Barcode Comparator

Compare the persistence barcodes produced when the same 30 households are described using official DWP deprivation indices vs community-defined dimensions (safety, trust, green space). The bottleneck distance between the two diagrams is the mathematical signature of the difference between being measured and being heard.

H₀ bottleneck distance0.1774diagrams differ by δ_B = 0.1774
H₁ bottleneck distance0.9263diagrams differ by δ_B = 0.9263
InterpretationBottleneck distance quantifies how different two persistence diagrams are. A value near 0 means the topological features are nearly identical. A positive value means the two measurement systems record structurally different patterns of deprivation in the same population.

Official deprivation indices

Income, employment, health, education, housing (DWP index dimensions)

H₀: 29H₁: 378Showing: 29 H0 intervals
Barcode
Point cloud

Community-defined dimensions

Safety, green space, neighbourhood trust, transport, childcare

H₀: 30H₁: 406Showing: 30 H0 intervals
Barcode
Point cloud
Show text description

Barcode comparator: official vs community deprivation dimensions, 30 households. Showing H0 barcodes. Official dataset: H₀ count 29, H₁ count 378. Community dataset: H₀ count 30, H₁ count 406. Bottleneck distances: H₀ = 0.1774, H₁ = 0.9263. The divergence is the topological signature of the difference between official and community measurement.