The Torquay projectA self-organising map of 479 Torbay census areas
Thirty-six nodes, five numbers per area, no labels, and two honest scores at the end.
Four Census 2021 tables are pulled from the Nomis API for every output area in Torbay: 479 areas, 63,001 households, 14,646 of them with no car or van. Each area is reduced to five numbers: population density, the share of one-person households, the share of detached homes, the share of purpose-built flats and the share of households without a car. The numbers are standardised so that no single one dominates. The map is a six-by-six grid whose 36 nodes start as random points. For 6,000 steps the program picks an area, finds the winning node, which is the one whose five numbers are closest, and pulls that node and its grid neighbours towards the area, with the pull and the neighbourhood both shrinking over time.
Self-organising map of Torbay output areas, averages over 10 random starts, our Python run on Census 2021 data from Nomis| Measure | Trained map | Untrained random grid |
|---|
| Quantisation error (distance from an area to its node) | 0.765 | 0.817 |
| Topographic error (closest two nodes not adjacent) | 1.3% | 73.3% |
| Areas on a node: fewest, median, most | 5, 12, 25 | not measured |
Two scores judge a map. Quantisation error is the average distance between an area and the node that represents it, and training lowered it only modestly, from 0.817 to 0.765. Topographic error is the share of areas whose two closest nodes are not next to each other on the grid. That one collapsed from 73.3% to 1.3%, which is the real achievement: the grid has become a map, where moving one step changes the description only slightly. The weights confirm it. Adjacent nodes sit 0.80 apart on average, all pairs of nodes 2.28 apart, and opposite corners 4.41 apart.
Two opposite corner nodes of one trained map, our calculation| Feature | One corner | Opposite corner |
|---|
| People per square kilometre | 8,418 | 413 |
| One-person households | 27.7% | 27.5% |
| Detached homes | 3.6% | 56.1% |
| Purpose-built flats | 19.8% | 4.7% |
| Households with no car or van | 27.2% | 10.6% |
For comparison the learner runs k-means with 36 clusters on the same data. It achieves a lower quantisation error, 0.636, because it is free to put its centres wherever they fit. What it cannot offer is a layout: cluster 7 has no particular relation to cluster 8. The map gives up a little accuracy to gain an arrangement people can read. Note also what the corners do not show. The one-person share is almost identical at both ends, so on this map it varies along a different direction from density and house type. The node descriptions are averages of the model, not statements about any street or household.
Ages 8 to 11
Arrange picture cards on a grid so that neighbours look alike, then swap cards to improve it.
Ages 11 to 15
Code a one-dimensional map in Python that sorts colours into a smooth strip without being told how.
Ages 15 and up
Build the six-by-six Torbay map, compute both error scores, and compare with k-means.
Census figures and our network
Counts come from the Office for National Statistics Census 2021, served by Nomis under the Open Government Licence. The map, its error scores and the node descriptions are entirely our own calculations. Results change slightly with each random start, which is why we report an average of ten.
