Tolga Bozkaya and Z. Meral Ozsoyoglu. Indexing large metric spaces for similarity search queries. ACM Transactions on Database Systems, 24(3):361--404, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....the data set in classes according to a certain metric. Clustering algorithms proposed in the literature include: BIRCH [36] DBSCAN [17] CLIQUE [2] BIRCH [20] WaveClusters [33] CURE [23] and CLARANS [28] Those techniques focus less on the eciency of data retrieval than the MVP Tree [6], M Tree [15] SLIM Tree [27] FQ Tree [3] see [12] for a survey) We combine ideas from these structures together with special randomized techniques coming from the approximate algorithms community [5] to design a simple and ecient indexing scheme called Antipole Tree. This data structure is ....

.... de nition of range search queries and k nearest neighbor query in general metric spaces and brie y review preceding works which are relevant for the problem we are dealing with putting special emphasis on those structures whichhave been shown to be the most e ective: M Trees [15] and MVP Trees [6]. In section 3 a technique to compute the approximate diameter in a generic metric space is presented together with an ecient approximation scheme for the Euclidean case. In section 4 we describe the Antipole Tree data structure. In section 5, we presentaprocedure for range search query execution ....

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T. Bozkaya and M. Ozsoyoglu. Indexing large metric spaces for similarity search queries. ACM Transaction on Database Systems, 24(3):361-404, 1999.

....processed back in the string domain. This way the number of strings required to compare is significantly reduced. We use a multidimensional index structure to accomplish query processing in the vector domain more efficiently. There is a wide range of indexing techniques proposed in the literature [5, 9, 12, 21] which can be applied to our framework. In this paper, we investigate effective distance functions that perform better on the widely used index structures for different kinds of queries. Especially if the index fits into main memory, the queries will be executed very efficiently. For approximate ....

T. Bozkaya and Z. M. Ozsoyoglu. Indexing large metric spaces for similarity search queries. TODS, 24(3):361--404, 1999.

....for indexing of time series. For example, Deng [1998] applied kdtrees to arrange series by their significant features, Chan and Fu [1999] combined wavelet transforms with R trees, and Bozkaya and her colleagues used vantage point trees for indexing series by numeric features [Bozkaya et al. 1997; Bozkaya and 0zsoyoglu, 1999]. Park et al. 2001] indexed series by their local extrema and by properties of the segments between consecutive extrema. Li et al. 1998] proposed a retrieval technique based on a multi level abstraction hierarchy of features. Aggarwal and Yu [2000] considered grid structures, but found that the ....

Tolga Bozkaya and Z. Meral Ozsoyoglu. Indexing large metric spaces for similarity search queries. ACM Transactions on Database Systems, 24(3):361-404, 1999.

....are primarily used to partition metric spaces. 4 DATA STRUCTURES FOR METRIC SPACES 11 12 5 6 3 AB C A B C 5 45 2 1 3 4 6 Figure 5: R tree 5 71 6234 1 3 2 6 4 5 7 Figure 6: vp tree 4 Data structures for metric spaces 4. 1 Vp tree The vp tree (or vantage point tree) [5] partitions the data space around selected points and forms a hierarchical tree structure (see Figure 6) These selected points are called vantage points. Each internal node of the tree is of the form (P V ,M,R,L) where: P V is the vantage point . M is the median distance among the distances ....

....from Q is less than or equal to r: 1. If d(Q, P V ) # r, then P V is in the answer set. 2. If d(Q, P V ) r # M , then recursively search the right subtree. 3. If d(Q, P V ) r # M , then recursively search the left subtree. 4. 2 M way vp tree M way vp tree (or multi way vp tree) [5] is one of the modifications of the vp tree which decreases the height of the tree. The structure of m way vp tree of order m is very similar to the vp tree. The main difference is that it splits objects into m groups according to their distances from the vantage point. The splitting values, ....

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Bozkaya T., Ozsoyoglu M.: Indexing Large Metric Spaces for Similarity Search Queries. ACM Trans. Database Syst. 24, 3 (Sep. 1999), Pages 361 - 404.

....are primarily used to partition metric spaces. 4 DATA STRUCTURES FOR METRIC SPACES 11 1 2 5 6 3 A B C A B C 5 4 5 2 1 3 4 6 Figure 5: R #tree 5 7 1 6 2 3 4 1 3 2 6 4 5 7 Figure 6: vp#tree 4 Data structures for metric spaces 4. 1 Vp#tree The vp#tree (or vantage point tree) [5] partitions the data space around selected points and forms a hierarchical tree structure (see Figure 6) These selected points are called vantage points. Each internal node of the tree is of the form (P V ; M;R;L) where: ffl P V is the vantage point ffl M is the median distance among the ....

....distance from Q is less than or equal to r: 1. If d(Q; P V ) r, then P V is in the answer set. 2. If d(Q; P V ) r M , then recursively search the right subtree. 3. If d(Q; P V ) Gamma r M , then recursively search the left subtree. 4. 2 M#way vp#tree M#way vp#tree (or multi#way vp#tree) [5] is one of the modi Thetacations of the vp tree which decreases the height of the tree. The structure of m#way vp tree of order m is very similar to the vp tree. The main difference is that it splits objects into m groups according to their distances from the vantage point. The splitting values, ....

[Article contains additional citation context not shown here]

Bozkaya T., Ozsoyoglu M.: Indexing Large Metric Spaces for Similarity Search Queries. ACM Trans. Database Syst. 24, 3 (Sep. 1999), Pages 361 - 404.

.... provided that we set r lo and r hi to the proper values that is, r lo = r i,1 and r hi = r i for the child corresponding to S i (unless tighter bounds are maintained) Another variant of vp trees that achieves a higher fan out, termed the mvp tree, was suggested by Bozkaya and Ozsoyoglu [7, 8]. Each node in the mvp tree is essentially equivalent to the result of collapsing the nodes at several levels of a vp tree. There is one crucial difference between the mvp tree and the result of such collapsing: only one pivot is used for each level inside an mvp tree node (although the number of ....

.... three pivots would be needed in the corresponding vp tree) Observe that some subsets are partitioned using pivots that are not members of the sets, which does not occur in the vp tree (e.g. p 2 is used to partition the subset inside the ball around p 1 in Figure 14a) Bozkaya and Ozsoyoglu [7, 8] suggest using multiple partitions for each pivot, as discussed above. Hence, with k pivots per node and m partitions per pivot, the fan out of the nonleaf nodes is m k . Furthermore, they propose storing, for each data object in a leaf node, the distances to some maximum number n of ancestral ....

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T. Bozkaya and M. Ozsoyoglu. Indexing large metric spaces for similarity search queries. ACM Transactions on Database Systems, 24(3):361--404, September 1999.

....Then, a binary tree degenerates into a simple list of vantage points. Another method [20] is the generalized hyper plane tree (gh tree) which partitions the data set into two by picking two points as representatives and assigning the remaining to the closest representative. Bozkaya and Ozsoyoglu [7] [6] proposed an extension of the vp tree called multi vantage point tree (mvp tree) which chooses in a clever way m vantage points for a node which has a fanout of m 2 . The Geometric Near Access Tree (GNAT) of Brin [8] can be viewed as a refinement of the second technique presented in [9] It ....

T. Bozkaya and Z. M. zsoyoglu, "Indexing Large Metric Spaces for Similarity Search Queries," ACM Transactions on Database Systems (TODS), Vol. 24, No. 3, September 1999, pp. 361-404.

....The kd tree technique is an extension of binary search trees, which uses different features of an object at different levels of the tree, and allows the both numeric and qualitative features [Gunopulos, 2000] Deng [1998] applied this structure to index sequences by their significant features. Bozkaya [1997; 1999] used vantage point trees for indexing time series by their numerical features. Aggarwal [2000] considered the use of grid structures for a similar problem, but found that generally their performance in high dimensional space is no better than exhaustive linear search. Gunopulos [2000] and ....

Tolga Bozkaya and Meral Ozsoyoglu. Indexing Large Metric Spaces for Similarity Search Queries. Association for Computing Machinery Transactions on Database System, pages 1--34, 1999.

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Tolga Bozkaya and Z. Meral Ozsoyoglu. Indexing large metric spaces for similarity search queries. ACM Transactions on Database Systems, 24(3):361--404, 1999.

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Tolga Bozkaya and Meral Ozsoyoglu. Indexing Large Metric Spaces for Similarity Search Queries. Association for Computing Machinery Transactions on Database System, pages 1--34, 1999.

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Tolga Bozkaya and Z. Meral  Ozsoyoglu. Indexing large metric spaces for similarity search queries. acm Transactions on Database Systems, 24(3):361-404, 1999.

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Tolga Bozkaya and Z. Meral Ozsoyoglu. Indexing large metric spaces for similarity search queries. acm Transactions on Database Systems, 24(3):361-- 404, 1999.

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T. Bozkaya and Z. Ozsoyoglu. Indexing large metric spaces for similarity search queries. ACM Trans. Database Syst., 24(3):361--404, 1999.

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T. Bozkaya and M. Ozsoyoglu. Indexing large metric spaces for similarity search queries. ACM Trans.

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T. Bozkaya and Z. Ozsoyoglu. Indexing large metric spaces for similarity search queries. TODS, 24(3):361--404, 1999.

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Tolga Bozkaya and Z. Meral Ozsoyoglu. Indexing large metric spaces for similarity search queries. acm Transactions on Database Systems, 24(3):361-- 404, 1999.

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Tolga Bozkaya and Z. Meral Ozsoyoglu. Indexing large metric spaces for similarity search queries. ACM Transactions on Database Systems, 24(3):361--404, 1999.

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