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

Efficient Document Indexing Using Pivot Tree

We present a novel method for efficiently searching top-k neighbors for documents represented in high dimensional space of terms based on the cosine similarity. Mostly, documents are stored as bag-of-words tf-idf representation. One of the most used ways of computing similarity between a pair of documents is cosine similarity between the vector representations, but cosine similarity is not a metric distance measure as it doesn't follow triangle inequality, therefore most metric searching methods can not be applied directly. We propose an efficient method for indexing documents using a pivot tree that leads to efficient retrieval. We also study the relation between precision and efficiency for the proposed method and compare it with a state of the art in the area of document searching based on inner product.Comment: 6 Pages, 2 Figure

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