# Geospatial searching with Xapian

Table of contents

- Introduction
- Metrics
- Indexing
- Searching
  - Sorting results by distance
  - Filtering results by distance
  - Ranking results on a combination of distance and relevance
- Performance
- References

# Introduction

This document describes a set of features present in Xapian which are designed to allow geospatial searches to be supported. Currently, the geospatial support allows sets of locations to be stored associated with each document, as latitude/longitude coordinates, and allows searches to be restricted or reordered on the basis of distance from a second set of locations.

Three types of geospatial searches are supported:

> - Returning a list of documents in order of distance from a query location. This may be used in conjunction with any Xapian query.
> - Returning a list of documents within a given distance of a query location. This may be used in conjunction with any other Xapian query, and with any Xapian sort order.
> - Returning a set of documents in a combined order based on distance from a query location, and relevance.

Locations are stored in value slots, allowing multiple independent locations to be used for a single document. It is also possible to store multiple coordinates in a single value slot, in which case the closest coordinate will be used for distance calculations.

# Metrics

A metric is a function which calculates the distance between two points.

Calculating the exact distance between two geographical points is an involved subject. In fact, even defining the meaning of a geographical point is very hard to do precisely - not only do you need to define a mathematical projection used to calculate the coordinates, you also need to choose a model of the shape of the Earth, and identify a few sample points to identify the coordinates of particular locations. Since the Earth is constantly changing shape, these coordinates also need to be defined at a particular date.

There are a few standard datums which define all these - a very common datum is the WGS84 datum, which is the datum used by the GPS system. Unless you have a good reason not to, we recommend using the WGS84 datum, since this will ensure that preset parameters of the functions built in to Xapian will have the correct values (currently, the only such parameter is the Earth radius used by the GreatCircleMetric, but more may be added in future).

Since there are lots of ways of calculating distances between two points, using different assumptions about the approximations which are valid, Xapian allows user-implemented metrics. These are subclasses of the Xapian::LatLongMetric class; see the API documentation for details on how to implement the various required methods.

There is currently only one built-in metric - the GreatCircleMetric. As the name suggests, this calculates the distance between a latitude and longitude based on the assumption that the world is a perfect sphere. The radius of the world can be specified as a constructor parameter, but defaults to a reasonable approximation of the radius of the Earth. The calculation uses the haversine formula, which is accurate for points which are close together, but can have significant error for coordinates which are on opposite sides of the sphere: on the other hand, such points are likely to be at the end of a ranked list of search results, so this probably doesn't matter.

# Indexing

To index a set of documents with location, you need to store serialised latitude-longitude coordinates in a value slot in your documents. To do this, use the LatLongCoord class. For example, this is how you might store a latitude and longitude corresponding to "London" in value slot 0:

    Xapian::Document doc;
    doc.add_value(0, Xapian::LatLongCoord(51.53, 0.08).serialise());

Of course, often a location is a bit more complicated than a single point - for example, postcode regions in the UK can cover a fairly wide area. If a search were to treat such a location as a single point, the distances returned could be incorrect by as much as a couple of miles. Xapian therefore allows you to store a set of points in a single slot - the distance calculation will return the distance to the closest of these points. This is often a good enough work around for this problem - if you require greater accuracy, you will need to filter the results after they are returned from Xapian.

To store multiple coordinates in a single slot, use the LatLongCoords class:

    Xapian::Document doc;
    Xapian::LatLongCoords coords;
    coords.append(Xapian::LatLongCoord(51.53, 0.08));
    coords.append(Xapian::LatLongCoord(51.51, 0.07));
    coords.append(Xapian::LatLongCoord(51.52, 0.09));
    doc.add_value(0, coords.serialise());

(Note that the serialised form of a LatLongCoords object containing a single coordinate is exactly the same as the serialised form of the corresponding LatLongCoord object.)

# Searching

## Sorting results by distance

If you simply want your results to be returned in order of distance, you can use the LatLongDistanceKeyMaker class to calculate sort keys. For example, to return results in order of distance from the coordinate (51.00, 0.50), based on the values stored in slot 0, and using the great-circle distance:

    Xapian::Database db("my_database");
    Xapian::Enquire enq(db);
    enq.set_query(Xapian::Query("my_query"));
    GreatCircleMetric metric;
    LatLongCoord centre(51.00, 0.50);
    Xapian::LatLongDistanceKeyMaker keymaker(0, centre, metric);
    enq.set_sort_by_key(keymaker, False);

## Filtering results by distance

To return only those results within a given distance, you can use the LatLongDistancePostingSource. For example, to return only those results within 5 miles of coordinate (51.00, 0.50), based on the values stored in slot 0, and using the great-circle distance:

    Xapian::Database db("my_database");
    Xapian::Enquire enq(db);
    Xapian::Query q("my_query");
    GreatCircleMetric metric;
    LatLongCoord centre(51.00, 0.50);
    double max_range = Xapian::miles_to_metres(5);
    Xapian::LatLongDistancePostingSource ps(0, centre, metric, max_range)
    q = Xapian::Query(Xapian::Query::OP_FILTER, q, Xapian::Query(ps));
    enq.set_query(q);

## Ranking results on a combination of distance and relevance

To return results ranked by a combination of their relevance and their distance, you can also use the LatLongDistancePostingSource. Beware that getting the right balance of weights is tricky: there is little solid theoretical basis for this, so the best approach is often to try various different parameters, evaluate the results, and settle on the best. The LatLongDistancePostingSource returns a weight of 1.0 for a document which is at the specified location, and a lower, but always positive, weight for points further away. It has two parameters, k1 and k2, which control how fast the weight decays, which can be specified to the constructor (but aren't in this example) - see the API documentation for details of these parameters.:

    Xapian::Database db("my_database");
    Xapian::Enquire enq(db);
    Xapian::Query q("my_query");
    GreatCircleMetric metric;
    LatLongCoord centre(51.00, 0.50);
    double max_range = Xapian::miles_to_metres(5);
    Xapian::LatLongDistancePostingSource ps(0, centre, metric, max_range)
    q = Xapian::Query(Xapian::Query::AND, q, Xapian::Query(ps));
    enq.set_query(q);

# Performance

The location information associated with each document is stored in a document value. This allows it to be looked up quickly at search time, so that the exact distance from the query location can be calculated. However, this method requires that the distance of each potential match is checked, which can be expensive.

To gain a performance boost, it is possible to store additional terms in documents to identify regions at various scales. There are various ways to generate such terms (for example, the O-QTM algorithm referenced below). However, the encoding for coordinates that Xapian uses has some nice properties which help here. Specifically, the standard encoded form for a coordinate used is a 6 byte representation, which identifies a point on the surface of the earth to an accuracy of 1/16 of a second (ie, at worst slightly less than 2 metre accuracy). However, this representation can be truncated to 2 bytes to represent a bounding box 1 degree on a side, or to 3, 4 or 5 bytes to get successively more accurate bounding boxes.

It would therefore be possible to gain considerable efficiency for range restricted searches by storing terms holding each of these successively more accurate representations, and to construct a query combining an appropriate set of these terms to ensure that only documents which are potentially in a range of interest are considered.

It is entirely possible that a more efficient implementation could be performed using "R trees" or "KD trees" (or one of the many other tree structures used for geospatial indexing - see http://en.wikipedia.org/wiki/Spatial_index for a list of some of these). However, using the QTM approach will require minimal effort and make use of the existing, and well tested, Xapian database. Additionally, by simply generating special terms to restrict the search, the existing optimisations of the Xapian query parser are taken advantage of.

# References

The following may be of interest.

The O-QTM algorithm is described in "Dutton, G. (1996). Encoding and handling geospatial data with hierarchical triangular meshes. In Kraak, M.J. and Molenaar, M. (eds.) Advances in GIS Research II. London: Taylor & Francis, 505-518." , a copy of which is available from http://www.spatial-effects.com/papers/conf/GDutton_SDH96.pdf

Some of the geometry needed to calculate the correct set of QTM IDs to cover a particular region is detailed in ftp://ftp.research.microsoft.com/pub/tr/tr-2005-123.pdf

Also, see: http://www.sdss.jhu.edu/htm/doc/c++/htmInterface.html