# Insights from Self-Organizing Maps for Predicting Accessibility Demand for Healthcare Infrastructure

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Study Area

#### 2.2. Data Sources

^{2}). The hexagonal shape of the cell was chosen to reduce sampling bias from edge effects and the size of the grid cell was designed to provide enough granularity in our spatial data while roughly matching the average size of a DA in Surrey. This helped to minimise downscaling errors when assigning census data to hexagonal cells. We followed the method of [26] to assign the census data to each hexagonal cell (see Section 1.1 of the Supplementary Materials for a brief summary).

#### 2.3. Data Preparation

#### 2.4. Principal Component Analysis and Hierarchical Clustering

#### 2.5. Self-Organizing Maps

#### 2.6. Accessibility Analysis

## 3. Results and Discussion

#### 3.1. Insights from Principal Component Analysis

#### 3.2. Self-Organising Maps

#### 3.2.1. Relating SOM Topology to Accessibility and Travel-Time

#### 3.2.2. Attribution of Differences over Time

#### 3.2.3. Accessibility to Nearest Facility

#### 3.2.4. Cluster Change

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**,

**b**) Percentage of variance explained by the PC modes, for (

**a**) 2016 and (

**b**) 2022; (

**c**,

**d**) Dendrogram showing cluster structure and distances between clusters, for (

**c**) 2016 and (

**d**) 2022. Only ~35 subclusters are shown for ease of display. Vertical positions of the solid horizontal bars linking different clusters indicate the distance between those clusters. Dashed lines show possible cut off levels related to decreasing distances between clusters below; (

**e**–

**g**) First three PCA modes for 2016 income data (y-axis is unitless), which reveal the features that contain the most variance across each dataset.

**Figure 2.**Spatially mapped PCA topology, coloured according to clustering, for (

**a**) 2016 and (

**b**) 2022. The modes and PCs were calculated using the 2016 dataset and the 2022 data were projected onto the 2016 modes to get the 2022 PCs. White cells show no data; (

**c**) Most representative frequency distributions for each PCA cluster, showing in bold the frequency that they occur in the 2016 and 2022 maps. The y-axis on these plots varies about zero because the inputs are demeaned and normalised using their standard deviations; (

**d**) Proportion of total city population belonging to each cluster, for 2016 And 2022; (

**e**) Median age of population belonging to each cluster, for 2016 and 2022.

**Figure 3.**Spatially mapped SOM topology grouped according to income level (clusters 1 and 5 are considered high income, clusters 4 and 8 care considered low income, clusters 2, 3, 6 and 7 are excluded from the groupings), for (

**a**) 2016 and (

**b**) 2022. The 2016 data were used to train the SOM algorithm and this was used to classify both the 2016 and 2022 data. White cells show no data; (

**c**) Proportion of total city population belonging to each income type, for 2016 and 2022; (

**d**) Median age of population belonging to each income type, for 2016 and 2022.

**Figure 4.**Mean number of (

**a**) hospitals and (

**b**) walk-in clinics accessible from each cluster’s grid cells, and mean number of (

**c**) hospitals and (

**d**) walk-in clinics accessible from low- and high-income cluster groupings. Error bars show standard deviation.

**Figure 5.**Difference (from 2016–2022) in the number of seniors with access to zero, up to half and up to all facilities, for (

**a**) hospitals (all clusters), (

**b**) walk-in clinics (all clusters), (

**c**) hospitals (low vs. high income clusters) and (

**d**) walk-in clinics (low vs. high income clusters). Vertical axes are curtailed to improve readability of graphs.

**Figure 6.**Cumulative frequency distributions of travel-time to closest (

**a**) hospital and (

**b**) walk-in clinic for each cell in 2016 and 2022, grouped into low (clusters 4 and 8) and high (clusters 1 and 5) income.

**Figure 7.**Pathways of cluster changes between 2016 and 2022. Value at the centre of each box corresponds to the proportion of the cluster’s population that remained the same between 2016 and 2022. Coloured arrows show the proportion of the population of a given cluster in 2016 that transitioned to a new cluster in 2022 (e.g., 45% of all residents belonging to cluster 2 in 2016 changed to cluster 1 in 2022). Pathways with frequencies <10% are not shown.

**Figure 8.**(

**a**,

**b**) Box-and-whisker plots of cluster distance, grouped by level of accessibility, to (

**a**) hospitals and (

**b**) walk-in clinics; (

**c**–

**f**) Scatterplots showing relationships between access to healthcare facilities and the Euclidean cluster distance for each cell, with a third (coloured) variable showing the difference in median age between 2016 and 2022.

**Table 1.**Attribution of difference between 2016 and 2022 accessibility patterns. Net difference is difference in population between 2016 and 2022; this difference is decomposed into the intra-pattern variability component, pattern frequency component and combined term. The largest component in each case is highlighted in green.

Scenario | Net Difference | Intra-Pattern Variability Component $({\mathit{f}}_{\mathit{n}}\Delta {\mathit{p}}_{\mathit{n}})$ | Pattern Frequency Component $(\Delta {\mathit{f}}_{\mathit{n}}{\mathit{p}}_{\mathit{n}})$ | Combined Term | ||
---|---|---|---|---|---|---|

Hospitals | Access = 0 | Seniors | 11,775 | 5317 | 6031 | 426 |

Total pop. | 27,575 | −16,454 | 47,389 | −3359 | ||

Access > 0 | Seniors | 5595 | 11,710 | −5650 | −464 | |

Total pop. | 16,495 | 56,801 | −44,311 | 4005 | ||

Walk-in clinics | Access = 0 | Seniors | 1429 | −110 | 1392 | 148 |

Total pop. | 2620 | −6091 | 10,277 | −1565 | ||

Access > 0 | Seniors | 15,941 | 17,137 | −1011 | −186 | |

Total pop. | 41,450 | 46,438 | −7199 | 2211 |

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## Share and Cite

**MDPI and ACS Style**

Mayaud, J.R.; Anderson, S.; Tran, M.; Radić, V. Insights from Self-Organizing Maps for Predicting Accessibility Demand for Healthcare Infrastructure. *Urban Sci.* **2019**, *3*, 33.
https://doi.org/10.3390/urbansci3010033

**AMA Style**

Mayaud JR, Anderson S, Tran M, Radić V. Insights from Self-Organizing Maps for Predicting Accessibility Demand for Healthcare Infrastructure. *Urban Science*. 2019; 3(1):33.
https://doi.org/10.3390/urbansci3010033

**Chicago/Turabian Style**

Mayaud, Jerome R., Sam Anderson, Martino Tran, and Valentina Radić. 2019. "Insights from Self-Organizing Maps for Predicting Accessibility Demand for Healthcare Infrastructure" *Urban Science* 3, no. 1: 33.
https://doi.org/10.3390/urbansci3010033