Comparing Structures

The knowledgespaces.metrics module provides distance measures and agreement indices for comparing two knowledge structures or surmise relations.

Distance between structures

from knowledgespaces.metrics import symmetric_difference, hausdorff, directional_distances

# Symmetric difference: states in one but not the other
d = symmetric_difference(ks_human, ks_ai)

# Hausdorff distance: max min-Hamming-distance between states
h = hausdorff(ks_human, ks_ai)

# Directional distances (asymmetric)
dd = directional_distances(ks_human, ks_ai)
print(dd.forward_mean)   # Human→AI: how far are Human states from AI?
print(dd.backward_mean)  # AI→Human: how far are AI states from Human?

Interpretation of directional distances:

forward (H→A)	backward (A→H)	Meaning
Low	Low	Similar structures
Low	High	AI adds states beyond Human
High	Low	Human has exclusive states
High	High	Divergent structures

Agreement on prerequisites

from knowledgespaces.metrics import cohens_kappa, graph_edit_distance

# Cohen's kappa on prerequisite relations
k = cohens_kappa(rel_human, rel_ai)  # [-1, 1], 1 = perfect agreement

# Graph edit distance (edge differences)
added, removed, total = graph_edit_distance(rel_human, rel_ai)

Domain validation

All metric functions require matching domains:

# This raises ValueError:
symmetric_difference(ks_with_domain_abc, ks_with_domain_xyz)