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

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

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The Karhunen-Loeve transform (KLT) [Fukunaga, 1990] is a linear transformation that allows coordinate axes to be determined in such a way as to retain as much distance information as possible. It is essentially equivalent to Principal Component Analysis (PCA) [Dunteman, 40 SIMILARITY SEARCH 1989]. , each basis vector has a length of one and any two basis vectors are orthogonal). The set V is chosen such that the spread of points in X along an axis (represented by a vector from V) is maximal. The transformation function fk{o) for an object o E X is then defined as the projection of the point o onto the first k basis vectors in V.

Range search for query R(q,r): (a) from the geometric point of view, (b) algorithm accessing the left-most leaf node. the range search constraint d(q^ Oj) < r are reported. However, in both types of nodes, we can apply some rules (bounding constraints) that would optimize the search procedure by avoiding (possibly expensive) distance computations. Such techniques are clarified in the following. , the metric objects of the searched collection. 9 demonstrates a situation in which such a bounding constraint can be beneficial with respect to the trivial sequential scan computing distances to all objects.

Tmax- Each element represents a subset of X, with an element eo of type 0 representing a single object in X. An element et of type t can give rise to one or more child elements of type 0 through t — 1, thus the search problem for et is decomposed into several smaller sub-problems. Each element of type t has an associated distance function dt{q^ et) which measures the distance from a query object q to elements of that type. For correctness, it is sufficient that dt{q^ et) < do{q, eo) for any object eo in the subset represented by et.

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

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