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  • VOS.VOSLODStatsAnalysisR(Last) -- DAVWikiAdmin? , 2017-06-13 05:38:14 Edit WebDAV System Administrator 2017-06-13 01:38:14

    Analyzing Linked Open Data with R

    Background

    The idea of statistical data analysis has never been more popular, from Nate Silver's book The Signal and the Noise: The Art and Science of Prediction to industry trends such as Big Data.

    Data itself comes in a vast variety of models, formats, and sources. Users of the R language are familiar with CSV and HDF5 files, ODBC databases, and more.

    Linked Data

    Against this sits Linked Data, based on a graph structure: simple triple statements (entity-attribute-value or EAV) using HTTP URIs to denote and dereference entities, linking pools of data by means of shared data and vocabularies (ontologies).

    For example, a photography website might use an entity for each photo it hosts, which, when dereferenced, displays a page-impression showcasing the photograph with other metadata surrounding it. This metadata is a blend of the WGS84 geo ontology (for expressing a photo's latitude and longitude) and the EXIF ontology (for expressing its ISO sensitivity). By standardizing on well-known ontologies for expressing these predicates, relationships can be built between diverse fields. For example, UK crime report data can be tied to Ordnance Survey map/gazetteer data; or a BBC service can share the same understanding of a musical genre as Last.FM by standardizing on a term from the MusicBrainz? ontology.

    The lingua franca of Linked Data is RDF, to express and store the triples, and SPARQL, to query over them.

    Worked Example

    The challenge: to explore the United Kingdom's population density using data from DBpedia.

    Collating the Data

    We start by inspecting a well-known data-point, the city of Edinburgh.

    The following URLs and URI patterns will come in handy:

    On examining the last of these, we see useful properties such as


    dbpedia-owl:populationTotal  495360  (xsd:integer)
    

    This tells us that dbpedia-owl:populationTotal is a useful predicate by which to identify a settlement's population. (Note: we do not need to search for entities of some kind of "settlement" type; merely having a populationTotal implies that the entity is a settlement and choosing the wrong kind of settlement - stipulating "it has to be a town or a city" would risk losing data such as villages and hamlets.)

    Looking further down the page, we see the two properties:


    geo:lat   55.953056  (xsd:float)
    geo:long  -3.188889  (xsd:float)
    

    Again, we do not need to know the type of the entity; that it has a latitude and longitude is sufficient.

    So far, we have some rudimentary filters we can apply to dbpedia: to make a table of latitude, longitude, and corresponding population.

    Finally, we can filter it down to places in the UK, as we see the property:


    dbpedia-owl:country  dbpedia:United_Kingdom
    

    Constructing the SPARQL Query

    We can build a SPARQL query using the above constraints, thus:


    prefix      dbpedia: <http://dbpedia.org/resource/> 
    prefix  dbpedia-owl: <http://dbpedia.org/ontology/> 
    
    SELECT DISTINCT  ?place 
                     ?latitude 
                     ?longitude 
                     ?population 
      WHERE 
        {
          ?place          dbpedia-owl:country  <http://dbpedia.org/resource/United_Kingdom> .
          ?place  dbpedia-owl:populationTotal  ?population                                  .
          ?place                      geo:lat  ?latitude                                    .
          ?place                     geo:long  ?longitude                                   .
        } 
      ORDER BY ?place 
      LIMIT 100
    

    and the resultset looks like:

    place latitude longitude population
    http://dbpedia.org/resource/Aberporth 52.1333 -4.55 2485
    http://dbpedia.org/resource/Accrington 53.7534 -2.36384 35203
    http://dbpedia.org/resource/Acomb,_North_Yorkshire 53.955 -1.126 22215
    http://dbpedia.org/resource/Adamstown,_Pitcairn_Islands -25.0667 -130.1 48
    http://dbpedia.org/resource/Aldeburgh 52.15 1.6 2793
    http://dbpedia.org/resource/Aldershot 51.247 -0.7598 33840
    http://dbpedia.org/resource/Alkborough 53.6835 -0.667179 455
    http://dbpedia.org/resource/Alkborough 53.6856 -0.667179 455
    http://dbpedia.org/resource/Alkborough 53.6835 -0.6658 455
    http://dbpedia.org/resource/Alkborough 53.6856 -0.6658 455
    http://dbpedia.org/resource/Ambleside 54.4251 -2.9626 2600
    http://dbpedia.org/resource/Applecross 57.433 -5.80958 544
    http://dbpedia.org/resource/Arthington 53.9 -1.58 561
    http://dbpedia.org/resource/Ashington 55.181 -1.568 27335

    Data Sanitization

    However, on executing this against the DBpedia SPARQL endpoint, we see some strange "noise" points. Some of these might be erroneous (Wikipedia being human-curated), but some of them arise from political arrangements such as the remains of the British Empire ? for example, Adamstown in the Pitcairn Islands (a British Overseas Territory, way out in the Pacific Ocean). Hence, to make plotting the map easier, the data is further filtered by latitude and longitude to points within a crude rectangle surrounding all the UK mainland.


    prefix      dbpedia: <http://dbpedia.org/resource/> 
    prefix  dbpedia-owl: <http://dbpedia.org/ontology/> 
    
    SELECT DISTINCT ?place 
                    ?latitude 
                    ?longitude 
                    ?population 
      WHERE 
        {
          ?place          dbpedia-owl:country  <http://dbpedia.org/resource/United_Kingdom> .
          ?place  dbpedia-owl:populationTotal  ?population                                  .
          ?place                      geo:lat  ?latitude                                    .
          ?place                     geo:long  ?longitude                                   .
          FILTER (      ?latitude > 50 
                   AND  ?latitude < 60 
                   AND ?longitude < 2
                   AND ?longitude > -7 
                 )
        }
    

    Map

    The GADM database of Global Administrative Areas site has free maps of country outlines available for download as Shapefiles, ESRI, KMZ, or R native. In this case, we download a Shapefile, unpack the zip archive, and move the file GBR_adm0.shp into the working directory.

    R

    There is an R module for executing SPARQL queries against an endpoint. We install some dependencies as follows:


    > install.packages("maptools")
    > install.packages("akima")
    > install.packages("SPARQL")
    

    The maptools library allows us to load a Shapefile into an R data frame; akima provides an interpolation function; and SPARQL provides the interface for executing queries.

    The Script


    #!/usr/bin/env Rscript
    
    library("maptools")
    library("akima")
    library("SPARQL")
    
    query<-"prefix      dbpedia: <http://dbpedia.org/resource/> 
    prefix  dbpedia-owl: <http://dbpedia.org/ontology/> 
    
    SELECT DISTINCT ?place 
                    ?latitude 
                    ?longitude 
                    ?population 
      WHERE 
        {
          ?place          dbpedia-owl:country  <http://dbpedia.org/resource/United_Kingdom> .
          ?place  dbpedia-owl:populationTotal  ?population                                  .
          ?place                      geo:lat  ?latitude                                    .
          ?place                     geo:long  ?longitude                                   .
          FILTER (      ?latitude > 50 
                   AND  ?latitude < 60 
                   AND ?longitude < 2
                   AND ?longitude > -7 
                 )
        }"
    
    plotmap<-function(map, pops, im) {
      image(im, col=terrain.colors(50))
      points(pops$results$longitude, pops$results$latitude, cex=0.25, col="#ff30000a") 
      contour(im, add=TRUE, col="brown")
      lines(map, xlim=c(-8,3), ylim=c(54,56), col="black")
    }
    
    q100<-paste(query, " limit 100")
    
    map<-readShapeLines("GBR_adm0.shp")
    
    if(!(exists("pops"))) {
      pops<-SPARQL("http://dbpedia.org/sparql/", query=query)
    }
    
    data <- pops$results[with(pops$results, order(longitude,latitude)), ]
    data <- data[with(data, order(latitude,longitude)), ]
    im <- with(data, interp(longitude, latitude, population**.25, duplicate="mean"), xo=seq(-7,1.25, length=200), yo=seq(50,58,200), linear=FALSE)
    
    plotmap(map, pops, im)
    
    fit<-lm(population ~ latitude*longitude, data)
    print(summary(fit))
    
    subd<-data[c("latitude","longitude","population")]
    print(cor(subd))
    

    Run this interactively from R:


    bash$ R
    ...
    > source("dbpedia-uk-map.R")
    ...
    

    After a few seconds to load and execute the query, you should see a map showing the outline of the UK (including a bit of Northern Ireland) with green/yellow heat-map and contour lines of the population density. Individual data-points are plotted using small blue dots.

    This is a rather na?ve plot: interpolation is not aware of water, so interpolates between Stranraer and Belfast regardless of the Irish Sea in the way; however, it looks reasonable on land, with higher values over large centers of population such as London, the Midlands, and the central belt in Scotland (from Edinburgh to Stirling to Glasgow).

    The script runs two statistical analyses:

    • a simple linear regression of population with latitude and longitude:

      Call: lm(formula = population ~ latitude * longitude, data = data) Residuals: Min 1Q Median 3Q Max -37155 -17695 -12856 -8212 62278176 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -273340.2 478917.6 -0.571 0.568 latitude 5489.0 9139.8 0.601 0.548 longitude -41694.5 146956.3 -0.284 0.777 latitude:longitude 776.8 2788.6 0.279 0.781 Residual standard error: 660500 on 9206 degrees of freedom Multiple R-squared: 7.733e-05, Adjusted R-squared: -0.0002485 F-statistic: 0.2373 on 3 and 9206 DF, p-value: 0.8704

    • correlation between latitude, longitude and population, shown as a matrix:

      latitude longitude population latitude 1.000000000 -0.291285847 0.008083111 longitude -0.291285847 1.000000000 -0.004161835 population 0.008083111 -0.004161835 1.000000000

      This shows a very slight correlation of population-density with longitude, and about twice as much correlation with latitude, but neither is statistically significant in the given data (as the p value should be less than 0.01, not up around 0.5-0.8).

    Next Steps

    SPARQL has a SERVICE keyword that allows federation, i.e., the execution of queries against multiple SPARQL endpoints, joining disparate data by common variables (a/k/a SPARQL-FED). For example, it should be possible to enrich the data by blending Geonames and the Ordnance Survey gazetteer in the query.

    Over to you to explore the data some more!