Hyperplane Arrangements and Locality-Sensitive Hashing with Lift

Locality-sensitive hashing converts high-dimensional feature vectors, such as image and speech, into bit arrays and allows high-speed similarity calculation with the Hamming distance. There is a hashing scheme that maps feature vectors to bit arrays depending on the signs of the inner products between feature vectors and the normal vectors of hyperplanes placed in the feature space. This hashing can be seen as a discretization of the feature space by hyperplanes. If labels for data are given, one can determine the hyperplanes by using learning algorithms. However, many proposed learning methods do not consider the hyperplanes' offsets. Not doing so decreases the number of partitioned regions, and the correlation between Hamming distances and Euclidean distances becomes small. In this paper, we propose a lift map that converts learning algorithms without the offsets to the ones that take into account the offsets. With this method, the learning methods without the offsets give the discretizations of spaces as if it takes into account the offsets. For the proposed method, we input several high-dimensional feature data sets and studied the relationship between the statistical characteristics of data, the number of hyperplanes, and the effect of the proposed method.Comment: 9 pages, 7 figure

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

Structural Regularities in Text-based Entity Vector Spaces

Entity retrieval is the task of finding entities such as people or products in response to a query, based solely on the textual documents they are associated with. Recent semantic entity retrieval algorithms represent queries and experts in finite-dimensional vector spaces, where both are constructed from text sequences. We investigate entity vector spaces and the degree to which they capture structural regularities. Such vector spaces are constructed in an unsupervised manner without explicit information about structural aspects. For concreteness, we address these questions for a specific type of entity: experts in the context of expert finding. We discover how clusterings of experts correspond to committees in organizations, the ability of expert representations to encode the co-author graph, and the degree to which they encode academic rank. We compare latent, continuous representations created using methods based on distributional semantics (LSI), topic models (LDA) and neural networks (word2vec, doc2vec, SERT). Vector spaces created using neural methods, such as doc2vec and SERT, systematically perform better at clustering than LSI, LDA and word2vec. When it comes to encoding entity relations, SERT performs best.Comment: ICTIR2017. Proceedings of the 3rd ACM International Conference on the Theory of Information Retrieval. 201

Memory vectors for similarity search in high-dimensional spaces

We study an indexing architecture to store and search in a database of high-dimensional vectors from the perspective of statistical signal processing and decision theory. This architecture is composed of several memory units, each of which summarizes a fraction of the database by a single representative vector. The potential similarity of the query to one of the vectors stored in the memory unit is gauged by a simple correlation with the memory unit's representative vector. This representative optimizes the test of the following hypothesis: the query is independent from any vector in the memory unit vs. the query is a simple perturbation of one of the stored vectors. Compared to exhaustive search, our approach finds the most similar database vectors significantly faster without a noticeable reduction in search quality. Interestingly, the reduction of complexity is provably better in high-dimensional spaces. We empirically demonstrate its practical interest in a large-scale image search scenario with off-the-shelf state-of-the-art descriptors.Comment: Accepted to IEEE Transactions on Big Dat