06032005  #1 
Oversees: Search Technology & Relevancy
Join Date: Jun 2004
Posts: 1,044

The Geometry of IR
Mike Grehan informed he recently bougth C.J. (Keith) van Rijsbergen’s book The Geometry of Information Retrieval (2004, Cambridge) of with I have a copy. For those interested, this is IR research material which covers
On set and kinds for IR Vectors and Hilbert Space Linear Transformations, operators and matrices Conditional Logic in IR The Geometry of IR Linear Algebra Quantum Mechanics Probability It’s a little book but with a lot of “meat”. Recognized as one of the top IR scientists of the world., Keith elegantly uses a quantum theory approach to IR, combined with Hilbert Spaces, matrix and linear algebra and quantum mechanics. Keith’s book is a kind of interfacing device for other disciplines. Those in other fields (physicists, computational chemists, etc) can see many connections in an interdisciplinary fashion. I have the privilege of exchanging emails with prof van Rijsbergen. He mentioned to me they have Terrier, an open source search engine and that they have had funded a new network to bring together IR folk in academia and industry in Europe. These are great news! On other matters, for those interested in historical data and additional sources, David Hilbert was a brilliant mathematician who discovered spacefilling curves (used today in storage algorithms). Early in his career, Mandelbrot realized that spacefilling curves (e.g., Hilbert, Peanno) are fractals. This leads me to mention that I'm providing a reference collection: Fractals in Information Retrieval for those interested in researching these and similar topics. Regards Orion 
06032005  #2 
Member
Join Date: Sep 2004
Location: Seattle, WA
Posts: 436

Dr. Garcia,
Thanks for this terrific resource collection. There's plenty of latenight reading in this list I do have a couple questions remaining on the nature of fractals in regards to IR  perhaps these are addressed in the papers, but it would be great to get a succinct version from you here on SEW: 1. Do you consider the link structure of the web to be fractal in nature? 2. Does that fractal nature carry down all the way to a single web site? 3. Does manipulation of results (i.e. link spam) inhibit the fractal model of links on the web? 4. Is it your belief that these fractal qualities are being exploited by any of the major commercial SEs in order to improve results (at the current time), or is this research simply too new? 
06032005  #3  
Oversees: Search Technology & Relevancy
Join Date: Jun 2004
Posts: 1,044

Thanks, Rand, my good friend.
Before proceeding any further, Keith’s book is not about fractal geometry, yet he uses Hilbert Space, which is a standard fixture in many disciplines. It was Mandelbrot, who later on realized that most of David Hilbert research give rise to fractals. Back in Hilbert’s and Poicare’s times these were called math aberrations and useless anomalies. We know now this perception was far from being accurate. Another things to remember is that the terms “selfsimilar, selfsimilarity, scalefree, scaleinvariance, scaleindependence, powerlaw scaling behaviours” and similar expressions all refer to fractals. I’ll try to address your questions briefly. Quote:
BernersLee http://www.w3.org/DesignIssues/Fractal.html Kleingberg http://www.trnmag.com/Stories/090600...ets_090600.htm Andrei Broder http://www9.org/w9cdrom/160/160.html Tomkin http://alme1.almaden.ibm.com/cs/peop...fs/fractal.pdf Barabasi http://www.ncbi.nlm.nih.gov/entrez/q..._uids=10521342 Quote:
how the semantic structure (and themes, topics) across documents was constructed. For small sites, probably not. For large sites, it depends on the above and on the number of length scales involved. Many sites are not selfsimilar in connectivity or semantics. Quote:
Quote:
I do know from personal experience and by beta testing software that fractal technology is being used to organize/manage large repositories of information and for datamining. Regards Orion Last edited by orion : 06032005 at 04:20 PM. 

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