Learning to Hash for Indexing Big Data - A Survey

The explosive growth in big data has attracted much attention in designing efficient indexing and search methods recently. In many critical applications such as large-scale search and pattern matching, finding the nearest neighbors to a query is a fundamental research problem. However, the straightforward solution using exhaustive comparison is infeasible due to the prohibitive computational complexity and memory requirement. In response, Approximate Nearest Neighbor (ANN) search based on hashing techniques has become popular due to its promising performance in both efficiency and accuracy. Prior randomized hashing methods, e.g., Locality-Sensitive Hashing (LSH), explore data-independent hash functions with random projections or permutations. Although having elegant theoretic guarantees on the search quality in certain metric spaces, performance of randomized hashing has been shown insufficient in many real-world applications. As a remedy, new approaches incorporating data-driven learning methods in development of advanced hash functions have emerged. Such learning to hash methods exploit information such as data distributions or class labels when optimizing the hash codes or functions. Importantly, the learned hash codes are able to preserve the proximity of neighboring data in the original feature spaces in the hash code spaces. The goal of this paper is to provide readers with systematic understanding of insights, pros and cons of the emerging techniques. We provide a comprehensive survey of the learning to hash framework and representative techniques of various types, including unsupervised, semi-supervised, and supervised. In addition, we also summarize recent hashing approaches utilizing the deep learning models. Finally, we discuss the future direction and trends of research in this area

Variable-Length Hashing

Hashing has emerged as a popular technique for large-scale similarity search. Most learning-based hashing methods generate compact yet correlated hash codes. However, this redundancy is storage-inefficient. Hence we propose a lossless variable-length hashing (VLH) method that is both storage- and search-efficient. Storage efficiency is achieved by converting the fixed-length hash code into a variable-length code. Search efficiency is obtained by using a multiple hash table structure. With VLH, we are able to deliberately add redundancy into hash codes to improve retrieval performance with little sacrifice in storage efficiency or search complexity. In particular, we propose a block K-means hashing (B-KMH) method to obtain significantly improved retrieval performance with no increase in storage and marginal increase in computational cost.Comment: 10 pages, 6 figure

A Survey on Learning to Hash

Nearest neighbor search is a problem of finding the data points from the database such that the distances from them to the query point are the smallest. Learning to hash is one of the major solutions to this problem and has been widely studied recently. In this paper, we present a comprehensive survey of the learning to hash algorithms, categorize them according to the manners of preserving the similarities into: pairwise similarity preserving, multiwise similarity preserving, implicit similarity preserving, as well as quantization, and discuss their relations. We separate quantization from pairwise similarity preserving as the objective function is very different though quantization, as we show, can be derived from preserving the pairwise similarities. In addition, we present the evaluation protocols, and the general performance analysis, and point out that the quantization algorithms perform superiorly in terms of search accuracy, search time cost, and space cost. Finally, we introduce a few emerging topics.Comment: To appear in IEEE Transactions On Pattern Analysis and Machine Intelligence (TPAMI

Rank Subspace Learning for Compact Hash Codes

The era of Big Data has spawned unprecedented interests in developing hashing algorithms for efficient storage and fast nearest neighbor search. Most existing work learn hash functions that are numeric quantizations of feature values in projected feature space. In this work, we propose a novel hash learning framework that encodes feature's rank orders instead of numeric values in a number of optimal low-dimensional ranking subspaces. We formulate the ranking subspace learning problem as the optimization of a piece-wise linear convex-concave function and present two versions of our algorithm: one with independent optimization of each hash bit and the other exploiting a sequential learning framework. Our work is a generalization of the Winner-Take-All (WTA) hash family and naturally enjoys all the numeric stability benefits of rank correlation measures while being optimized to achieve high precision at very short code length. We compare with several state-of-the-art hashing algorithms in both supervised and unsupervised domain, showing superior performance in a number of data sets.Comment: 10 page

Exploring Auxiliary Context: Discrete Semantic Transfer Hashing for Scalable Image Retrieval

Unsupervised hashing can desirably support scalable content-based image retrieval (SCBIR) for its appealing advantages of semantic label independence, memory and search efficiency. However, the learned hash codes are embedded with limited discriminative semantics due to the intrinsic limitation of image representation. To address the problem, in this paper, we propose a novel hashing approach, dubbed as \emph{Discrete Semantic Transfer Hashing} (DSTH). The key idea is to \emph{directly} augment the semantics of discrete image hash codes by exploring auxiliary contextual modalities. To this end, a unified hashing framework is formulated to simultaneously preserve visual similarities of images and perform semantic transfer from contextual modalities. Further, to guarantee direct semantic transfer and avoid information loss, we explicitly impose the discrete constraint, bit--uncorrelation constraint and bit-balance constraint on hash codes. A novel and effective discrete optimization method based on augmented Lagrangian multiplier is developed to iteratively solve the optimization problem. The whole learning process has linear computation complexity and desirable scalability. Experiments on three benchmark datasets demonstrate the superiority of DSTH compared with several state-of-the-art approaches

Unsupervised Cross-Media Hashing with Structure Preservation

Recent years have seen the exponential growth of heterogeneous multimedia data. The need for effective and accurate data retrieval from heterogeneous data sources has attracted much research interest in cross-media retrieval. Here, given a query of any media type, cross-media retrieval seeks to find relevant results of different media types from heterogeneous data sources. To facilitate large-scale cross-media retrieval, we propose a novel unsupervised cross-media hashing method. Our method incorporates local affinity and distance repulsion constraints into a matrix factorization framework. Correspondingly, the proposed method learns hash functions that generates unified hash codes from different media types, while ensuring intrinsic geometric structure of the data distribution is preserved. These hash codes empower the similarity between data of different media types to be evaluated directly. Experimental results on two large-scale multimedia datasets demonstrate the effectiveness of the proposed method, where we outperform the state-of-the-art methods

Set-to-Set Hashing with Applications in Visual Recognition

Visual data, such as an image or a sequence of video frames, is often naturally represented as a point set. In this paper, we consider the fundamental problem of finding a nearest set from a collection of sets, to a query set. This problem has obvious applications in large-scale visual retrieval and recognition, and also in applied fields beyond computer vision. One challenge stands out in solving the problem---set representation and measure of similarity. Particularly, the query set and the sets in dataset collection can have varying cardinalities. The training collection is large enough such that linear scan is impractical. We propose a simple representation scheme that encodes both statistical and structural information of the sets. The derived representations are integrated in a kernel framework for flexible similarity measurement. For the query set process, we adopt a learning-to-hash pipeline that turns the kernel representations into hash bits based on simple learners, using multiple kernel learning. Experiments on two visual retrieval datasets show unambiguously that our set-to-set hashing framework outperforms prior methods that do not take the set-to-set search setting.Comment: 9 page

Shared Predictive Cross-Modal Deep Quantization

With explosive growth of data volume and ever-increasing diversity of data modalities, cross-modal similarity search, which conducts nearest neighbor search across different modalities, has been attracting increasing interest. This paper presents a deep compact code learning solution for efficient cross-modal similarity search. Many recent studies have proven that quantization-based approaches perform generally better than hashing-based approaches on single-modal similarity search. In this paper, we propose a deep quantization approach, which is among the early attempts of leveraging deep neural networks into quantization-based cross-modal similarity search. Our approach, dubbed shared predictive deep quantization (SPDQ), explicitly formulates a shared subspace across different modalities and two private subspaces for individual modalities, and representations in the shared subspace and the private subspaces are learned simultaneously by embedding them to a reproducing kernel Hilbert space, where the mean embedding of different modality distributions can be explicitly compared. In addition, in the shared subspace, a quantizer is learned to produce the semantics preserving compact codes with the help of label alignment. Thanks to this novel network architecture in cooperation with supervised quantization training, SPDQ can preserve intramodal and intermodal similarities as much as possible and greatly reduce quantization error. Experiments on two popular benchmarks corroborate that our approach outperforms state-of-the-art methods

SNAP: A General Purpose Network Analysis and Graph Mining Library

Large networks are becoming a widely used abstraction for studying complex systems in a broad set of disciplines, ranging from social network analysis to molecular biology and neuroscience. Despite an increasing need to analyze and manipulate large networks, only a limited number of tools are available for this task. Here, we describe Stanford Network Analysis Platform (SNAP), a general-purpose, high-performance system that provides easy to use, high-level operations for analysis and manipulation of large networks. We present SNAP functionality, describe its implementational details, and give performance benchmarks. SNAP has been developed for single big-memory machines and it balances the trade-off between maximum performance, compact in-memory graph representation, and the ability to handle dynamic graphs where nodes and edges are being added or removed over time. SNAP can process massive networks with hundreds of millions of nodes and billions of edges. SNAP offers over 140 different graph algorithms that can efficiently manipulate large graphs, calculate structural properties, generate regular and random graphs, and handle attributes and meta-data on nodes and edges. Besides being able to handle large graphs, an additional strength of SNAP is that networks and their attributes are fully dynamic, they can be modified during the computation at low cost. SNAP is provided as an open source library in C++ as well as a module in Python. We also describe the Stanford Large Network Dataset, a set of social and information real-world networks and datasets, which we make publicly available. The collection is a complementary resource to our SNAP software and is widely used for development and benchmarking of graph analytics algorithms

SHOE: Supervised Hashing with Output Embeddings

We present a supervised binary encoding scheme for image retrieval that learns projections by taking into account similarity between classes obtained from output embeddings. Our motivation is that binary hash codes learned in this way improve both the visual quality of retrieval results and existing supervised hashing schemes. We employ a sequential greedy optimization that learns relationship aware projections by minimizing the difference between inner products of binary codes and output embedding vectors. We develop a joint optimization framework to learn projections which improve the accuracy of supervised hashing over the current state of the art with respect to standard and sibling evaluation metrics. We further boost performance by applying the supervised dimensionality reduction technique on kernelized input CNN features. Experiments are performed on three datasets: CUB-2011, SUN-Attribute and ImageNet ILSVRC 2010. As a by-product of our method, we show that using a simple k-nn pooling classifier with our discriminative codes improves over the complex classification models on fine grained datasets like CUB and offer an impressive compression ratio of 1024 on CNN features