Encoding Multiple Edges in Matrices

For the traditional node-link representation of a DBN found in the literature [135, 105, 170], all transitions from one time-slice to the next are required and the nodes are repeated in every time- slice, as shown in Figure 3.13. The resulting network is read from left to right following the sequence of time. DBNs can become very long when they extend to many time-slices and are therefore hard to visualise. A more compact representation requires additional visual encoding to help distinguish between the different edge types. Figure 6.1(a) shows how the network becomes much smaller when the nodes are not repeated and edge types are encoded using colour. However, this approach creates visual clutter for more dense networks because of edge crossings [9].

Figure 6.1(b) shows how the same DBN can be represented as a directed adjacency matrix, again using colour to encode edge types. Edges are represented by adjacent cells in the matrix read by column and row (i.e. top-down). This representation is less cluttered than node-link diagrams when the networks are dense [9, 75], but when there are multiple edge types for the same pair of nodes, the visual encoding becomes challenging. For instance, in Figure 6.1(b) it is not clear how to encode two edge types coexisting in the one cell that corresponds to the pair of nodes D and B. One possibility is to create a glyph by splitting the cell into as many parts as edge types and use a different colour for each part. In the following section, we explore the design space for encoding networks with multiple edge types as matrices.

6.3.1 Matrix Cell Designs

In Section 3.3.2 we discussed different approaches to the problem of multivariate network visu- alisation. We found that integrated approaches are more efficient than multiple and coordinated views [96, 77]. However, embedding additional multivariate data into standard network represen- tations that use node-link diagrams or adjacency matrices, is not intuitive and it often results in visual clutter. Because we were interested in extending BayesPiles to also support the analysis of DBNs, we only considered integrated approaches for matrix-based representations. Node-link diagrams were not considered, not only because they are not supported in BayesPiles, but also because there are limitations in embedding additional multivariate data in edges represented as arrows. Moreover, node-link diagrams often suffer from visual clutter caused by multiple edge crossings even for networks that are not multivariate [9, 73]. On the other hand, matrices provide more opportunity for encoding multivariate data in their edges. The available plane space in each matrix cell could be used to encode not only the existence of an edge but also its type. Encoding multiple types in the same cell could be done either by splitting the cell or by using icons and glyphs.

Criteria: Based on the task identification, modellers’ feedback and a literature review, we de- veloped several potential visual encodings for representing DBNs through matrices (Figure 6.2). The goal of our design was to find a representation that fulfils the following criteria per edge: C1) multiple edge types and C2) in a given order. In matters of scalability, we expected that a success- ful encoding would be able to represent clearly at least four different edge types in a single cell. For our empirical tests and prototypes, we considered matrices of up to 50 nodes in size, which were either displayed within BayesPiles or in images that could fit in a standard laptop monitor. Given the limited amount of space in each matrix cell, to avoid unnecessary visual complexity and clutter, we tried to maximise the data-to-ink ratio [174] utilising the maximum number of pixels within the cell. In other words, we allowed a minimum number of pixels to remain unused, those that were necessary for distinguishing between the visual marks that encoded the different edge types. This approach produced more salient marks to encode edge types in the matrix represen- tation. Also, we based the design of those encodings on primary visual variables, such as colour, opacity, size, shape, texture, orientation, position and their combinations.

Figure 6.2: Examples of visual designs considered for encoding multiple types of edges in matrices. The top row shows an example of a single matrix and the bottom row shows the encoding for each ML type. The encodings use one or more visual variables to represent multiple edges: a) uses a coloured pie chart, b) uses opacity in a pie chart, c) uses a segmented and coloured pie chart d) uses orientation, e) combines position and colour, f) uses size and g) combines size and colour to create a glyph.

Design Space: Figure 6.2 shows some of our initial designs, created through iterations and dis- cussions with the modellers. The upper row in this figure shows the encodings for a single matrix where we need to visualise potentially multiple edge types (C1) and their order (C2). For example, design (a) uses colour and design (b) uses shades of grey to differentiate types of edges. Design (c) is a variation of design (a), using equally-spaced and coloured segments of a pie chart to indicate the presence of a lag (one segment per lag type). Design (d) uses orientation (angle) to differentiate edge types and encode their order. Design (e) uses position and colour within each cell, resulting in a striped cell design. Design (f) uses size and design (g) is a variation of design (f) which uses both size and colour to encode category and order, but instead of superimposed squares, it uses rings.

Figure 6.3: Proposed visual encodings for the different types of edges (MLs) tested in the user study: a) orientation without colour (ORI), b) orientation with colour (ORI+COL), c) position without colour (POS) and d) position with colour (POS+COL). Columns (i), (ii), (iii) and (iv) show the encoding of edge types ML0, ML1, ML2 and ML3 accordingly. Columns (v), (vii) and (vii) show how the combination of two, three and four edge types look in the different encodings.

Final Designs After we identified criteria for potentially successful encodings and explored the design space of possible combinations, we discussed potential solutions in three one-hour sessions with a team of four visualisation experts and two domain experts (i.e. computational biologists), to select the four most promising encodings which we decided to compare in our final study (Figure 6.3). We rejected designs that would easily get cluttered when they were combining multiple edge types in the same cell and those that do not make it easy to distinguish between the different types of edges. For instance, we found that encodings that used texture were easily getting cluttered and they were hard to discern in the limited space of a matrix cell. Our selected encodings use at least one of the following visual variables: position, orientation and colour hue as they can not only easily encode the four types of edges found in DBNs, but also they can scale to encode up to a dozen different types. Orientation and position can stand alone or in combination with colour, however, colour can only be used in combination with another visual variable.

When colour was used as double encoding in addition to position or orientation, several colour- ing schemes were tested. However, we found that a colour scheme using ColorBrewer [84] was more appropriate since the colours looked more balanced and distinct. Examples of the final en- codings used on the same multivariate network are shown in Figure 6.4. All four selected encod- ings could sufficiently represent networks with multiple types of edges, such as DBNs. However, we wanted to compare them and find which was the most effective for supporting the identified analysis tasks that modellers most commonly perform when they infer DBNs. Therefore, we ran a quantitative evaluation study to assess the effectiveness of the final encodings. The study involved participants from the general public who were asked to perform simple visual analysis tasks on matrices that use those encodings.

Figure 6.4: An example of the final encodings showing the same multivariate network: a) orientation without colour (ORI), b) orientation with colour (ORI+COL), c) position without colour (POS) and d) position with colour (POS+COL).