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  • Mapping (5.1)

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Context

Analysis | Visual | Mapping

New Feature: Mapping

Mapping allows you to select metrics for Nodes and Arcs and have these metrics represented graphically as node diameter and arc thickness respectively.

 Please note that the Mapping visualization is performed "live" using the current evidence set. Any changes to the evidence, while the Mapping window is open, will instantly update the Mapping.

You can also use Interactive Inference with a Scenario File or a Data Set, and thus "scroll through" visualizations of a sequence of evidence sets. If you go through these evidence sets quickly, you will get animation-like effect from the Mapping function.

Examples

The following examples will explain how the respective metrics for Nodes and Arcs are computed and visualized. We use the familiar VisitAsia network for this purpose. 

Node Analysis

The diameter of a node is computed based on the selected Node Analysis metric.

If no metric is selected, all nodes will have the same, constant diameter. Setting evidence will not have any impact.

As an option, you can choose to Display Comment Instead of Name.

The diameter of each node is is proportional to its current entropy, computed as follows,

where represents the current set of evidence, if any.

From the contextual menu of the map, you can choose to display the values of the selected metric for each node.

The number of digits used for displaying the score can be defined under Settings | Reporting

Setting evidence is will dynamically update the current Mapping. You can set evidence either via the Monitors or by using the Interactive Inference.

The diameter of each node is determined by its current Binary Entropy.

For nodes with more than two states, the Reference State is used for binarization, i.e. the Reference State versus all the other states.

When the option Display Scores on Nodes is set, the Reference State is displayed in each node

The option Fix Node Scores disables the dynamic updating of the nodes' diameter given new sets of evidence.

The diameter of each node is proportional to the probability of its Reference State.

You can define the minimum and maximum node size and arc thickness from the contextual menu via Edit Sizes.

The Relative Node Size checkbox allows you to apply the maximum size to the node with the highest score. In this case, regardless of the values of the scores, at least one node will be displayed in the maximum size.

This option is useful to rank the nodes' scores, but not suitable for comparing scores across different scenarios.

The diameter of each node is proportional to its (normalized) expected mean.

where represents the current set of evidence, if any, and is the value associated to the state n.

For nodes that are not numerical, the values associated with the states are used. If no values are associated, the first state is considered to have a value of 0, the second a value of 1, and so on.

The diameter of each node is proportional to its Node Force. This mapping is identical to the one generated in Node Force Analysis.

The diameter of each node is proportional to its Mutual Information with the Target Node.

The Target Node is Cancer in the example shown below.

When some nodes are Not Observable, you can choose to exclude them from the analysis. The diameter of the corresponding nodes are then set to the minimum.

The diameter of each node is proportional to its Mutual Information with the binarized Target Node. For Target Nodes having more than two states, the target state is used for binarization, i.e. the target state versus all the other states.

The Target Node is Cancer in the example shown below.

Arc Analysis

The thickness and color of the arcs are a function of selected Arc Analysis metric.

The thickness of the edges is constant and does not depend on any metric.

The thickness of the edges between N1 and N2 depends on the Consistency that is defined as follows:

where and are the reference states of N1 and N2 respectively, and represents the current set of evidence, if any.

The Consistency is equivalent to the Bayes Factor.

The red link between Age and Smoker indicates that the Bayes Factor is negative. That mean, given Smoker = Yes, the posterior probability of Age=Senior is lower than its marginal one. Conversely, observing Age=Senior reduces the probability of Smoker=Yes.

Hovering over an edge brings up a tooltip showing the value of the arc metric.

The thickness of each arc is proportional to its force as defined by the Kullback-Leibler Divergence:

where P is a Bayesian network including this particular arc, and Q is a network excluding this arc. If applicable, represents the current set of evidence.

The option Fix Arc Score disables the dynamic updating of the arcs' thickness given new sets of evidence.

The thickness of the arcs is proportional to its force as defined by the Mutual Information between the two linked nodes N1 and N2:

where  represents the current set of evidence, if applicable.

The thickness of the arcs is proportional to its force as defined by the Normalized Symmetric Mutual Information between the two linked nodes N1 and N2:

where H is the entropy:

and represents the current set of evidence, if any.

The thickness of the arcs is proportional to its force as defined by the Pearson's Correlation between the two linked nodes N1 and N2:

where

  • is the value associated with state n,
  • is the mean of node N,  
  • is the standard deviation of node N,
  • and is the current set of evidence, if applicable.

For nodes that are not numerical, the values associated with the states will be used for the computation. If no values are associated, the first state is considered to have a value of 0, the second a value of 1, and so on.

Layout

The initial layout of the mapping matches the current network layout in the Graph Window. However, the nodes in the Mapping Window can be moved manually and independently from the Graph Window.

Also, the graph in the Mapping Window can be rotated, either as a whole or only a selected subset of nodes. The keyboard shortcut 'P' performs the automatic layout algorithm as defined in Options | Settings | Automatic Layout.