qwLSH: Cache-conscious Indexing for Processing Similarity Search Query Workloads in High-Dimensional Spaces

Similarity search queries in high-dimensional spaces are an important type of queries in many domains such as image processing, machine learning, etc. Since exact similarity search indexing techniques suffer from the well-known curse of dimensionality in high-dimensional spaces, approximate search techniques are often utilized instead. Locality Sensitive Hashing (LSH) has been shown to be an effective approximate search method for solving similarity search queries in high-dimensional spaces. Often times, queries in real-world settings arrive as part of a query workload. LSH and its variants are particularly designed to solve single queries effectively. They suffer from one major drawback while executing query workloads: they do not take into consideration important data characteristics for effective cache utilization while designing the index structures. In this paper, we present qwLSH, an index structure for efficiently processing similarity search query workloads in high-dimensional spaces. We intelligently divide a given cache during processing of a query workload by using novel cost models. Experimental results show that, given a query workload, qwLSH is able to perform faster than existing techniques due to its unique cost models and strategies.Comment: Extended version of the published wor

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

Angle Tree: Nearest Neighbor Search in High Dimensions with Low Intrinsic Dimensionality

We propose an extension of tree-based space-partitioning indexing structures for data with low intrinsic dimensionality embedded in a high dimensional space. We call this extension an Angle Tree. Our extension can be applied to both classical kd-trees as well as the more recent rp-trees. The key idea of our approach is to store the angle (the "dihedral angle") between the data region (which is a low dimensional manifold) and the random hyperplane that splits the region (the "splitter"). We show that the dihedral angle can be used to obtain a tight lower bound on the distance between the query point and any point on the opposite side of the splitter. This in turn can be used to efficiently prune the search space. We introduce a novel randomized strategy to efficiently calculate the dihedral angle with a high degree of accuracy. Experiments and analysis on real and synthetic data sets shows that the Angle Tree is the most efficient known indexing structure for nearest neighbor queries in terms of preprocessing and space usage while achieving high accuracy and fast search time.Comment: To be submitted to IEEE Transactions on Pattern Analysis and Machine Intelligenc