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HD (to, be) ∩ (HD (or, not) − 2) ∩ (HD (to, be) − 4). Thus instead of intersecting six long lists when working with W , we now have to intersect only three small lists. Obviously, this generalizes to k-tuples of words, for any k. Content-Based Information Retrieval by Group Theoretical Methods 35 After these rather classical examples let us now turn to our third example which deals with content-based music information retrieval. The reader should notice the analogy to full-text retrieval. Figure 1.
Obviously, this generalizes to k-tuples of words, for any k. Content-Based Information Retrieval by Group Theoretical Methods 35 After these rather classical examples let us now turn to our third example which deals with content-based music information retrieval. The reader should notice the analogy to full-text retrieval. Figure 1. notation. S. Bach’s Fugue in C major, BWV 846, in the piano roll Suppose we have a collection T = (T1 , . . , TN ) of scores. That is, each Ti is a score representation of a piece of music containing the notes of that piece as well as additional information such as meter, tempo or speciﬁcations of dynamics.
Definition 19 The real projective plane Π2 is the elliptic plane. The study of the elliptic plane and elliptic isometries is elliptic geometry. In the next section, we return to the study of aﬃne geometries of higher dimensional pseudo-euclidean spaces. However, we shall not study the formal properties of these spaces. Rather, our objective is to eﬃciently deﬁne the horosphere of a pseudo-euclidean space, and study some of its properties. 20. Aﬃne Geometry of pseudo-euclidean space We have seen that a projective space can be considered to be an aﬃne space with idealized points at inﬁnity .