Ptolemaic indexing of the signature quadratic form distance

Abstract

The signature quadratic form distance has been introduced as an adaptive similarity measure coping with flexible content representations of multimedia data. While this distance has shown high retrieval quality, its high computational complexity underscores the need for efficient search methods. Recent research has shown that a huge improvement in search efficiency is achieved when using metric indexing. In this paper, we analyze the applicability of Ptolemaic indexing to the signature quadratic form distance. We show that it is a Ptolemaic metric and present an application of Ptolemaic pivot tables to image databases, resolving queries nearly four times as fast as the state-of-the-art metric solution, and up to 300 times as fast as sequential scan.

Combining CPU and GPU architectures for fast similarity search

“…The similarity function f s is used to determine similarity values between all pairs of representatives from the feature signatures. In our implementation we use the similarity function f s (r i , r j ) = e −αL 2 (r i ,r j ) 2 , where α is a constant for controlling the precision-indexability tradeoff, as investigated in our previous works [1,19], and L 2 denotes the Euclidean distance. In particular, lower values of the parameter α lead to better indexability, that is, to a smaller intrinsic dimensionality (iDIM) [8].…”

“…Nevertheless, recent papers showed that SQFD can be indexed by metric access methods [1] and ptolemaic indexing [19], achieving a speed-up of up to two orders of magnitude with respect to the sequential scan. In this section we review both approaches and detail the simplest and most intuitive metric/ptolemaic index: the pivot tables.…”

“…In order to reduce the computational effort, indexing [31] approaches have been applied to the SQFD. It has been shown that metric indexing [1] and ptolemaic indexing [19] reach a speed-up of more than two orders of magnitude with respect to the sequential scan. However, even when using indexing approaches, the speed-up is generally limited due to the high intrinsic dimensionality [31].…”

Visual Image Search: Feature Signatures or/and Global Descriptors

“…Furthermore, w q = (w The similarity function f s is used to determine similarity values between all pairs of representatives from the feature signatures. In our implementation, we use the similarity function f s (r i , r j ) = e −αL2(ri,rj ) 2 , where α is a constant for controlling the precision-indexability tradeoff, as investigated in previous works [4,19], and L 2 denotes the Euclidean distance. In particular, the lower values of α lead to better indexability (allowing fast search), that is, to lower values of so-called intrinsic dimensionality (iDIM) [8].…”

“…Nevertheless, recent papers showed that SQFD can be indexed by metric access methods [4] and ptolemaic indexing [19], achieving a speed-up of up to two orders of magnitude with respect to the sequential scan.…”