Introduction sdcSpatial: privacy protected density maps

q Plotting data on a map is a popular and helpful tool to analyze spatial data. R makes it easy to plot spatial data with packages such as ggplot2, tmap, mapview or leaflet. However when plotting the spatial distribution of a sensitive variable, e.g. income or unemployment, you may accidentally reveal a sensitive value of an individual observation. Statistical disclosure control (SDC) deals with problems related to privacy in connection with publishing statistics. SDC provides measures to assess disclosure risk and methods to reduce disclosure risk in publications while trying to minimize information loss.

Several open source tools are available; see sdcTools for a collection of them. Commonly used tools include the standalone software tools μ-argus and τ-argus as well as the R-packages sdcTable and sdcMicro.

Traditionally, SDC software operates on values of (aggregated) records, where it does not directly make use of spatial characteristics that might be present in the data.

sdcSpatial contains functions to create spatial distribution maps, assess the risk of disclosure in locations on the map and to suppress or adjust locations with revealing sensitive values.

library(sdcSpatial)

Data

sdcSpatial contains two simulated datasets with realistic locations: dwellings and enterprises. Lets have a look at the dataset enterprises.

data("enterprises")
head(enterprises)
#> Loading required package: sp
#>       coordinates production fined
#> 1 (80782, 448985)   408.8129 FALSE
#> 2 (81007, 448947)   587.0074 FALSE
#> 3 (81042, 448875)   566.2759 FALSE
#> 4 (81003, 448940)   581.8662 FALSE
#> 5 (80886, 448804)   854.1555 FALSE
#> 6 (80986, 448934)   624.2627 FALSE

enterprises is a SpatialPointsDataFrame object, but sdc_raster works equally well with sf and data.frame objects with point data (locations).

summary(enterprises)
#> Warning in CPL_crs_from_input(x): GDAL Message 1: +init=epsg:XXXX syntax is
#> deprecated. It might return a CRS with a non-EPSG compliant axis order.
#> Object of class SpatialPointsDataFrame
#> Coordinates:
#>      min    max
#> x  68507  82498
#> y 440024 448999
#> Is projected: TRUE 
#> proj4string :
#> [+init=epsg:28992 +proj=sterea +lat_0=52.15616055555555
#> +lon_0=5.38763888888889 +k=0.9999079 +x_0=155000 +y_0=463000
#> +ellps=bessel
#> +towgs84=565.2369,50.0087,465.658,-0.406857,0.350733,-1.87035,4.0812
#> +units=m +no_defs]
#> Number of points: 8348
#> Data attributes:
#>    production          fined        
#>  Min.   :    59.46   Mode :logical  
#>  1st Qu.:  1019.98   FALSE:7931     
#>  Median :  1954.32   TRUE :417      
#>  Mean   :  3249.59                  
#>  3rd Qu.:  3901.44                  
#>  Max.   :114467.56

enterprises contains two simulated variables: production (numeric) and fined (logical), and we are interested in their spatial distribution.

View the data

Let’s first plot the locations of enterprises:

sp::plot(enterprises)

There are many locations and a lot of over-plotting or occlusion is taking place: a better visualization method to reveal spatial patterns in this case is to create a raster or density plot. Since we are interested in the spatial distribution of production we would like to rasterize the data, which can be done with raster::rasterize or ggplot2::geom_tile but for didactic sake we use sdc_raster to create a raster map with a 500m grid.

production <- sdc_raster(enterprises, "production", r = 500)
plot(production, value="mean", sensitive=FALSE, main="mean production")

We have plotted the mean production, other stats are kept in the production$value object:

raster::plot(production$value[[1:3]])

The important question is:

Can we publish this map or does it contain sensitive values?

Sensitive locations

Let us see how many of the values are sensitive:

print(production)
#> numeric sdc_raster object: 
#>    resolution: 500 500 ,  max_risk: 0.95 , min_count: 10 
#>    mean sensitivity score [0,1]:  0.6432039

Printing the production object shows that when we demand that a raster cell should at least have 10 observations (min_count) and its value should not be dominated by one enterprise (max_risk), then 64% of the data in the map is sensitive!

For a 500m by 500m block a threshold of 10 enterprises is on the high side, so let us change that into 5:

production$min_count <- 5
production$max_risk <- 0.9
# or equally 
production <- sdc_raster(enterprises, "production"
                        , r = 500, min_count = 5, max_risk = 0.9)
sensitivity_score(production)
#> [1] 0.3567961

The score dropped, but which cells are we talking about?

plot(production)

sensitive_cells <- is_sensitive(production)

sensitive_cells is a raster which can be used for further inspection.

Reducing sensitivity

Let us try to reduce the sensitivity of the map using a smoothing method:

production_smoothed <- protect_smooth(production, bw = 500)
plot(production_smoothed)

In this case smoothing reduced the number of sensitive locations drastically!

Let us remove the remaining sensitive cells

production_safe <- remove_sensitive(production_smoothed)
sensitivity_score(production_safe) # check, double check
#> [1] 0

We can improve upon the “blocky” map by using raster::disaggregate. We can plot the following:

mean_production <- mean(production_safe)
mean_production <- raster::disaggregate(mean_production, 10, "bilinear")
# generated with R >= 3.6
# col <- hcl.colors(10, "YlOrRd", rev = TRUE)
col <- c("#FFFFC8", "#FEF1B2", "#FADC8A", "#F7C252", "#F5A400", "#F18000", 
         "#EB5500", "#D12D00", "#A90D00", "#7D0025")
raster::plot(mean_production, col=col)


# library(leaflet)
# leaflet() %>% 
#   leaflet::addTiles() %>% 
#   leaflet::addRasterImage(mean_production, colors = col, opacity = 0.5)

protect_quadtree is also a protecting method, which we demonstrate with the variable fined.

First we create a more fine grained (pun not intended) raster for the variable fined.

fined <- sdc_raster(enterprises, "fined", min_count = 5, r = 200, max_risk = 0.8)
print(fined)
#> logical sdc_raster object: 
#>    resolution: 200 200 ,  max_risk: 0.8 , min_count: 5 
#>    mean sensitivity score [0,1]:  0.7802503

Which is rather sensitive, let us have a look at the locations:

# col <- hcl.colors(10, rev=TRUE) # generated with R >= 3.6
col <- c("#FDE333", "#BBDD38", "#6CD05E", "#00BE7D", "#00A890"
        , "#008E98",  "#007094", "#185086", "#422C70", "#4B0055")
plot(fined, "mean", col=col)

The quadtree method aggregates sensitive cells with its 3 neighbors and does this recursively: the result is as follows:

fined_qt <- protect_quadtree(fined)
plot(fined_qt, col=col)

which has a sensitivity score of 0.

The method has the advantage of locally selecting the necessary resolution to suppress sensitive values, while the protect_smooth method uses a fixed bandwidth.

The protection result is blocky in comparison with the smoothing method, but safer if you look at the sensitive cells in high fined areas.

fined_smooth <- protect_smooth(fined, bw = 500, keep_resolution=FALSE)
plot(fined_smooth, col = col)

sensitivity_score(fined_smooth)
#> [1] 0

Thanks to `raster`

sdcSpatial builds heavily upon the excellent raster package: it creates raster maps and uses the machinery of raster to calculate sensitivity and to apply protection methods to raster maps.