Stability of hotspots¶
The Stability of Hotspots (SoH) is a metric to determine the stability between two different hot spot analyses.
In its downward property (from parent to child, injective) it is defined as: $$ SoH^\downarrow = \frac{ParentsWithChildNodes}{Parents} = \frac{|Parents \cap Children|}{|Parents|} $$
And for its upward property (from child to parent, surjective): $$ SoH^\uparrow = \frac{ChildrenWithParent}{Children} = 1 - \frac{|Children - Parents|}{|Children|} $$
where:
- ParentsWithChildNodes is the number of parents that have at least one child, Parents is the total number of parents,
- ChildrenWithParent is the number of children and Children as the total number of children.
The SoH is defined for a range between 0 and 1, where 1 represents a perfectly stable transformation while 0 would be a transformation with no stability at all.
If |Children|=0 or |Parents|=0 SoH is 0.
Related demos: