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

Efficient Large-scale Approximate Nearest Neighbor Search on the GPU

We present a new approach for efficient approximate nearest neighbor (ANN) search in high dimensional spaces, extending the idea of Product Quantization. We propose a two-level product and vector quantization tree that reduces the number of vector comparisons required during tree traversal. Our approach also includes a novel highly parallelizable re-ranking method for candidate vectors by efficiently reusing already computed intermediate values. Due to its small memory footprint during traversal, the method lends itself to an efficient, parallel GPU implementation. This Product Quantization Tree (PQT) approach significantly outperforms recent state of the art methods for high dimensional nearest neighbor queries on standard reference datasets. Ours is the first work that demonstrates GPU performance superior to CPU performance on high dimensional, large scale ANN problems in time-critical real-world applications, like loop-closing in videos