Detecting geographic clusters

Question

I have a R data.frame containing longitude, latitude which spans over the entire USA map. When X number of entries are all within a small geographic region of say a few degrees longitude & a few degrees latitude, I want to be able to detect this and then have my program then return the coordinates for the geographic bounding box. Is there a Python or R CRAN package that already does this? If not, how would I go about ascertaining this information?

Answer 1

I was able to combine Joran's answer along with Dan H's comment. This is an example ouput:

The python code emits functions for R: map() and rect(). This USA example map was created with:

map('state', plot = TRUE, fill = FALSE, col = palette())

and then you can apply the rect()'s accordingly from with in the R GUI interpreter (see below).

import math
from collections import defaultdict

to_rad = math.pi / 180.0   # convert lat or lng to radians
fname = "site.tsv"        # file format: LAT\tLONG
threshhold_dist=50         # adjust to your needs
threshhold_locations=15    # minimum # of locations needed in a cluster

def dist(lat1,lng1,lat2,lng2):
    global to_rad
    earth_radius_km = 6371

    dLat = (lat2-lat1) * to_rad
    dLon = (lng2-lng1) * to_rad
    lat1_rad = lat1 * to_rad
    lat2_rad = lat2 * to_rad

    a = math.sin(dLat/2) * math.sin(dLat/2) + math.sin(dLon/2) * math.sin(dLon/2) * math.cos(lat1_rad) * math.cos(lat2_rad)
    c = 2 * math.atan2(math.sqrt(a), math.sqrt(1-a)); 
    dist = earth_radius_km * c
    return dist

def bounding_box(src, neighbors):
    neighbors.append(src)
    # nw = NorthWest se=SouthEast
    nw_lat = -360
    nw_lng = 360
    se_lat = 360
    se_lng = -360

    for (y,x) in neighbors:
        if y > nw_lat: nw_lat = y
        if x > se_lng: se_lng = x

        if y < se_lat: se_lat = y
        if x < nw_lng: nw_lng = x

    # add some padding
    pad = 0.5
    nw_lat += pad
    nw_lng -= pad
    se_lat -= pad
    se_lng += pad

    # sutiable for r's map() function
    return (se_lat,nw_lat,nw_lng,se_lng)

def sitesDist(site1,site2): 
    #just a helper to shorted list comprehension below 
    return dist(site1[0],site1[1], site2[0], site2[1])

def load_site_data():
    global fname
    sites = defaultdict(tuple)

    data = open(fname,encoding="latin-1")
    data.readline() # skip header
    for line in data:
        line = line[:-1]
        slots = line.split("\t")
        lat = float(slots[0])
        lng = float(slots[1])
        lat_rad = lat * math.pi / 180.0
        lng_rad = lng * math.pi / 180.0
        sites[(lat,lng)] = (lat,lng) #(lat_rad,lng_rad)
    return sites

def main():
    sites_dict = {}
    sites = load_site_data()
    for site in sites: 
        #for each site put it in a dictionary with its value being an array of neighbors 
        sites_dict[site] = [x for x in sites if x != site and sitesDist(site,x) < threshhold_dist] 

    results = {}
    for site in sites: 
        j = len(sites_dict[site])
        if j >= threshhold_locations:
            coord = bounding_box( site, sites_dict[site] )
            results[coord] = coord

    for bbox in results:
        yx="ylim=c(%s,%s), xlim=c(%s,%s)" % (results[bbox]) #(se_lat,nw_lat,nw_lng,se_lng)
        print('map("county", plot=T, fill=T, col=palette(), %s)' % yx)
        rect='rect(%s,%s, %s,%s, col=c("red"))' % (results[bbox][2], results[bbox][0], results[bbox][3], results[bbox][2])
        print(rect)
        print("")

main()

Here is an example TSV file (site.tsv)

LAT     LONG
36.3312 -94.1334
36.6828 -121.791
37.2307 -121.96
37.3857 -122.026
37.3857 -122.026
37.3857 -122.026
37.3895 -97.644
37.3992 -122.139
37.3992 -122.139
37.402  -122.078
37.402  -122.078
37.402  -122.078
37.402  -122.078
37.402  -122.078
37.48   -122.144
37.48   -122.144
37.55   126.967

With my data set, the output of my python script, shown on the USA map. I changed the colors for clarity.

rect(-74.989,39.7667, -73.0419,41.5209, col=c("red"))
rect(-123.005,36.8144, -121.392,38.3672, col=c("green"))
rect(-78.2422,38.2474, -76.3,39.9282, col=c("blue"))

---

Addition on 2013-05-01 for Yacob

---

These 2 lines give you the over all goal...

map("county", plot=T )
rect(-122.644,36.7307, -121.46,37.98, col=c("red"))

If you want to narrow in on a portion of a map, you can use ylim and xlim

map("county", plot=T, ylim=c(36.7307,37.98), xlim=c(-122.644,-121.46))
# or for more coloring, but choose one or the other map("country") commands
map("county", plot=T, fill=T, col=palette(), ylim=c(36.7307,37.98), xlim=c(-122.644,-121.46))
rect(-122.644,36.7307, -121.46,37.98, col=c("red"))

You will want to use the 'world' map...

map("world", plot=T )

It has been a long time since I have used this python code I have posted below so I will try my best to help you.

threshhold_dist is the size of the bounding box, ie: the geographical area
theshhold_location is the number of lat/lng points needed with in
    the bounding box in order for it to be considered a cluster.

Here is a complete example. The TSV file is located on pastebin.com. I have also included an image generated from R that contains the output of all of the rect() commands.

# pyclusters.py
# May-02-2013
# -John Taylor

# latlng.tsv is located at http://pastebin.com/cyvEdx3V
# use the "RAW Paste Data" to preserve the tab characters

import math
from collections import defaultdict

# See also: http://www.geomidpoint.com/example.html
# See also: http://www.movable-type.co.uk/scripts/latlong.html

to_rad = math.pi / 180.0  # convert lat or lng to radians
fname = "latlng.tsv"      # file format: LAT\tLONG
threshhold_dist=20        # adjust to your needs
threshhold_locations=20   # minimum # of locations needed in a cluster
earth_radius_km = 6371

def coord2cart(lat,lng):
    x = math.cos(lat) * math.cos(lng)
    y = math.cos(lat) * math.sin(lng)
    z = math.sin(lat)
    return (x,y,z)

def cart2corrd(x,y,z):
    lon = math.atan2(y,x)
    hyp = math.sqrt(x*x + y*y)
    lat = math.atan2(z,hyp)
    return(lat,lng)

def dist(lat1,lng1,lat2,lng2):
    global to_rad, earth_radius_km

    dLat = (lat2-lat1) * to_rad
    dLon = (lng2-lng1) * to_rad
    lat1_rad = lat1 * to_rad
    lat2_rad = lat2 * to_rad

    a = math.sin(dLat/2) * math.sin(dLat/2) + math.sin(dLon/2) * math.sin(dLon/2) * math.cos(lat1_rad) * math.cos(lat2_rad)
    c = 2 * math.atan2(math.sqrt(a), math.sqrt(1-a)); 
    dist = earth_radius_km * c
    return dist

def bounding_box(src, neighbors):
    neighbors.append(src)
    # nw = NorthWest se=SouthEast
    nw_lat = -360
    nw_lng = 360
    se_lat = 360
    se_lng = -360

    for (y,x) in neighbors:
        if y > nw_lat: nw_lat = y
        if x > se_lng: se_lng = x

        if y < se_lat: se_lat = y
        if x < nw_lng: nw_lng = x

    # add some padding
    pad = 0.5
    nw_lat += pad
    nw_lng -= pad
    se_lat -= pad
    se_lng += pad

    #print("answer:")
    #print("nw lat,lng : %s %s" % (nw_lat,nw_lng))
    #print("se lat,lng : %s %s" % (se_lat,se_lng))

    # sutiable for r's map() function
    return (se_lat,nw_lat,nw_lng,se_lng)

def sitesDist(site1,site2): 
    # just a helper to shorted list comprehensioin below 
    return dist(site1[0],site1[1], site2[0], site2[1])

def load_site_data():
    global fname
    sites = defaultdict(tuple)

    data = open(fname,encoding="latin-1")
    data.readline() # skip header
    for line in data:
        line = line[:-1]
        slots = line.split("\t")
        lat = float(slots[0])
        lng = float(slots[1])
        lat_rad = lat * math.pi / 180.0
        lng_rad = lng * math.pi / 180.0
        sites[(lat,lng)] = (lat,lng) #(lat_rad,lng_rad)
    return sites

def main():
    color_list = ( "red", "blue", "green", "yellow", "orange", "brown", "pink", "purple" )
    color_idx = 0
    sites_dict = {}
    sites = load_site_data()
    for site in sites: 
        #for each site put it in a dictionarry with its value being an array of neighbors 
        sites_dict[site] = [x for x in sites if x != site and sitesDist(site,x) < threshhold_dist] 

    print("")
    print('map("state", plot=T)') # or use: county instead of state
    print("")


    results = {}
    for site in sites: 
        j = len(sites_dict[site])
        if j >= threshhold_locations:
            coord = bounding_box( site, sites_dict[site] )
            results[coord] = coord

    for bbox in results:
        yx="ylim=c(%s,%s), xlim=c(%s,%s)" % (results[bbox]) #(se_lat,nw_lat,nw_lng,se_lng)

        # important!
        # if you want an individual map for each cluster, uncomment this line
        #print('map("county", plot=T, fill=T, col=palette(), %s)' % yx)
        if len(color_list) == color_idx:
            color_idx = 0
        rect='rect(%s,%s, %s,%s, col=c("%s"))' % (results[bbox][2], results[bbox][0], results[bbox][3], results[bbox][1], color_list[color_idx])
        color_idx += 1
        print(rect)
    print("")


main()