FastMap Algorithm

The FastMap algorithm, which was introduced by Faloutsos and Lin, can be used to plot document positions in a document space. A FastMap algorithm is an algorithm to map objects into points in some k-dimensional space (k is user-defined), such that the dis-similarities are preserved. The reason of using this algorithm may be, (1)it can calculate plotting position easily with existing distance calculation methods, (2)therefore more convenient in graphing the document space in any k-dimensional space, and (3)still can remain the distance differences in the graph.

The design of FastMap as a linear algorithm fulfills goals such as:

1. It solves the general problem ('distance' problem which represents difficulty in plotting N points in a k-dimensional space such that the distances are maintained as well as possible.)
   
2. It is linear on the database size, and therefore much faster than MDS and
   
3. At the same time, it leads to fast indexing, being able to map a new, arbitrary object into a k-d point in O(k) distance calculations regardless of the database size N.
   

The two benefits mentioned by the authors were: (1) efficient retrieval, and (2) visualization and data-mining, in terms of having the objects plot as points in 2-D or 3-D space, which reveals potential clusters and correlations among attributes and other regularities that data-mining is looking for.