ix4

2.  Sjmilarity Measures

     In the present system, documents and queries are represented as

vectors in n-dimensional Euclidean space, ~~here n is the number of

allowable concepts or index terms in the system.  Documents are retrieved

on the basis of their closeness to the query vector, with `Tcloseness"

meaning small E~iclidean distance between the vectors.  Since the document

vectors are of varying length, however, perpendicular distance at scme

fixed distance from the origin may not always be a good measure.

Normalization of the document vectors so th~t their endpoints lie on the

unit hypersphere, and use of the arc-length along the hypersphere as a

distance measure, removes this problem.  The measures used in the present

stu~r are functions of this arc length through the cosine of the angle

bet~een two document vectors.  The measures used are defined in the

following ways:


           (1) Cosine measure

                                      dd
                          5dd     =    1  2
                             12      d11~1d2

           (2) Tanimoto1s measure [4]

                          S       =          d1 ~
                             dd     ______________
                             1 2     d1~d1 + d *d  - d *d
                                              22       12

where d  and d are document vectors and S       is the similarity of
       1     2                            dld2
document one with document two.

     Bonner uses the coefficient (2) to form his document-doc~nt similarity

matrices, while Rocchio uses the cosine measure to compare documents.