FastMap: A Fast Algorithm for Indexing, Data-Mining and Visualization of Traditional and Multimedia Datasets.

@inproceedings{DBLP:conf/sigmod/FaloutsosL95,
  author    = {Christos Faloutsos and
               King-Ip Lin},
  editor    = {Michael J. Carey and
               Donovan A. Schneider},
  title     = {FastMap: A Fast Algorithm for Indexing, Data-Mining and Visualization
               of Traditional and Multimedia Datasets},
  booktitle = {Proceedings of the 1995 ACM SIGMOD International Conference on
               Management of Data, San Jose, California, May 22-25, 1995},
  publisher = {ACM Press},
  year      = {1995},
  pages     = {163-174},
  ee        = {http://doi.acm.org/10.1145/223784.223812, db/conf/sigmod/sigmod95-12.html},
  crossref  = {DBLP:conf/sigmod/95},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

Abstract

A very promising idea for fast searching in traditional and multimedia databases is to map objects into points in k-d space, using k feature-extraction functions, provided by a domain expert [Jagadish, SIGMOD Conf. 1991: 208-217]. Thus, we can subsequently use highly fine-tuned spatial access methods (SAMs), to answer several types of queries, including the `Query By Example' type (which translates to a range query); the `all pairs' query (which translates to a spatial join [Brinkhoff, SIGMOD Conf. 1994: 197-208]); the nearest-neighbor or best-match query, etc.

However, designing feature extraction functions can be hard. It is relatively easier for a domain expert to assess the similarity/distance of two objects. Given only the distance information though, it is not obvious how to map objects into points.

This is exactly the topic of this paper. We describe a fast algorithm to map objects into points in some k-dimensional space (k is user-defined), such that the dis-similarities are preserved. There are two benefits from this mapping: (a) efficient retrieval, in conjunction with a SAM, as discussed before and (b) visualization and data-mining: the objects can now be plotted as points in 2-d or 3-d space, revealing potential clusters, correlations among attributes and other regularities that data-mining is looking for.

We introduce an older method from pattern recognition, namely, Multi-Dimensional Scaling (MDS); although unsuitable for indexing, we use it as yardstick for our method. Then, we propose a much faster algorithm to solve the problem in hand, while in addition it allows for indexing. Experiments on real and synthetic data indeed show that the proposed algorithm is significantly faster than MDS, (being linear, as opposed to quadratic, on the database size N), while it manages to preserve distances and the overall structure of the data-set.

Copyright © 1995 by the ACM, Inc., used by permission. Permission to make digital or hard copies is granted provided that copies are not made or distributed for profit or direct commercial advantage, and that copies show this notice on the first page or initial screen of a display along with the full citation.

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