Effect of Neighborhood Approximation on Downstream Analytics

Nearest neighbor search algorithms have been successful in finding practically useful solutions to computationally difficult problems. In the nearest neighbor search problem, the brute force approach is often more efficient than other algorithms for high-dimensional spaces. A special case exists for objects represented as sparse vectors, where algorithms take advantage of the fact that an object has a zero value for most features. In general, since exact nearest neighbor search methods suffer from the “curse of dimensionality,” many practitioners use approximate nearest neighbor search algorithms when faced with high dimensionality or large datasets. To a reasonable degree, it is known that relying on approximate nearest neighbors leads to some error in the solutions to the underlying data mining problems the neighbors are used to solve. However, no one has attempted to quantify this error or provide practitioners with guidance in choosing appropriate search methods for their task. In this thesis, we conduct several experiments on recommender systems with a goal to find the degree to which approximate nearest neighbor algorithms are subject to these types of error propagation problems. Additionally, we provide persuasive evidence on the trade-off between search performance and analytics effectiveness. Our experimental evaluation demonstrates that a state-of-the-art approximate nearest neighbor search method (L2KNNGApprox) is not an effective solution in most cases. When tuned to achieve high search recall (80% or higher), it provides a fairly competitive recommendation performance compared to an efficient exact search method but offers no advantage in terms of efficiency (0.1x—1.5x speedup). Low search recall (\u3c60%) leads to poor recommendation performance. Finally, medium recall values (60%—80%) lead to reasonable recommendation performance but are hard to achieve and offer only a modest gain in efficiency (1.5x—2.3x)

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

An Efficient Index for Visual Search in Appearance-based SLAM

Vector-quantization can be a computationally expensive step in visual bag-of-words (BoW) search when the vocabulary is large. A BoW-based appearance SLAM needs to tackle this problem for an efficient real-time operation. We propose an effective method to speed up the vector-quantization process in BoW-based visual SLAM. We employ a graph-based nearest neighbor search (GNNS) algorithm to this aim, and experimentally show that it can outperform the state-of-the-art. The graph-based search structure used in GNNS can efficiently be integrated into the BoW model and the SLAM framework. The graph-based index, which is a k-NN graph, is built over the vocabulary words and can be extracted from the BoW's vocabulary construction procedure, by adding one iteration to the k-means clustering, which adds small extra cost. Moreover, exploiting the fact that images acquired for appearance-based SLAM are sequential, GNNS search can be initiated judiciously which helps increase the speedup of the quantization process considerably

Simultaneous nearest neighbor search

Motivated by applications in computer vision and databases, we introduce and study the Simultaneous Nearest Neighbor Search (SNN) problem. Given a set of data points, the goal of SNN is to design a data structure that, given a collection of queries, finds a collection of close points that are compatible with each other. Formally, we are given k query points Q=q_1,...,q_k, and a compatibility graph G with vertices in Q, and the goal is to return data points p_1,...,p_k that minimize (i) the weighted sum of the distances from q_i to p_i and (ii) the weighted sum, over all edges (i,j) in the compatibility graph G, of the distances between p_i and p_j. The problem has several applications in computer vision and databases, where one wants to return a set of *consistent* answers to multiple related queries. Furthermore, it generalizes several well-studied computational problems, including Nearest Neighbor Search, Aggregate Nearest Neighbor Search and the 0-extension problem. In this paper we propose and analyze the following general two-step method for designing efficient data structures for SNN. In the first step, for each query point q_i we find its (approximate) nearest neighbor point p'_i; this can be done efficiently using existing approximate nearest neighbor structures. In the second step, we solve an off-line optimization problem over sets q_1,...,q_k and p'_1,...,p'_k; this can be done efficiently given that k is much smaller than n. Even though p'_1,...,p'_k might not constitute the optimal answers to queries q_1,...,q_k, we show that, for the unweighted case, the resulting algorithm satisfies a O(log k/log log k)-approximation guarantee. Furthermore, we show that the approximation factor can be in fact reduced to a constant for compatibility graphs frequently occurring in practice, e.g., 2D grids, 3D grids or planar graphs. Finally, we validate our theoretical results by preliminary experiments. In particular, we show that the empirical approximation factor provided by the above approach is very close to 1