如何限定 Voronoi 多边形的外部区域并与地图数据相交

Question

背景

我正在尝试使用美国地图上的 voronoi多边形 可视化以下数据在进行kmeans聚类过程后的结果。

以下是我目前正在运行的代码：

input <- read.csv("LatLong.csv", header = T, sep = ",")

# K Means Clustering

set.seed(123)
km <- kmeans(input, 17)
cent <- data.frame(km$centers)


# Visualization
states <- map_data("state")
StateMap <- ggplot() + geom_polygon(data = states, aes(x = long, y = lat, group = group), col = "white")

# Voronoi
V <- deldir(cent$long, cent$lat)

ll <-apply(V$dirsgs, 1, FUN = function(x){
  readWKT(sprintf("LINESTRING(%s %s, %s %s)", x[1], x[2], x[3], x[4]))
})

pp <- gPolygonize(ll)=
v_df <- fortify(pp)


# Plot
StateMap +
  geom_point(data = input, aes(x = long, y = lat), col = factor(km$cluster)) +
  geom_polygon(data = v_df, aes(x = long, y = lat, group = group, fill = id), alpha = .3) +
  geom_label(data = cent, aes(x = long, y = lat, label = row.names(cent)), alpha = .3)

生成以下内容

问题

我想能够绑定多边形的外部区域，并将结果区域与我的美国地图相交，以便多边形完全代表美国陆地面积。但是我一直没有弄清楚如何做到这一点。非常感谢任何帮助。

- Rick Arko

Answer 1

我的最终目标是编写一个脚本，可以任意更改 kmeans 群集的数量，并快速可视化结果，使用 voronoi 多边形覆盖所需区域。

我还没有完全实现这一点，但我已经取得了足够的进展，我认为发布我所拥有的内容可能会带来更快的解决方案。

# Create Input Data.Frame
input <- as.data.frame(cbind(x$long, x$lat))
colnames(input) <- c("long", "lat")

# Set Seed and Run Clustering Procedure
set.seed(123)
km <- kmeans(input, 35)

# Format Output for Plotting
centers <- as.data.frame(cbind(km$centers[,1], km$centers[,2]))
colnames(centers) <- c("long", "lat")
cent.id <- cbind(ID = 1:dim(centers)[1], centers)

# Create Spatial Points Data Frame for Calculating Voronoi Polygons
coords  <- centers[,1:2]
vor_pts <- SpatialPointsDataFrame(coords, centers, proj4string = CRS("+proj=longlat +datum=WGS84"))

我在网上寻找解决方案时，也发现了以下内容：function。

# Function to Extract Voronoi Polygons 

SPdf_to_vpoly <- function(sp) {
  
  # tile.list extracts the polygon data from the deldir computation
  vor_desc <- tile.list(deldir(sp@coords[,1], sp@coords[,2]))
  
  lapply(1:length(vor_desc), function(i) {
    
    # tile.list gets us the points for the polygons but we 
    # still have to close them, hence the need for the rbind
    
    tmp <- cbind(vor_desc[[i]]$x, vor_desc[[i]]$y)
    tmp <- rbind(tmp, tmp[1,])
    
    # Now we can make the polygons
    Polygons(list(Polygon(tmp)), ID = i)
  }) -> vor_polygons
  # Hopefully the caller passed in good metadata
  sp_dat <- sp@data
  
  # This way the IDs should match up with the data & voronoi polys
  rownames(sp_dat) <- sapply(slot(SpatialPolygons(vor_polygons), 'polygons'), slot, 'ID')
  
  SpatialPolygonsDataFrame(SpatialPolygons(vor_polygons), data = sp_dat)
}

有了上述函数的定义，就可以相应地提取多边形。

vor     <- SPdf_to_vpoly(vor_pts)
vor_df  <- fortify(vor)

为了使 voronoi 多边形与美国地图相匹配，我从 Census 网站下载了 cb_2014_us_state_20m 并运行了以下命令：

# US Map Plot to Intersect with Voronoi Polygons - download from census link and place in working directory
us.shp <- readOGR(dsn = ".", layer = "cb_2014_us_state_20m")
state.abb <- state.abb[!state.abb %in% c("HI", "AK")]

Low48 <- us.shp[us.shp@data$STUSPS %in% state.abb,]

# Define Area Polygons and Projections and Calculate Intersection
Low48.poly <- as(Low48, "SpatialPolygons")
vor.poly   <- as(vor, "SpatialPolygons")

proj4string(vor.poly) <- proj4string(Low48.poly)
intersect  <- gIntersection(vor.poly, Low48.poly, byid = T)


# Convert to Data Frames to Plot with ggplot
Low48_df <- fortify(Low48.poly)
int_df   <- fortify(intersect)

从这里开始，我可以像以前一样使用ggplot来可视化我的结果：

# Plot Results
StateMap <- ggplot() + geom_polygon(data = Low48_df, aes(x = long, y = lat, group = group), col = "white")

StateMap +
  geom_polygon(data = int_df, aes(x = long, y = lat, group = group, fill = id), alpha = .4) +
  geom_point(data = input, aes(x = long, y = lat), col = factor(km$cluster)) +
  geom_label(data = centers, aes(x = long, y = lat, label = row.names(centers)), alpha =.2) +
  scale_fill_hue(guide = 'none') +
  coord_map("albers", lat0 = 30, lat1 = 40)

更新摘要

重叠的voronoi多边形仍然不是完美匹配（我猜测这是由于太平洋西北地区缺乏输入数据），尽管我想这应该是一个简单的修复，我会尽快更新。此外，如果我在函数开始时更改kmeans质心的数量，然后重新运行所有内容，多边形看起来并不好看，这不是我最初希望的。我将继续更新以进行改进。

- Rick Arko