| content
| - ---+ Analyzing Linked Open Data with R
%TOC%
---++ Background
The idea of statistical data analysis has never been more popular, from Nate
Silver's book <i>The Signal and the Noise: The Art and Science of Prediction</i> to
industry trends such as <i>Big Data.</i>
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 [[http://en.wikipedia.org/wiki/Linked_data][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 <i>lingua franca</i> 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:
* [[http://dbpedia.org/sparql][http://dbpedia.org/sparql]] - the DBpedia SPARQL endpoint against which
queries are executed
* [[http://en.wikipedia.org/wiki/Edinburgh][http://en.wikipedia.org/wiki/Edinburgh]] - a page in Wikipedia about
Edinburgh
* <b><tt>dbpprop:title</tt></b> - a CURIE, identifying the <i>title</i> attribute within
the <i>dbpprod</i> namespace ([[http://dbpedia.org/property/][http://dbpedia.org/property/]]), thereby assigning a
title ("The City of Edinburgh").
* [[http://dbpedia.org/resource/Edinburgh][http://dbpedia.org/resource/Edinburgh]] - an identifier for a DBpedia
resource, comprised of data automatically extracted from the corresponding Wikipedia page; if
you view it in a Web browser, it redirects to:
* [[http://dbpedia.org/page/Edinburgh][http://dbpedia.org/page/Edinburgh]] - a human-readable view of the DBpedia
resource, showing its attributes and values
On examining the last of these, we see useful properties such as
<verbatim>
dbpedia-owl:populationTotal 495360 (xsd:integer)
</verbatim>
This tells us that <b><tt>dbpedia-owl:populationTotal</tt></b> 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 <tt>populationTotal</tt>
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:
<verbatim>
geo:lat 55.953056 (xsd:float)
geo:long -3.188889 (xsd:float)
</verbatim>
Again, we do not need to know the type of the entity; that it has a <tt>latitude</tt>
and <tt>longitude</tt> is sufficient.
So far, we have some rudimentary filters we can apply to <tt>dbpedia:</tt> 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:
<verbatim>
dbpedia-owl:country dbpedia:United_Kingdom
</verbatim>
---+++Constructing the SPARQL Query
We can build a SPARQL query using the above constraints, thus:
<verbatim>
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
</verbatim>
and the resultset looks like:
| *place* | *latitude* | *longitude* | *population* |
| [[http://dbpedia.org/resource/Aberporth][http://dbpedia.org/resource/Aberporth]] | 52.1333 | -4.55 | 2485 |
| [[http://dbpedia.org/resource/Accrington][http://dbpedia.org/resource/Accrington]] | 53.7534 | -2.36384 | 35203 |
| [[http://dbpedia.org/resource/Acomb,_North_Yorkshire][http://dbpedia.org/resource/Acomb,_North_Yorkshire]] | 53.955 | -1.126 | 22215 |
| [[http://dbpedia.org/resource/Adamstown,_Pitcairn_Islands][http://dbpedia.org/resource/Adamstown,_Pitcairn_Islands]] | -25.0667 | -130.1 | 48 |
| [[http://dbpedia.org/resource/Aldeburgh][http://dbpedia.org/resource/Aldeburgh]] | 52.15 | 1.6 | 2793 |
| [[http://dbpedia.org/resource/Aldershot][http://dbpedia.org/resource/Aldershot]] | 51.247 | -0.7598 | 33840 |
| [[http://dbpedia.org/resource/Alkborough][http://dbpedia.org/resource/Alkborough]] | 53.6835 | -0.667179 | 455 |
| [[http://dbpedia.org/resource/Alkborough][http://dbpedia.org/resource/Alkborough]] | 53.6856 | -0.667179 | 455 |
| [[http://dbpedia.org/resource/Alkborough][http://dbpedia.org/resource/Alkborough]] | 53.6835 | -0.6658 | 455 |
| [[http://dbpedia.org/resource/Alkborough][http://dbpedia.org/resource/Alkborough]] | 53.6856 | -0.6658 | 455 |
| [[http://dbpedia.org/resource/Ambleside][http://dbpedia.org/resource/Ambleside]] | 54.4251 | -2.9626 | 2600 |
| [[http://dbpedia.org/resource/Applecross][http://dbpedia.org/resource/Applecross]] | 57.433 | -5.80958 | 544 |
| [[http://dbpedia.org/resource/Arthington][http://dbpedia.org/resource/Arthington]] | 53.9 | -1.58 | 561 |
| [[http://dbpedia.org/resource/Ashington][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.
<verbatim>
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
)
}
</verbatim>
---++ Map
The [[http://gadm.org/][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 <tt>GBR_adm0.shp</tt> into the working directory.
---++R
There is an R module for executing SPARQL queries against an endpoint. We
install some dependencies as follows:
<verbatim>
> install.packages("maptools")
> install.packages("akima")
> install.packages("SPARQL")
</verbatim>
The <i>maptools</i> library allows us to load a Shapefile into an R data frame; <i>akima</i>
provides an interpolation function; and <i>SPARQL</i> provides the interface for executing queries.
---+++ The Script
<verbatim>
#!/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))
</verbatim>
Run this interactively from R:
<verbatim>
bash$ R
...
> source("dbpedia-uk-map.R")
...
</verbatim>
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.
<img src="%ATTACHURLPATH%/Rplot001.png" style="wikiautogen" width="512" height="512" />
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:
<verbatim>
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
</verbatim>
* correlation between latitude, longitude and population, shown as a matrix:
<verbatim>
latitude longitude population
latitude 1.000000000 -0.291285847 0.008083111
longitude -0.291285847 1.000000000 -0.004161835
population 0.008083111 -0.004161835 1.000000000
</verbatim>
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 <i>p</i> value should be less than 0.01, not up
around 0.5-0.8).
---++ Next Steps
SPARQL has a <tt>SERVICE</tt> 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!
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