodes we calculate the Euclidean distance between their vectors. If this value is over a certain threshold, then we add to the graph an edge between these two nodes. The threshold is controlled by the horizontal slider. This is how the internal node-and-edge graph is constructed.
In our physical simulation, graph nodes become physical bodies with repulsion forces, and edges become connecting springs. We then use a physics simulation engine to animate the clusters. After 10 seconds, the simulation halts and the graph reaches a final static state.