Original link: http://vis.pku.edu.cn/blog/%E5%A4%9A%E8%A7%86%E5%9B%BE%E5%8F%AF%E8%A7%86%E5% 8C%96%E8%AE%BE%E8%AE%A1%E7%9A%84%E5%BC%95%E5%AF%BC%E5%BC%8F%E8%AF%AD%E4%B9% 89%E6%8D%95%E6%8D%89%EF%BC%88semantic-snapping-for-guided-multi-view-visuali/
Figure 1: Semantic snapping guides user interaction to modify a multi-view visualization design
Visual information displays typically consist of multiple visualizations used to facilitate understanding of the data. However, non-expert users can create misleading or other questionable results when designing multi-view visualizations due to lack of expertise in visualization design. For example, violate the consistency constraint that the same data should be displayed in the same way and different data should be displayed in different ways. However, having users manually detect and resolve conflicts is error-prone, especially for beginners, and it can be time-consuming to come up with alternative representations. Therefore, an automatic or semi-automatic method is expected to help users detect and resolve potential problems. Challenges remain in examining relationships between views, identifying potential improvements, and implementing changes accordingly. Traditional Snapping creates a “gravity field” around geometric images, making it easier to put them together in a specific way. In this paper, Semantic Snapping means resolving mutual conflicts and redundancies when fusing together multiple separate views.
In Figure 1, the lower-left and lower-right views use the same red color, but with different semantics, which may lead to wrong inferences, which can be distinguished by changing the fill color. Also, when combining well-designed charts individually, they may display overlapping information, or use redundant screen real estate. These problems can be solved by displaying the same data in fewer views. In Figure 1, the two line graphs can be mirrored, making the overall design more compact.
Figure 2: Relationships and operations of the semantic model
In multi-view visualizations, views tend to have a dimensional grouping and multiple visual channels. Each channel has a data map, a data domain and the final visual output. The author uses four elements such as Chart grouping (G), Channel (C), Data mapping (D), and Visual output (V) to represent the features of views, and defines the relationship between individual views as semantic inconsistency and redundancy, using A semantic space with two axes to express consistency and compactness. Each relationship can be identified as a potential problem. Multi-view visualizations and their possible modifications can be placed in the semantic space. As shown in Figure 2, each modified design has more or less consistency, and more or less compactness. It is important to note that consistency and compactness are not always better, they are sometimes compromised by other design considerations. Every time the design is changed, the system re-finds the view’s relationships to infer the currently available operations.
Figure 3: Description of view relationships and predicate logic expressions
In this paper, the authors describe the relationship between views using concise predicate logic expressions. Each channel of the view has a corresponding (G, C, D, V) tuple, where G is always the same and (C, D, V) is unique for each channel. There are two views in Figure 3, with x-axis, y-axis, and a tuple of three channels for the fill color. Since the channel of the fill color has no data mapping, it is represented as D equal to 0. When comparing tuples of two views, use the corresponding lowercase letter to indicate equality or inequality. For example, g is equal to 1 if they have the same dimension grouping. d is equal to 1 if the two fields are semantically identical. The authors summarize these relationships according to existing visualization guidelines. A relationship exists between two views if there is a pair of channels from different views that satisfy one of the predicate logic formulas. Obviously, if there is a relationship between views A and B, and there is a relationship between view A and view C, then there is also a relationship between view B and view C.
Figure 4: Relationship and Expression Summary of the Semantic Model
As shown in Figure 4, the authors extracted six paradigms of view relations from the evaluation constraints of Qu et al.  and the algebraic model of Kindlmann et al. . A view’s relationship is a manifestation of redundancy or inconsistency between views. They can help users identify potential problems in the overall visual design. The six different view relationships will be introduced separately below.
Figure 5: Case of Partial Redundancy and Multiples
R1: Full Redundancy. A fully redundant relationship exists between two views if they display the exact same data, that is, they have the same grouping for all channel pairs and display the same data.
R2: Partial Redundancy. Two views are considered partially redundant if view one shows all the data that view two shows, and data that view two doesn’t. For example, in Figures 5(A) and 5(C), the two bar charts have the same grouping, with bar heights mapped to average price, but only one chart represents other quantitative data through its fill color channel. Therefore, when comparing fill color channels, they have different data mappings, and one of them does not map to any information, satisfying a partially redundant logical expression.
R3: Multiples (1). Both views have the same dimension grouping, but different data. For example, in Figure 5(A) and Figure 5(B), there are two identically grouped histograms showing different quantities through the column height channel.
R4: Multiples (2). The two views have different dimension groupings, but the data is the same. For example, in Figures 5(A) and 5(D), two differently grouped bar charts pass through the column height channel, showing the same aggregated dimension.
Figure 6: A case study on the COVID-19 dashboard
R5: Hallucinator. A hallucinator occurs when the same data is displayed in different ways, i.e., two views grouped by the same dimension, and there are the same channels that display the same data but with different visual outputs. For example, in Figure 6(2), the color channel encodes gender but uses different color scales.
R6: Confuser. If the same channel of two views has the same visual output, but the data mapping is different, it will cause confusion on the canvas. For example, in Figure 6(1), two views use the same fill color to display different data.
The view relationship determinations summarized above correspond to opportunities to improve redundancy, inconsistency. The system detects the relationship of views by iterating over all views and checking if they satisfy the expression corresponding to the rule. Each relationship has corresponding actions that break a specific relationship by changing one or more of the affected views. The four operations provided in this article are described below.
O1: Delete. Delete is the easiest operation. If there is a Full Redundancy or Partial Redundancy relationship between two views, the user can delete a view.
O2: Homogenize. The Homogenize operation is used to solve multiples and hallucinators, i.e. the problem of the same data being displayed in different ways. For example, the bar and area charts in Figure 6 display the same data dimensions in different color schemes, and these conflicts can be resolved by homogenizing the visual outputs of the views.
O3: Differentiate. The Differention operation is used to solve the Confuser’s problem that two views display different data in the same way. For example, if the same color scheme is used to display different data in Figure 6, the Difference operation will modify one of the views to a different color scheme.
O4: Integrate. The Integrate operation is used to resolve the relationship of Partial Redundancy and certain Multiples to create a more compact visual effect on the canvas. For the relationship of Partial Redundancy, there are two possible solutions: delete the view showing less data, or integrate the “missing” mapping into this view while deleting the other view. For the Multiples relationship with the same data grouping and data mapping on the x-axis, there are four ways to perform the Integrate operation: stacking, grouping, stacking, and mirroring. Overlay is the integration of multiple views into the same coordinate system, which can be applied to scatter and line charts. The mirror operation aligns two views and then mirrors one of the views, which can be applied to line, area, and bar charts. The grouping action bundles multiple views into a single view, and the stacking action stacks the views into a single view.
Figure 7: System interface and workflow of Semantic snapping
As shown in Figure 7, there are two main views in the interface of the system: the singles view and the canvas view. When a single visualization of a singles view is dragged into a canvas view, or the design of a multi-view is modified through the actions provided earlier, the system redetects the relationship and updates the corresponding action. The logic of each of the above relationships is mapped to a relationship function that contains two views. The Snapping algorithm will identify all relationships between all subsets of views. When the user selects a view, the view’s relationships are looked up and used to determine which operations are possible. After the user performs an action, the system generates a new set of views and recalculates the relationships.
This paper proposes Semantic snapping, a semi-automatic guided approach that allows users to incrementally improve multi-view visualizations, proposing concepts for precisely detecting relationships between views, and how each relationship can be resolved through manipulation. where each operation is a step in the semantic space, and the two orthogonal axes represent consistency and compactness. Users can perform system-provided operations to gradually refine the multi-view visualization design.
 YS Kristiansen, L. Garrison and S. Bruckner, “Semantic Snapping for Guided Multi-View Visualization Design,” in IEEE Transactions on Visualization and Computer Graphics , vol. 28, no. 1, pp. 43-53, Jan . 2022.
 Z. Qu and J. Hullman, “Keeping Multiple Views Consistent: Constraints, Validations, and Exceptions in Visualization Authoring,” in IEEE Transactions on Visualization and Computer Graphics , vol. 24, no. 1, pp. 468-477 , Jan. 2018.
 G. Kindlmann and C. Scheidegger, “An Algebraic Process for Visualization Design,” in IEEE Transactions on Visualization and Computer Graphics, vol. 20, no. 12, pp. 2181-2190, 31 Dec. 2014.
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