In cpanse/recmap: Compute the Rectangular Statistical Cartogram

Introduction

This package contains a C++ implementation of the RecMap algorithm [@recmap], [@2016arXiv160600464P] to draw maps according to given statistical values. These so-called cartograms or value-by-area-maps may be used to visualize any geospatial-related data, e.g., political, economic or public health data. The input consists of a map represented by overlapping rectangles. This map is defined by the following parameters for each map region:

• a tuple of (x, y) values corresponding to the (longitude, latitude) position,
• a tuple of (dx, dy) of expansion along (longitude, latitude),
• and a statistical value z.

The (x, y) coordinates represent the center of the minimal bounding boxes (MBB), The coordinates of the MBB are derived by adding or subtracting the (dx, dy) tuple accordingly. The tuple (dx, dy) also defines the ratio of the map region. The statistical values define the desired area of each map region.

The output is a rectangular cartogram where the map regions are:

• Non-overlapping,
• connected,
• ratio and area of each rectangle correspond to the desired areas,
• rectangles are placed parallel to the axes.

The construction heuristic places the rectangles in a way that important spatial constraints, in particular

• the topology of the pseudo dual graph,
• the relative position of MBB centers.

are tried to be preserved.

The ratios are preserved, and the area of each region corresponds to the as input given statistical value z.

The graphic below depicts a typical example of a rectangular cartogram drawing.

options(prompt = "R> ",
  continue = "+  ",
  width = 70,
  useFancyQuotes = FALSE,
  warn = -1)

library(recmap)
op <- par(mar = c(0,0,0,0), bg = NA)
recmap:::.draw_recmap_us_state_ev()
par(op)
# detach("package:recmap", unload=TRUE)

The Usage

attach the package

library(recmap)

look into for documentation

help(package="recmap") 

Input - using the U.S. state Facts and Figures Dataset

usa <- data.frame(x = state.center$x, 
    y = state.center$y, 
    # make the rectangles overlapping by correcting lines of longitude distance
    dx = sqrt(state.area) / 2 / (0.8 * 60 * cos(state.center$y*pi/180)), 
    dy = sqrt(state.area) / 2 / (0.8 * 60) , 
    z = sqrt(state.area),
    name = state.name)

Compute Pseudo Dual Graph (PD)

The rectangles have to overlap to compute the dual graph. This enables to generate valid input having only the (x, y) coordinates of the map region.

library(recmap)
op <- par(mfrow = c(1 ,1), mar = c(0, 0, 0, 0), bg = NA)
plot.recmap(M <- usa[!usa$name %in% c("Hawaii", "Alaska"), ],  
            col.text = 'black', lwd=2)

Apply a Metaheuristic

The index order of the input map has an impact to the resulting cartogram. This algorithmic property is caused due to the computation of the dual graph. In [@recmap] a genetic algorithm was applied as metaheuristic. Due to the limited computing resources on the CRAN check systems, we do not use all the potential of the metaheuristic.

Study the examples of the reference manual ?recmapGA on how the GA package can be used.

Objective Functions

The topology error is an indicator of the deviation of the neighborhood relationships. The error is computed by counting the differences between dual graphs or adjacency graphs of map and cartogram

The relative positions error measures the angle difference between all region centers.

Output

The output is a data.frame object.

Cartogram <- recmap(Map <- usa[!usa$name %in% c("Hawaii", "Alaska"), ])
head(Cartogram)

Application

Rectangular Map Approximation

smp <- c(29, 22, 30, 3, 17, 8, 9, 41, 18, 15, 38, 35, 21, 23, 19, 6, 31, 32, 20, 
        28, 48, 4, 13, 14, 42, 37, 5, 16, 36 , 43, 25, 33, 12, 7, 39, 44, 2, 47,
        45, 46, 24, 10, 1,11 ,40 ,26 ,27 ,34)

op <- par(mfrow = c(1 ,1), mar = c(0, 0, 0, 0), bg = NA)
plot(Cartogram.Area <- recmap(M[smp, ]),
            col.text = 'black', lwd = 2)

summary.recmap(M)
summary(Cartogram.Area)

state.x77[, 'Population']

op <- par(mfrow = c(1 ,1), mar = c(0, 0, 0, 0), bg = NA)
usa$z <- state.x77[, 'Population']
M <- usa[!usa$name %in% c("Hawaii", "Alaska"), ]
plot(Cartogram.Population <- recmap(M[order(M$x), ]),
            col.text = 'black', lwd = 2)

# index order

smp <- c(20,47,4,40,9,6,32,33,3,10,34,22,2,28,15,12,39,7,42,45,19,13,43,30,24,
         25,11,17,37,41,26,29,21,35,8,36,14,16,31,48,46,38,23,18,1,5,44,27)

op <- par(mfrow = c(1 ,1), mar = c(0, 0, 0, 0), bg = NA)
plot(Cartogram.Population <- recmap(M[smp,]), col.text = 'black', lwd = 2)

state.x77[, 'Income']

usa$z <- state.x77[, 'Income']
M <- usa[!usa$name %in% c("Hawaii", "Alaska"), ]
op <- par(mfrow = c(1 ,1), mar = c(0, 0, 0, 0), bg = NA)
plot(Cartogram.Income <- recmap(M[order(M$x),]),
  col.text = 'black', lwd = 2)

state.x77[, 'Frost']

usa$z <- state.x77[, 'Frost'] 
M <- usa[!usa$name %in% c("Hawaii", "Alaska"), ]
op <- par(mfrow = c(1 ,1), mar = c(0, 0, 0, 0), bg = NA)
gaControl("useRcpp" = FALSE)
Frost <- recmapGA(M, seed = 1)
plot(Frost$Cartogram, 
            col.text = 'black', lwd = 2)

summary(Frost)

More interactive examples using state.x77 data are available by running the code snippet below.

# Requires to install the suggested packages
# install.packages(c('colorspace', 'maps', 'noncensus', 'shiny'))

library(shiny)

recmap_shiny <- system.file("shiny-examples", package = "recmap")
shiny::runApp(recmap_shiny, display.mode = "normal")

Synthetic input maps - checkerboard

Checkerboards provide examples of sets of map regions which do not have ideal cartogram solutions according to Definition 1 [@cartodraw].

op <- par(mar = c(0, 0, 0, 0), mfrow = c(1, 3), bg = NA)

plot(checkerboard8x8 <- checkerboard(8),
            col=c('white','white','white','black')[checkerboard8x8$z])

# found by a greedy randomized search
index.greedy <- c(8, 56, 18, 5, 13, 57, 3, 37, 62, 58, 7, 16, 40, 59, 17, 34,
                  29, 41, 46, 27, 54, 43, 2, 21, 38, 52, 31, 20, 28, 48, 1, 22,
                  55, 11, 25, 19, 50, 10, 24, 53, 47, 30, 45, 44, 32, 35, 51,
                  15, 64, 12, 14, 39, 26, 6, 42, 33, 4, 36, 63, 49, 60, 61, 9,
                  23)

plot(Cartogram.checkerboard8x8.greedy <- recmap(checkerboard8x8[index.greedy,]),
            col = c('white','white','white','black')[Cartogram.checkerboard8x8.greedy$z])

# found by a genetic algorithm
index.ga <- c(52, 10, 27, 63, 7, 20, 32, 18, 47, 28, 6, 55, 11, 61, 38, 50, 5,
              21, 36, 34, 2, 22, 3, 1, 29, 57, 43, 4, 51, 58, 31, 49, 44, 25,
              59, 33, 17, 40, 8, 41, 26, 37, 19, 56, 45, 35, 62, 53, 24, 64,
              30, 15, 39, 12, 60, 48, 16, 23, 46, 42, 13, 54, 14, 9)

plot(Cartogram.checkerboard8x8.ga <- recmap(checkerboard8x8[index.ga,]),
            col = c('white','white','white','black')[Cartogram.checkerboard8x8.ga$z])

History

The work on RecMap was initiated by understanding the limits of contiguous cartogram drawing [@cartodraw] and after studying the visualizations drawn by Erwin Raisz [@ErwinRaisz]. The purpose of the first implementation [@recmap] was a feasibility check on how computer-generated rectangular cartograms with zero area error could look like. The recmap R package on CRAN provides a rectangular cartogram algorithm to be used by any R user. Now, it is easy to generate input (e.g., no complex polygon mesh), the code is maintainable (less than 500 lines of C++-11 code), and the algorithm is made robust to the price of not having all features implemented (simplified local placement; no empty space error; no MP1 variant). Recent research publications on rectangular cartogram drawing include [@Speckmann2004], [@Speckmann2007], [@Speckmann2012], [@Buchin:2016]. However, according to a recent publication [@TheStateoftheArtInCartograms], recmap remains the only rectangular cartogram algorithm that 'maintains zero cartographic error'. The interested reader can find more details on the package usage and its implementation in [@2016arXiv160600464P].

Session Info

sessionInfo()

References

cpanse/recmap documentation built on Jan. 3, 2024, 11:45 p.m.