Topology and Spatial Relationships¶

Question: Which features are dominant peaks in a geographical distribution, and how isolated are they?

Topological measures borrow concepts from physical geography — mountain isolation and prominence — and apply them to any attribute that can be treated as a virtual elevation surface.

Key concepts:

• Isolation — the horizontal distance from a local peak to the nearest observation with a higher value. A large isolation value means the feature is a dominant high point with no nearby competitor.

• Prominence — the vertical “drop” from a peak down to the saddle point connecting it to any higher peak. A large prominence means the feature stands well above its surroundings relative to its parent peak.

Together, isolation and prominence identify which local maxima are genuinely self-contained (high on both metrics) versus sub-features of a larger regional trend.