HD-Index: Pushing the Scalability-Accuracy Boundary for Approximate kNN Search in High-Dimensional Spaces

Nearest neighbor searching of large databases in high-dimensional spaces is inherently difficult due to the curse of dimensionality. A flavor of approximation is, therefore, necessary to practically solve the problem of nearest neighbor search. In this paper, we propose a novel yet simple indexing scheme, HD-Index, to solve the problem of approximate k-nearest neighbor queries in massive high-dimensional databases. HD-Index consists of a set of novel hierarchical structures called RDB-trees built on Hilbert keys of database objects. The leaves of the RDB-trees store distances of database objects to reference objects, thereby allowing efficient pruning using distance filters. In addition to triangular inequality, we also use Ptolemaic inequality to produce better lower bounds. Experiments on massive (up to billion scale) high-dimensional (up to 1000+) datasets show that HD-Index is effective, efficient, and scalable.Comment: PVLDB 11(8):906-919, 201

Effectiveness of landmark analysis for establishing locality in p2p networks

Locality to other nodes on a peer-to-peer overlay network can be established by means of a set of landmarks shared among the participating nodes. Each node independently collects a set of latency measures to landmark nodes, which are used as a multi-dimensional feature vector. Each peer node uses the feature vector to generate a unique scalar index which is correlated to its topological locality. A popular dimensionality reduction technique is the space filling Hilbert’s curve, as it possesses good locality preserving properties. However, there exists little comparison between Hilbert’s curve and other techniques for dimensionality reduction. This work carries out a quantitative analysis of their properties. Linear and non-linear techniques for scaling the landmark vectors to a single dimension are investigated. Hilbert’s curve, Sammon’s mapping and Principal Component Analysis have been used to generate a 1d space with locality preserving properties. This work provides empirical evidence to support the use of Hilbert’s curve in the context of locality preservation when generating peer identifiers by means of landmark vector analysis. A comparative analysis is carried out with an artificial 2d network model and with a realistic network topology model with a typical power-law distribution of node connectivity in the Internet. Nearest neighbour analysis confirms Hilbert’s curve to be very effective in both artificial and realistic network topologies. Nevertheless, the results in the realistic network model show that there is scope for improvements and better techniques to preserve locality information are required

M-Grid : A distributed framework for multidimensional indexing and querying of location based big data

The widespread use of mobile devices and the real time availability of user-location information is facilitating the development of new personalized, location-based applications and services (LBSs). Such applications require multi-attribute query processing, handling of high access scalability, support for millions of users, real time querying capability and analysis of large volumes of data. Cloud computing aided a new generation of distributed databases commonly known as key-value stores. Key-value stores were designed to extract value from very large volumes of data while being highly available, fault-tolerant and scalable, hence providing much needed features to support LBSs. However complex queries on multidimensional data cannot be processed efficiently as they do not provide means to access multiple attributes. In this thesis we present MGrid, a unifying indexing framework which enables key-value stores to support multidimensional queries. We organize a set of nodes in a P-Grid overlay network which provides fault-tolerance and efficient query processing. We use Hilbert Space Filling Curve based linearization technique which preserves the data locality to efficiently manage multi-dimensional data in a key-value store. We propose algorithms to dynamically process range and k nearest neighbor (kNN) queries on linearized values. This removes the overhead of maintaining a separate index table. Our approach is completely independent from the underlying storage layer and can be implemented on any cloud infrastructure. Experiments on Amazon EC2 show that MGrid achieves a performance improvement of three orders of magnitude in comparison to MapReduce and four times to that of MDHBase scheme --Abstract, pages iii-iv