如何界定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kmeans在以下数据voronoi polygons上可视化聚类过程的结果.

这是我到目前为止运行的代码:

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)

制作以下内容

题

我希望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区域.我虽然无法弄清楚如何做到这一点.任何帮助是极大的赞赏.

Answer 1

我提出这个问题的最终目标是编写一个脚本，在其中我可以任意更改簇的数量，并使用覆盖我所需区域的多边形kmeans快速可视化结果。voronoi

我还没有完全完成这一点，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"))

我还发现了以下内容。在线搜索解决方案时使用该功能。

# 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)
}

通过上述函数定义的多边形可以相应地提取

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

为了使voronoi多边形与美国地图完美契合，我从网站下载了cb_2014_us_state_20mCensus并运行以下命令：

# 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)

从这里我可以像以前一样使用可视化结果ggplot：

# 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的配合（我猜测是由于太平洋西北部缺乏输入数据），尽管我认为这应该是一个简单的修复，我会尝试尽快更新。kmeans centroids另外，如果我改变函数开头的数量，然后重新运行所有内容，多边形看起来根本就不是很好，这不是我最初希望的。我将继续更新改进。