Normalized Mutual Information

Definition

Based on Mutual Information, Normalized Mutual Information includes a normalization factor:

$$\frac{1}{{{{\log }_2}({S_X})}}$$

where $S_X$ denotes the number of states of $X$.

This means that the Mutual Information $I(X,Y)$ is divided by the maximum possible entropy of $X$, i.e., ${\log _2}({S_X})$.

With that, the formal definition of Normalized Mutual Information is:

$${I_N}(X,Y) = \frac{{I(X,Y)}}{{{{\log }_2}({S_X})}}$$

Usage

• BayesiaLab reports the Normalized Mutual Information in the Target Analysis Report: Main Menu > Analysis > Report > Target > Relationship with Target Node.

• Note that this table shows the Normalized Mutual Information of each node, e.g., XRay, Dyspnea, etc., with regard to the Target Node, Cancer.

• The Normalized Mutual Information can also be shown by selecting Main Menu > Analysis > Visual > Overall > Arc > Mutual Information and then clicking the Show Arc Comments icon or selecting Main Menu > View > Show Arc Comments.

• Note that the corresponding options under Main Menu > Preferences > Analysis > Visual Analysis > Arc's Mutual Information Analysis have to be selected first:
• In Preferences, Child refers to the Normalized Mutual Information from the Parent onto the Child node, i.e., in the direction of the arc.

• Conversely, Parent refers to the Normalized Mutual Information from the Child onto the Parent node, i.e., in the opposite direction of the arc.