Normalized Mutual Information

Definition

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

1logโก2(SX)\frac{1}{{{{\log }_2}({S_X})}}

where SXS_X denotes the number of states of XX.

This means that the Mutual Information I(X,Y)I(X,Y) is divided by the maximum possible entropy of XX, i.e., logโก2(SX){\log _2}({S_X}).

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

IN(X,Y)=I(X,Y)logโก2(SX){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.

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