GGNN: Graph-based GPU Nearest Neighbor Search

Approximate nearest neighbor (ANN) search in high dimensions is an integral part of several computer vision systems and gains importance in deep learning with explicit memory representations. Since PQT and FAISS started to leverage the massive parallelism offered by GPUs, GPU-based implementations are a crucial resource for today's state-of-the-art ANN methods. While most of these methods allow for faster queries, less emphasis is devoted to accelerate the construction of the underlying index structures. In this paper, we propose a novel search structure based on nearest neighbor graphs and information propagation on graphs. Our method is designed to take advantage of GPU architectures to accelerate the hierarchical building of the index structure and for performing the query. Empirical evaluation shows that GGNN significantly surpasses the state-of-the-art GPU- and CPU-based systems in terms of build-time, accuracy and search speed

Nearest neighbor search with multiple random projection trees : core method and improvements

Nearest neighbor search is a crucial tool in computer science and a part of many machine learning algorithms, the most obvious example being the venerable k-NN classifier. More generally, nearest neighbors have usages in numerous fields such as classification, regression, computer vision, recommendation systems, robotics and compression to name just a few examples. In general, nearest neighbor problems cannot be answered in sublinear time – to identify the actual nearest data points, clearly all objects have to be accessed at least once. However, in the class of applications where nearest neighbor searches are repeatedly made within a fixed data set that is available upfront, such as recommendation systems (Spotify, e-commerce, etc.), we can do better. In a computationally expensive offline phase the data set is indexed with a data structure, and in the online phase the index is used to answer nearest neighbor queries at a superior rate. The cost of indexing is usually much larger than that of performing a single query, but with a high number of queries the initial indexing cost gets eventually compensated. The urge for efficient index structures for nearest neighbors search has sparked a lot of research and hundreds of papers have been published to date. We look into the class of structures called binary space partitioning trees, specifically the random projection tree. Random projection trees have favorable properties especially when working with data sets with low intrinsic dimensionality. However, they have rarely been used in real-life nearest neighbor solutions due to limiting factors such as the relatively high cost of projection computations in high dimensional spaces. We present a new index structure for approximate nearest neighbor search that consists of multiple random projection trees, and several variants of algorithms to use it for efficient nearest neighbor search. We start by specifying our variant of the random projection tree and show how to construct an index of multiple random projection trees (MRPT), along with a simple query that combines the results from independent random projection trees to achieve much higher query accuracy with faster query times. This is followed by discussion of further methods to optimize accuracy and storage. The focus will be on algorithmic details, accompanied by a thorough analysis of memory and time complexity. Finally we will show experimentally that a real-life implementation of these ideas leads to an algorithm that achieves faster query times than the currently available open source libraries for high-recall approximate nearest neighbor search

Efficient Computation of K-Nearest Neighbor Graphs for Large High-Dimensional Data Sets on GPU Clusters

The k-Nearest Neighbor Graph (k-NNG) and the related k-Nearest Neighbor (k-NN) methods have a wide variety of applications in areas such as bioinformatics, machine learning, data mining, clustering analysis, and pattern recognition. Our application of interest is manifold embedding. Due to the large dimensionality of the input data (\u3c15k), spatial subdivision based techniques such OBBs, k-d tree, BSP etc., are not viable. The only alternative is the brute-force search, which has two distinct parts. The first finds distances between individual vectors in the corpus based on a pre-defined metric. Given the distance matrix, the second step selects k nearest neighbors for each member of the query data set. This thesis presents the development and implementation of a distributed exact k-Nearest Neighbor Graph (k-NNG) construction method. The proposed method uses Graphics Processing Units (GPUs) and exploits multiple levels of parallelism for distributed computational systems using GPUs. It is scalable for different cluster sizes, with each compute node in the cluster containing multiple GPUs. The distance computation is formulated as a basic matrix multiplication and reduction operation. The optimized CUBLAS matrix multiplication library is used for this purpose. Various distance metrics such as Euclidian, cosine, and Pearson are supported. For k-NNG construction, two different methods are presented. The first is based on an approach called batch index sorting to build the k-NNG with three sorting operations. This method uses the optimized radix sort implementation in the Thrust library for GPU. The second is an efficient implementation using the latest GPU functionalities of a variant of the quick select algorithm. Overall, the batch index sorting based k-NNG method is approximately 13x faster than a distributed MATLAB implementation. The quick select algorithm itself has a 5x speedup over state-of-the art GPU methods. This has enabled the processing of k-NNG construction on a data set containing 20 million image vectors, each with dimension 15,000, as part of a manifold embedding technique for analyzing the conformations of biomolecules

Online supervised hashing

Fast nearest neighbor search is becoming more and more crucial given the advent of large-scale data in many computer vision applications. Hashing approaches provide both fast search mechanisms and compact index structures to address this critical need. In image retrieval problems where labeled training data is available, supervised hashing methods prevail over unsupervised methods. Most state-of-the-art supervised hashing approaches employ batch-learners. Unfortunately, batch-learning strategies may be inefficient when confronted with large datasets. Moreover, with batch-learners, it is unclear how to adapt the hash functions as the dataset continues to grow and new variations appear over time. To handle these issues, we propose OSH: an Online Supervised Hashing technique that is based on Error Correcting Output Codes. We consider a stochastic setting where the data arrives sequentially and our method learns and adapts its hashing functions in a discriminative manner. Our method makes no assumption about the number of possible class labels, and accommodates new classes as they are presented in the incoming data stream. In experiments with three image retrieval benchmarks, our method yields state-of-the-art retrieval performance as measured in Mean Average Precision, while also being orders-of-magnitude faster than competing batch methods for supervised hashing. Also, our method significantly outperforms recently introduced online hashing solutions.https://pdfs.semanticscholar.org/555b/de4f14630d8606e37096235da8933df228f1.pdfAccepted manuscrip

A Learned Index for Exact Similarity Search in Metric Spaces

Indexing is an effective way to support efficient query processing in large databases. Recently the concept of learned index has been explored actively to replace or supplement traditional index structures with machine learning models to reduce storage and search costs. However, accurate and efficient similarity query processing in high-dimensional metric spaces remains to be an open challenge. In this paper, a novel indexing approach called LIMS is proposed to use data clustering and pivot-based data transformation techniques to build learned indexes for efficient similarity query processing in metric spaces. The underlying data is partitioned into clusters such that each cluster follows a relatively uniform data distribution. Data redistribution is achieved by utilizing a small number of pivots for each cluster. Similar data are mapped into compact regions and the mapped values are totally ordinal. Machine learning models are developed to approximate the position of each data record on the disk. Efficient algorithms are designed for processing range queries and nearest neighbor queries based on LIMS, and for index maintenance with dynamic updates. Extensive experiments on real-world and synthetic datasets demonstrate the superiority of LIMS compared with traditional indexes and state-of-the-art learned indexes.Comment: 14 pages, 14 figures, submitted to Transactions on Knowledge and Data Engineerin

Hashing for Similarity Search: A Survey

Similarity search (nearest neighbor search) is a problem of pursuing the data items whose distances to a query item are the smallest from a large database. Various methods have been developed to address this problem, and recently a lot of efforts have been devoted to approximate search. In this paper, we present a survey on one of the main solutions, hashing, which has been widely studied since the pioneering work locality sensitive hashing. We divide the hashing algorithms two main categories: locality sensitive hashing, which designs hash functions without exploring the data distribution and learning to hash, which learns hash functions according the data distribution, and review them from various aspects, including hash function design and distance measure and search scheme in the hash coding space