[英]How to Bound the Outer Area of Voronoi Polygons and Intersect with Map Data
I'm trying to visualize the results of a kmeans
clustering procedure on the following data using voronoi polygons
on a US map. 我正在尝试在美国地图上使用voronoi polygons
对以下数据进行kmeans
聚类过程的结果可视化。
Here is the code I've been running so far: 这是到目前为止我一直在运行的代码:
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$cluster)) +
geom_polygon(data = v_df, aes(x = long, y = lat, group = group, fill = id), alpha = .3) +
geom_label(data = cent, aes(x = long, y = lat, label = row.names(cent)), alpha = .3)
I'd like to be able to bind the outer area of the polygons and intersect the resulting area with my map of the United States so that the polygons entirely represent US land area. 我希望能够绑定多边形的外部区域并将其与我的美国地图相交,以便多边形完全代表美国的陆地区域。 I haven't been able to figure out how to do this though. 我还没办法弄清楚该怎么做。 Any help is greatly appreciated. 任何帮助是极大的赞赏。
My end goal in asking this question was to write a script where I can arbitrarily change the number of kmeans
clusters and quickly visualize the results with voronoi
polygons that cover my desired area region. 我提出这个问题的最终目的是编写一个脚本,在其中我可以任意更改kmeans
簇的数量,并使用覆盖我想要的区域的voronoi
多边形快速可视化结果。
I haven't quite accomplished this yet, but I have made enough progress that I figured posting what I have may lead to a quicker solution. 我还没有完全做到这一点,但是我已经取得了足够的进步,以至于我发现发布的内容可能会导致更快的解决方案。
# Create Input Data.Frame
input <- as.data.frame(cbind(x$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$centers[,2]))
colnames(centers) <- c("long", "lat")
cent.id <- cbind(ID = 1:dim(centers)[1], centers)
# Create Spatial Points Data Frame for Calculating Voronoi Polygons
coords <- centers[,1:2]
vor_pts <- SpatialPointsDataFrame(coords, centers, proj4string = CRS("+proj=longlat +datum=WGS84"))
I also found the below. 我还发现了以下内容。 function while searching for a solution online. 功能 ,同时寻找解决的办法上网。
# Function to Extract Voronoi Polygons
SPdf_to_vpoly <- function(sp) {
# tile.list extracts the polygon data from the deldir computation
vor_desc <- tile.list(deldir(sp@coords[,1], sp@coords[,2]))
lapply(1:length(vor_desc), function(i) {
# tile.list gets us the points for the polygons but we
# still have to close them, hence the need for the rbind
tmp <- cbind(vor_desc[[i]]$x, vor_desc[[i]]$y)
tmp <- rbind(tmp, tmp[1,])
# Now we can make the polygons
Polygons(list(Polygon(tmp)), ID = i)
}) -> vor_polygons
# Hopefully the caller passed in good metadata
sp_dat <- sp@data
# This way the IDs should match up with the data & voronoi polys
rownames(sp_dat) <- sapply(slot(SpatialPolygons(vor_polygons), 'polygons'), slot, 'ID')
SpatialPolygonsDataFrame(SpatialPolygons(vor_polygons), data = sp_dat)
}
With the above function defined polygons can be extracted accordingly 通过上述功能,可以相应地提取多边形
vor <- SPdf_to_vpoly(vor_pts)
vor_df <- fortify(vor)
In order to get the voronoi
polygons to fit nicely with a US map I downloaded cb_2014_us_state_20m from the Census
website and ran the following: 为了使voronoi
多边形与美国地图很好地匹配,我从Census
网站下载了cb_2014_us_state_20m并运行了以下命令:
# US Map Plot to Intersect with Voronoi Polygons - download from census link and place in working directory
us.shp <- readOGR(dsn = ".", layer = "cb_2014_us_state_20m")
state.abb <- state.abb[!state.abb %in% c("HI", "AK")]
Low48 <- us.shp[us.shp@data$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)
From here I could visualize my results using ggplot
like before: 从这里,我可以像以前一样使用ggplot
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)
The overlapping voronoi
polygons still aren't a perfect fit (I'm guessing due to a lack of input data in the pacific northwest) although I'd imagine that should be a simple fix and I'll try to update that as soon as possible. 重叠的voronoi
多边形仍然不是一个完美的拟合(我想是由于西北太平洋地区缺乏输入数据),尽管我认为这应该是一个简单的解决方法,我会尽快对其进行更新。可能。 Also if I alter the number of kmeans centroids
in the beginning of my function and then re-run everything the polygons don't look very nice at all which is not what I was originally hoping for. 另外,如果我在函数开始时更改了kmeans centroids
的数量,然后重新运行所有多边形,这些多边形看起来根本不是很好,这并不是我最初希望的。 I'll continue to update with improvements. 我将继续改进。
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