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Ranking
Local WLC - neighbourhood-adaptive weighted linear combination
Range-sensitive neighbourhood-local additive utility - criterion weights scale with local criterion variance within each spatial neighbourhood
Malczewski, J.2011doi:10.1111/j.1467-9671.2011.01275.x ↗
Overview
V(A^q_i) reflects both criterion performance and how important each criterion is within the alternative's spatial neighbourhood. An alternative that excels on a criterion which is locally highly variable (high r^q_k/r_k) benefits more than one that excels on a criterion where all neighbours are similar. Always inspect the local weight table (output G.local_weights) and the range-ratio table (output G.range_ratios) to understand what drove the ranking in each neighbourhood.
- Output
- locally-adjusted utility, higher is better
- Data
- Crisp, complete numeric + neighbourhood assignments
- Weights
- Needs a weight source
- Size
- 4+ alternatives, 2-8 criteria works best
- Used for
- Land suitability analysis, ecological zoning, urban vulnerability assessment, Regional planning, GIS-based environmental monitoring
Fits when / Look elsewhere when
Fits when
- •Automatically adjusts criterion importance to reflect local data variability (range-sensitivity principle)
- •No additional subjective input required beyond global weights and neighbourhood definition
- •Interpretable: the range-ratio table explains why local weights differ from global weights
- •Reduces to standard WLC when criterion variability is spatially homogeneous
Look elsewhere when
- •Non-spatial problem - no neighbourhood structure. Use SAW.
- •Only one alternative per neighbourhood. Local range undefined.
- •All neighbourhoods have equal criterion spreads. Standard WLC is sufficient.
Assumptions to verify
- Neighbourhood partition is meaningful and justified (not arbitrary zone boundaries)
- Each neighbourhood contains at least 2 alternatives
- Range-sensitivity principle holds: criteria with wider local spread should receive higher local weight
- Global normalisation is appropriate (all alternatives in same measurement context)
Limitations
- •Neighbourhood definition choice is critical and subjective
- •Zero local range is a degenerate case requiring special handling
- •Requires at least 2 alternatives per neighbourhood
- •Cross-neighbourhood score comparisons rely on global normalisation being sensible
Edge cases and pitfalls
Neighbourhood boundary choice is critical. Redrawing zones changes local ranges and hence local weights. Always perform sensitivity analysis over neighbourhood scheme.
Zero local range (all alternatives in a neighbourhood identical on one criterion) is pathological. Criterion provides no discriminating power locally. Apply fallback to global weight (E-4 warning).
Cross-neighbourhood score comparisons are valid because global normalisation (F1) is applied before local weights. Do not apply local normalisation instead of global - this would make scores incomparable across neighbourhoods.
How to cite
Malczewski, J. (2011). Local weighted linear combination. Transactions in GIS. https://doi.org/10.1111/j.1467-9671.2011.01275.x
System ID, as it appears in reports and the API
LOCAL-WLC