How to correctly project heat map onto map

Question

I'm importing the NGA ASAM piracy database into Mathematica for analysis.

asamjson=Import["http://msi.nga.mil/MSI_JWS/ASAM_JSON/getJSON?typename=\
DateRange_AllRefNumbers&fromDate=19900101&toDate=20140801", 
 "JSON"];
Needs["GeneralUtilities`"]
asamdataset = Dataset[ToAssociations@asamjson];
piracyLocations = 
 Map[GeoPosition[ ToExpression@{#["lat"], #["lng"] }]   &, 
  asamdataset];

I can import the data fine, and get lat/longs (for some reason they're included twice in the ASAM data). I can then draw them with GeoListPlot and get map of all the piracy events.

GeoListPlot[Take[piracyLocations, 300]]

However, when I then go to make a heat map histogram things fall apart. What displayed nicely now shows up with a wildly out of skew map. It looks like I need to choose some different form of projection, but which?

dat = Map[ ToExpression@{#["lat"], #["lng"]}&,Take[asamdataset, 4000]];

histo = SmoothDensityHistogram[dat, .3, 
 ColorFunction -> "SunsetColors", PlotPoints -> 150, Mesh -> 20, 
 MeshStyle -> Opacity[.1], PlotRange -> All];

Show[histo, 
 Graphics[{FaceForm[], EdgeForm[Directive[White, Opacity[.7]]], 
 CountryData["World", "Polygon"]}]]

How do I project my heatmap of piracy events correctly onto the world?

EDIT: My first problem is that Geoposition and related functions take Lat/Long pairs. Which is Y/X, whereas other Mathematica functions take X/Y pairs.

Answer 1

You can also exploit the GeoGraphics in version 10. Using some of your variables (noting there seems to be an issue with plotting more than 4000 points or generating density histogrm with more points...that I do not fully understand):

Getting a feel:

GeoGraphics[{Red, PointSize[0.005], 
  Point[(Normal@piracyLocations)[[1 ;; 4000]]]}]

Now generating heat map:

sdh = SmoothDensityHistogram[
   Reverse[First[#]] & /@ (Normal@piracyLocations)[[1 ;; 4000]], 
   ColorFunction -> "SunsetColors", 
   PlotRange -> {{-180, 180}, {-90, 90}}];
GeoGraphics[{Opacity[0.6], sdh[[1]]}, GeoBackground -> "ReliefMap"]

Answer 2

You have mixed up latitudes and longitudes. So first of all change ToExpression@{#["lat"], #["lng"] } into ToExpression@{#["lng"], #["lat"] }. The second problem you have is that when you combine graphics with Show all the common options are taken to be that of the first graphics which in your case is the histogram, but what you really want is the aspect ratio, size etc. of the map. Just to demonstrate I did a quick fix:

Show[Graphics[{FaceForm[], EdgeForm[Directive[White, Opacity[.7]]], 
   CountryData["World", "Polygon"]}], histo, 
 Graphics[{FaceForm[], EdgeForm[Directive[White, Opacity[.7]]], 
   CountryData["World", "Polygon"]}]]

Answer 3

Off Topic, but to show another approach on showing the concentration of events using Histogram3D, which can convey the concentration of events a wee bit better.

asamjson = 
  Import["http://msi.nga.mil/MSI_JWS/ASAM_JSON/getJSON?typename=\
DateRange_AllRefNumbers&fromDate=19900101&toDate=20140801", "JSON"];
Needs["GeneralUtilities`"]
asamdataset = Dataset[ToAssociations@asamjson];
coord10 = 
  Normal@Map[ToExpression@{#["lat"], #["lng"]} &, asamdataset];
coord10[[All, 2]] = -coord10[[All, 2]];
geoRange = GeoRange -> {{-45, 68}, {-180, 180}};
background = 
  Graphics3D[{Texture[GeoGraphics[geoRange]], EdgeForm[], 
    Polygon[{{-45., 180., 0.}, {-45., -180., 0.}, {68., -180., 
       0.}, {68., 180., 0.}}, 
     VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1, 1}, {0, 1}}]}, 
   Lighting -> "Neutral"];
Show[Histogram3D[coord10, {1}, BoxRatios -> {68 + 45, 360, 90}, 
  Axes -> False, ChartStyle -> Red, Boxed -> False, 
  ViewPoint -> {-1, 0, 3}, ImageSize -> 800], background]