Asymmetric LSH (ALSH) for Sublinear Time Maximum Inner Product Search (MIPS)

We present the first provably sublinear time algorithm for approximate \emph{Maximum Inner Product Search} (MIPS). Our proposal is also the first hashing algorithm for searching with (un-normalized) inner product as the underlying similarity measure. Finding hashing schemes for MIPS was considered hard. We formally show that the existing Locality Sensitive Hashing (LSH) framework is insufficient for solving MIPS, and then we extend the existing LSH framework to allow asymmetric hashing schemes. Our proposal is based on an interesting mathematical phenomenon in which inner products, after independent asymmetric transformations, can be converted into the problem of approximate near neighbor search. This key observation makes efficient sublinear hashing scheme for MIPS possible. In the extended asymmetric LSH (ALSH) framework, we provide an explicit construction of provably fast hashing scheme for MIPS. The proposed construction and the extended LSH framework could be of independent theoretical interest. Our proposed algorithm is simple and easy to implement. We evaluate the method, for retrieving inner products, in the collaborative filtering task of item recommendations on Netflix and Movielens datasets

Collaborative Learning for Extremely Low Bit Asymmetric Hashing

Hashing techniques are in great demand for a wide range of real-world applications such as image retrieval and network compression. Nevertheless, existing approaches could hardly guarantee a satisfactory performance with the extremely low-bit (e.g., 4-bit) hash codes due to the severe information loss and the shrink of the discrete solution space. In this paper, we propose a novel \textit{Collaborative Learning} strategy that is tailored for generating high-quality low-bit hash codes. The core idea is to jointly distill bit-specific and informative representations for a group of pre-defined code lengths. The learning of short hash codes among the group can benefit from the manifold shared with other long codes, where multiple views from different hash codes provide the supplementary guidance and regularization, making the convergence faster and more stable. To achieve that, an asymmetric hashing framework with two variants of multi-head embedding structures is derived, termed as Multi-head Asymmetric Hashing (MAH), leading to great efficiency of training and querying. Extensive experiments on three benchmark datasets have been conducted to verify the superiority of the proposed MAH, and have shown that the 8-bit hash codes generated by MAH achieve $94.3\%$ of the MAP (Mean Average Precision (MAP)) score on the CIFAR-10 dataset, which significantly surpasses the performance of the 48-bit codes by the state-of-the-arts in image retrieval tasks

Compositional Coding for Collaborative Filtering

Efficiency is crucial to the online recommender systems. Representing users and items as binary vectors for Collaborative Filtering (CF) can achieve fast user-item affinity computation in the Hamming space, in recent years, we have witnessed an emerging research effort in exploiting binary hashing techniques for CF methods. However, CF with binary codes naturally suffers from low accuracy due to limited representation capability in each bit, which impedes it from modeling complex structure of the data. In this work, we attempt to improve the efficiency without hurting the model performance by utilizing both the accuracy of real-valued vectors and the efficiency of binary codes to represent users/items. In particular, we propose the Compositional Coding for Collaborative Filtering (CCCF) framework, which not only gains better recommendation efficiency than the state-of-the-art binarized CF approaches but also achieves even higher accuracy than the real-valued CF method. Specifically, CCCF innovatively represents each user/item with a set of binary vectors, which are associated with a sparse real-value weight vector. Each value of the weight vector encodes the importance of the corresponding binary vector to the user/item. The continuous weight vectors greatly enhances the representation capability of binary codes, and its sparsity guarantees the processing speed. Furthermore, an integer weight approximation scheme is proposed to further accelerate the speed. Based on the CCCF framework, we design an efficient discrete optimization algorithm to learn its parameters. Extensive experiments on three real-world datasets show that our method outperforms the state-of-the-art binarized CF methods (even achieves better performance than the real-valued CF method) by a large margin in terms of both recommendation accuracy and efficiency.Comment: SIGIR201

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

Efficient Similarity Search in Dynamic Data Streams

The Jaccard index is an important similarity measure for item sets and Boolean data. On large datasets, an exact similarity computation is often infeasible for all item pairs both due to time and space constraints, giving rise to faster approximate methods. The algorithm of choice used to quickly compute the Jaccard index $\frac{\vert A \cap B \vert}{\vert A\cup B\vert}$ of two item sets $A$ and $B$ is usually a form of min-hashing. Most min-hashing schemes are maintainable in data streams processing only additions, but none are known to work when facing item-wise deletions. In this paper, we investigate scalable approximation algorithms for rational set similarities, a broad class of similarity measures including Jaccard. Motivated by a result of Chierichetti and Kumar [J. ACM 2015] who showed any rational set similarity $S$ admits a locality sensitive hashing (LSH) scheme if and only if the corresponding distance $1-S$ is a metric, we can show that there exists a space efficient summary maintaining a $(1\pm \varepsilon)$ multiplicative approximation to $1-S$ in dynamic data streams. This in turn also yields a $\varepsilon$ additive approximation of the similarity. The existence of these approximations hints at, but does not directly imply a LSH scheme in dynamic data streams. Our second and main contribution now lies in the design of such a LSH scheme maintainable in dynamic data streams. The scheme is space efficient, easy to implement and to the best of our knowledge the first of its kind able to process deletions

Privacy-preserving Targeted Advertising

Recommendation systems form the center piece of a rapidly growing trillion dollar online advertisement industry. Even with numerous optimizations and approximations, collaborative filtering (CF) based approaches require real-time computations involving very large vectors. Curating and storing such related profile information vectors on web portals seriously breaches the user's privacy. Modifying such systems to achieve private recommendations further requires communication of long encrypted vectors, making the whole process inefficient. We present a more efficient recommendation system alternative, in which user profiles are maintained entirely on their device, and appropriate recommendations are fetched from web portals in an efficient privacy preserving manner. We base this approach on association rules.Comment: A preliminary version was presented at the 11th INFORMS Workshop on Data Mining and Decision Analytics (2016

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

Self-Taught Hashing for Fast Similarity Search

The ability of fast similarity search at large scale is of great importance to many Information Retrieval (IR) applications. A promising way to accelerate similarity search is semantic hashing which designs compact binary codes for a large number of documents so that semantically similar documents are mapped to similar codes (within a short Hamming distance). Although some recently proposed techniques are able to generate high-quality codes for documents known in advance, obtaining the codes for previously unseen documents remains to be a very challenging problem. In this paper, we emphasise this issue and propose a novel Self-Taught Hashing (STH) approach to semantic hashing: we first find the optimal $l$-bit binary codes for all documents in the given corpus via unsupervised learning, and then train $l$ classifiers via supervised learning to predict the $l$-bit code for any query document unseen before. Our experiments on three real-world text datasets show that the proposed approach using binarised Laplacian Eigenmap (LapEig) and linear Support Vector Machine (SVM) outperforms state-of-the-art techniques significantly

Conditional Restricted Boltzmann Machines for Structured Output Prediction

Conditional Restricted Boltzmann Machines (CRBMs) are rich probabilistic models that have recently been applied to a wide range of problems, including collaborative filtering, classification, and modeling motion capture data. While much progress has been made in training non-conditional RBMs, these algorithms are not applicable to conditional models and there has been almost no work on training and generating predictions from conditional RBMs for structured output problems. We first argue that standard Contrastive Divergence-based learning may not be suitable for training CRBMs. We then identify two distinct types of structured output prediction problems and propose an improved learning algorithm for each. The first problem type is one where the output space has arbitrary structure but the set of likely output configurations is relatively small, such as in multi-label classification. The second problem is one where the output space is arbitrarily structured but where the output space variability is much greater, such as in image denoising or pixel labeling. We show that the new learning algorithms can work much better than Contrastive Divergence on both types of problems

Data-Parallel Hashing Techniques for GPU Architectures

Hash tables are one of the most fundamental data structures for effectively storing and accessing sparse data, with widespread usage in domains ranging from computer graphics to machine learning. This study surveys the state-of-the-art research on data-parallel hashing techniques for emerging massively-parallel, many-core GPU architectures. Key factors affecting the performance of different hashing schemes are discovered and used to suggest best practices and pinpoint areas for further research