Learning binary codes for maximum inner product search

Binary coding or hashing techniques are recognized to accomplish efficient near neighbor search, and have thus attracted broad interests in the recent vision and learning studies. However, such studies have rarely been dedicated to Maximum Inner Product Search (MIPS), which plays a critical role in various vision applications. In this paper, we investigate learning binary codes to exclusively handle the MIPS problem. Inspired by the latest advance in asymmetric hashing schemes, we propose an asymmetric binary code learning framework based on inner product fitting. Specifically, two sets of coding functions are learned such that the inner products between their generated binary codes can reveal the inner products between original data vectors. We also propose an alternative simpler objective which maximizes the correlations between the inner products of the produced binary codes and raw data vectors. In both objectives, the binary codes and coding functions are simultaneously learned without continuous relaxations, which is the key to achieving high-quality binary codes. We evaluate the proposed method, dubbed Asymmetric Inner-product Binary Coding (AIBC), relying on the two objectives on several large-scale image datasets. Both of them are superior to the state-of-the-art binary coding and hashing methods in performing MIPS tasks

Optimized Cartesian KK-Means

Product quantization-based approaches are effective to encode high-dimensional data points for approximate nearest neighbor search. The space is decomposed into a Cartesian product of low-dimensional subspaces, each of which generates a sub codebook. Data points are encoded as compact binary codes using these sub codebooks, and the distance between two data points can be approximated efficiently from their codes by the precomputed lookup tables. Traditionally, to encode a subvector of a data point in a subspace, only one sub codeword in the corresponding sub codebook is selected, which may impose strict restrictions on the search accuracy. In this paper, we propose a novel approach, named Optimized Cartesian $K$-Means (OCKM), to better encode the data points for more accurate approximate nearest neighbor search. In OCKM, multiple sub codewords are used to encode the subvector of a data point in a subspace. Each sub codeword stems from different sub codebooks in each subspace, which are optimally generated with regards to the minimization of the distortion errors. The high-dimensional data point is then encoded as the concatenation of the indices of multiple sub codewords from all the subspaces. This can provide more flexibility and lower distortion errors than traditional methods. Experimental results on the standard real-life datasets demonstrate the superiority over state-of-the-art approaches for approximate nearest neighbor search.Comment: to appear in IEEE TKDE, accepted in Apr. 201

Survey of Vector Database Management Systems

There are now over 20 commercial vector database management systems (VDBMSs), all produced within the past five years. But embedding-based retrieval has been studied for over ten years, and similarity search a staggering half century and more. Driving this shift from algorithms to systems are new data intensive applications, notably large language models, that demand vast stores of unstructured data coupled with reliable, secure, fast, and scalable query processing capability. A variety of new data management techniques now exist for addressing these needs, however there is no comprehensive survey to thoroughly review these techniques and systems. We start by identifying five main obstacles to vector data management, namely vagueness of semantic similarity, large size of vectors, high cost of similarity comparison, lack of natural partitioning that can be used for indexing, and difficulty of efficiently answering hybrid queries that require both attributes and vectors. Overcoming these obstacles has led to new approaches to query processing, storage and indexing, and query optimization and execution. For query processing, a variety of similarity scores and query types are now well understood; for storage and indexing, techniques include vector compression, namely quantization, and partitioning based on randomization, learning partitioning, and navigable partitioning; for query optimization and execution, we describe new operators for hybrid queries, as well as techniques for plan enumeration, plan selection, and hardware accelerated execution. These techniques lead to a variety of VDBMSs across a spectrum of design and runtime characteristics, including native systems specialized for vectors and extended systems that incorporate vector capabilities into existing systems. We then discuss benchmarks, and finally we outline research challenges and point the direction for future work.Comment: 25 page

Hashing with binary autoencoders

An attractive approach for fast search in image databases is binary hashing, where each high-dimensional, real-valued image is mapped onto a low-dimensional, binary vector and the search is done in this binary space. Finding the optimal hash function is difficult because it involves binary constraints, and most approaches approximate the optimization by relaxing the constraints and then binarizing the result. Here, we focus on the binary autoencoder model, which seeks to reconstruct an image from the binary code produced by the hash function. We show that the optimization can be simplified with the method of auxiliary coordinates. This reformulates the optimization as alternating two easier steps: one that learns the encoder and decoder separately, and one that optimizes the code for each image. Image retrieval experiments, using precision/recall and a measure of code utilization, show the resulting hash function outperforms or is competitive with state-of-the-art methods for binary hashing.Comment: 22 pages, 11 figure