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

Incremental dimension reduction of tensors with random index

We present an incremental, scalable and efficient dimension reduction technique for tensors that is based on sparse random linear coding. Data is stored in a compactified representation with fixed size, which makes memory requirements low and predictable. Component encoding and decoding are performed on-line without computationally expensive re-analysis of the data set. The range of tensor indices can be extended dynamically without modifying the component representation. This idea originates from a mathematical model of semantic memory and a method known as random indexing in natural language processing. We generalize the random-indexing algorithm to tensors and present signal-to-noise-ratio simulations for representations of vectors and matrices. We present also a mathematical analysis of the approximate orthogonality of high-dimensional ternary vectors, which is a property that underpins this and other similar random-coding approaches to dimension reduction. To further demonstrate the properties of random indexing we present results of a synonym identification task. The method presented here has some similarities with random projection and Tucker decomposition, but it performs well at high dimensionality only (n>10^3). Random indexing is useful for a range of complex practical problems, e.g., in natural language processing, data mining, pattern recognition, event detection, graph searching and search engines. Prototype software is provided. It supports encoding and decoding of tensors of order >= 1 in a unified framework, i.e., vectors, matrices and higher order tensors.Comment: 36 pages, 9 figure

De Novo Assembly of Nucleotide Sequences in a Compressed Feature Space

Sequencing technologies allow for an in-depth analysis of biological species but the size of the generated datasets introduce a number of analytical challenges. Recently, we demonstrated the application of numerical sequence representations and data transformations for the alignment of short reads to a reference genome. Here, we expand out approach for de novo assembly of short reads. Our results demonstrate that highly compressed data can encapsulate the signal suffi- ciently to accurately assemble reads to big contigs or complete genomes

Off the Beaten Path: Let's Replace Term-Based Retrieval with k-NN Search

Retrieval pipelines commonly rely on a term-based search to obtain candidate records, which are subsequently re-ranked. Some candidates are missed by this approach, e.g., due to a vocabulary mismatch. We address this issue by replacing the term-based search with a generic k-NN retrieval algorithm, where a similarity function can take into account subtle term associations. While an exact brute-force k-NN search using this similarity function is slow, we demonstrate that an approximate algorithm can be nearly two orders of magnitude faster at the expense of only a small loss in accuracy. A retrieval pipeline using an approximate k-NN search can be more effective and efficient than the term-based pipeline. This opens up new possibilities for designing effective retrieval pipelines. Our software (including data-generating code) and derivative data based on the Stack Overflow collection is available online

Indexability, concentration, and VC theory

Degrading performance of indexing schemes for exact similarity search in high dimensions has long since been linked to histograms of distributions of distances and other 1-Lipschitz functions getting concentrated. We discuss this observation in the framework of the phenomenon of concentration of measure on the structures of high dimension and the Vapnik-Chervonenkis theory of statistical learning.Comment: 17 pages, final submission to J. Discrete Algorithms (an expanded, improved and corrected version of the SISAP'2010 invited paper, this e-print, v3