Abstract. In 1953, Blumenthal showed that every semi-metric space that is isometrically embeddable in a Hilbert space has the n-point property; we have previously called such spaces supermetric spaces. Although this is a strictly stronger property than triangle inequality, it is nonetheless closely related and many useful metric spaces possess it. These include Euclidean, Cosine and Jensen-Shannon spaces of any dimension. A simple corollary of the n-point property is that, for any (n + 1) objects sampled from the space, there exists an n-dimensional simplex in Euclidean space whose edge lengths correspond to the distances among the objects. We show how the construction of such simplexes in higher dimensions can be used to give arbitrarily tight lower and upper bounds on distances within the original space. This allows the construction of an n-dimensional Euclidean space, from which lower and upper bounds of the original space can be calculated, and which is itself an indexable space with the n-point property. For similarity search, the engineering tradeoffs are good: we show significant reductions in data size and metric cost with little loss of accuracy, leading to a significant overall improvement in search performance.

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There are many published methods for detecting similar and near-duplicate images. Here, we consider their use in the context of unsupervised near-duplicate detection, where the task is to find a (relatively small) nearduplicate intersection of two large candidate sets. Such scenarios are of particular importance in forensic near-duplicate detection. The essential properties of a such a function are: performance, sensitivity, and specificity. We show that, as collection sizes increase, then specificity becomes the most important of these, as without very high specificity huge numbers of false positive matches will be identified. This makes even very fast, highly sensitive methods completely useless. Until now, to our knowledge, no attempt has been made to measure the specificity of near-duplicate finders, or even to compare them with each other. Recently, a benchmark set of near-duplicate images has been established which allows such assessment by giving a near-duplicate ground truth over a large general image collection. Using this we establish a methodology for calculating specificity. A number of the most likely candidate functions are compared with each other and accurate measurement of sensitivity vs. specificity are given. We believe these are the first such figures be to calculated for any such function.

Abstract. Persistent programming systems are designed as an implementation technology for long lived, concurrently accessed and potentially large bodies of data and programs, known here as persistent application systems (PASs). Within a PAS the persistence concept is used to abstract over the physical properties of data such as where it is kept, how long it is kept and in what form it is kept. As such it is seen as having a number of benefits in simplifying the task of PAS programming. Here, we describe the integrated design of the Napier88 persistent programming system and how Napier88 may be used to develop PASs.

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A GLObal Smart Space (GLOSS) provides support for interaction amongst people, artefacts and places while taking account of both context and movement on a global scale. Crucial to the definition of a GLOSS is the provision of a set of location-aware services that detect, convey, store and exploit location information. We use one of these services, hearsay, to illustrate the implementation dimensions of a GLOSS. The focus of the paper is on both local and global software architecture to support the implementation of such services. The local architecture is based on XML pipe-lines and is used to construct location-aware components. The global architecture is based on a hybrid peer-to-peer routing scheme and provides the local architectures with the means to communicate in the global context.Comment: 4th International Conference on Mobile Data Management (MDM 2003

Metric search is concerned with the efficient evaluation of queries in metric spaces. In general, a large space of objects is arranged in such a way that, when a further object is presented as a query, those objects most similar to the query can be efficiently found. Most mechanisms rely upon the triangle inequality property of the metric governing the space. The triangle inequality property is equivalent to a finite embedding property, which states that any three points of the space can be isometrically embedded in two-dimensional Euclidean space. In this paper, we examine a class of semimetric space which is finitely four-embeddable in three-dimensional Euclidean space. In mathematics this property has been extensively studied and is generally known as the four-point property. All spaces with the four-point property are metric spaces, but they also have some stronger geometric guarantees. We coin the term supermetric 1 space as, in terms of metric arXiv:1707.08361v2 [cs.IR] 22 Oct 2017 search, they are significantly more tractable. Supermetric spaces include all those governed by Euclidean, Cosine 2 , Jensen-Shannon and Triangular distances, and are thus commonly used within many domains. In previous work we have given a generic mathematical basis for the supermetric property and shown how it can improve indexing performance for a given exact search structure. Here we present a full investigation into its use within a variety of different hyperplane partition indexing structures, and go on to show some more of its flexibility by examining a search structure whose partition and exclusion conditions are tailored, at each node, to suit the individual reference points and data set present there. Among the results given, we show a new best performance for exact search using a well-known benchmark.

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