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Abstract |
Similarity search is a very important operation in multimedia databases and other database applications involving complex objects, and involves finding objects in a data set S similar to a query object q, based on some distance measure d, usually a distance metric. Existing methods for handling similarity search in this setting fall into one of two classes. The first is based on mapping to a low-dimensional vector space (making use of data structures such as the R-tree), while the second directly indexes the objects based on distances (making use of data structures such as the M-tree). We introduce a general framework for performing search based on distances, and present an incremental nearest neighbor algorithm that operates on an arbitrary “search hierarchy”. We show how this framework can be applied in both classes of similarity search methods, by defining a suitable search hierarchy for a number of different indexing structures. Armed with an appropriate search hierarchy, our algorithm thus performs incremental similarity search, wherein the result objects are reported one by one in order of similarity to a query object, with as little effort as possible expended to produce each new result object. This is especially important in interactive database applications, as it makes it possible to display partial query results early. The incremental aspect also provides significant benefits in situations when the number of desired neighbors is unknown in advance. Furthermore, our algorithm is at least as efficient as existing k-nearest neighbor algorithms, in terms of the number of distance computations and index node accesses. In fact, provided that the search hierarchy is properly defined, our algorithm can be shown to be optimal in the sense of performing as few distance computations and node accesses as possible, given the available index structure. An experimental study confirms our reasoning, and suggests that the overhead due to the incremental aspect is modest, especially if distance computations are expensive and/or the indexing structure or data objects are stored on disk. |
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