Connection Map Diagrams

Three Data Views

An example of a connection map diagram window.

The goal is to display the information contained in the similarity profiles so the relationships therein can be analyzed at both a global and a local level. The global analysis is coarse-grained: a quick visual scan should reveal collections of generally similar elements. These clusters of elements with similar patterns of similarity are of particular interest. When viewing the local relationships inside a cluster of generally similar elements, the user should be able to assess the fine-grained similarities and differences between the similarity profiles of the cluster constituents.

An example of an information window after four clicks on the "journey" element while in similarity mode.

An example of the ParameterExplorer window.

The focus element is `thunder'. The current threshold (and thus the contents of the connection map) was determined by pausing an animation after 12 updates. Note the correspondence between some of the elements in the static `Top 10 Matches' list and the dynamically updated `Top 10 Most Recent' list. The orange square on the top row corresponds to the `pound' verb and has a black border to highlight that it was added in the most recent step of the animation. After the animation was paused, the brown square was clicked on, causing the name of the element it represents (i.e. `rasp') to appear below the map.

How a Connection Map is Made Based on an Undirected Graph

The above image shows an Artificial Neural Network (ANN) with symmetric connections and its Hinton diagram. For clarity, only the weights of the two highlighted edges are shown and the dashed red arrows indicate which squares in the diagram represent these highlighted edges. This type of diagram was the inspiration for the development of connection map diagrams.

The above figure shows an undirected graph and its connection map diagram. The diagram construction process is described in the figures that follow. Note that including self-connections makes it easier to see that elements h and i form a connected component.

First each of the graph nodes is assigned to a grid position. In this case, a was assigned to position 1, c to position 2, an d so on, up to i at position 9. The element arrangement process attempts to minimize the distance between nodes that are connected.

Once each node in the graph has been assigned a grid position, creating a connection map for each node is straightforward. As seen in the preceeding figure, the connection map for node i is a collection of squares on an mxm grid, where a square appears at position j iff there is an edge directly connecting i to j in the underlying graph. The final step is to arrange the connection maps themselves in an mxm grid, such that the map for the node at grid position i is placed at position i in the main grid. Since there is a parallel between the arrangement of the squares in each map and the arrangement of the maps on the main grid, the position of each square in a connection map can be seen as a pointer to the element at that position in the main grid.