Download Similarity Search The Metric Space Approach by Zezula P., Amato G., Dohnal V., Batko M. PDF

By Zezula P., Amato G., Dohnal V., Batko M.

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To be able to exploit the index structure, the concept of lower-bound distance functions is used, as explained in the following. e. Voi,02 G V : dp{oi,02) < 4(01,02),dp(oi,02) < c/^(oi,02). Therefore, we can use dp to search the index structure which has been built using di) and retrieve only "promising" objects. Next, we use du to filter out irrelevant (false positive) matches. More specifically, we retrieve a correct result-set for the user-specified query. Following the equations above, we can use dp in a particular evaluation of a similarity query in the index structure, because every distance measured by dp will always be less than or equal to d^.

15a shows an example of generalized hyperplane partitioning in which pivots pi,p2 are used to divide the space into two subspaces - objects nearer pi belonging to the left subspace and objects nearer to p2 to the right. The vertical dashed line represents points equidistant from both pivots. With this partitioning we cannot establish an upper bound on the distance from query object q to database objects o^, because the database objects may be arbitrarily far away from the pivots. Thus only lower limits can be defined.

For all objects o G Ui ^i» ^^e algorithm evaluates all query predicates and establishes theirfinalranks. Then thefirstk objects are returned as a result. This algorithm is correct, but its performance is not very optimal and the expected query execution costs can be quite high. , 1998b] have concentrated on complex similarity queries expressed through a generic language. , from the same metric space. Contrary to the language level that deals with similarity scores, the proposed evaluation process is based on distances between feature values, because metric indexes can use just distances to evaluate predicates.

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