text: When facing large-scale image datasets, online hashing serves as a promising solution for online retrieval and prediction tasks. It encodes the online streaming data into compact binary codes, and simultaneously updates the hash functions to renew codes of the existing dataset. To this end, the existing methods update hash functions solely based on the new data batch, without investigating the correlation between such new data and the existing dataset. In addition, existing works update the hash functions using a relaxation process in its corresponding approximated continuous space. And it remains as an open problem to directly apply discrete optimizations in online hashing. In this paper, we propose a novel supervised online hashing method, termed Balanced Similarity for Online Discrete Hashing (BSODH), to solve the above problems in a unified framework. BSODH employs a well-designed hashing algorithm to preserve the similarity between the streaming data and the existing dataset via an asymmetric graph regularization. We further identify the "data-imbalance" problem brought by the constructed asymmetric graph, which restricts the application of discrete optimization in our problem. Therefore, a novel balanced similarity is further proposed, which uses two equilibrium factors to balance the similar and dissimilar weights and eventually enables the usage of discrete optimizations. Extensive experiments conducted on three widely-used benchmarks demonstrate the advantages of the proposed method over the state-of-the-art methods.
  @cite_19: Hashing has emerged as a popular technique for fast nearest neighbor search in gigantic databases. In particular, learning based hashing has received considerable attention due to its appealing storage and search efficiency. However, the performance of most unsupervised learning based hashing methods deteriorates rapidly as the hash code length increases. We argue that the degraded performance is due to inferior optimization procedures used to achieve discrete binary codes. This paper presents a graph-based unsupervised hashing model to preserve the neighborhood structure of massive data in a discrete code space. We cast the graph hashing problem into a discrete optimization framework which directly learns the binary codes. A tractable alternating maximization algorithm is then proposed to explicitly deal with the discrete constraints, yielding high-quality codes to well capture the local neighborhoods. Extensive experiments performed on four large datasets with up to one million samples show that our discrete optimization based graph hashing method obtains superior search accuracy over state-of-the-art un-supervised hashing methods, especially for longer codes.
  @cite_16: Recently, learning based hashing techniques have attracted broad research interests because they can support efficient storage and retrieval for high-dimensional data such as images, videos, documents, etc. However, a major difficulty of learning to hash lies in handling the discrete constraints imposed on the pursued hash codes, which typically makes hash optimizations very challenging (NP-hard in general). In this work, we propose a new supervised hashing framework, where the learning objective is to generate the optimal binary hash codes for linear classification. By introducing an auxiliary variable, we reformulate the objective such that it can be solved substantially efficiently by employing a regularization algorithm. One of the key steps in this algorithm is to solve a regularization sub-problem associated with the NP-hard binary optimization. We show that the sub-problem admits an analytical solution via cyclic coordinate descent. As such, a high-quality discrete solution can eventually be obtained in an efficient computing manner, therefore enabling to tackle massive datasets. We evaluate the proposed approach, dubbed Supervised Discrete Hashing (SDH), on four large image datasets and demonstrate its superiority to the state-of-the-art hashing methods in large-scale image retrieval.
summary: However, existing sketch-based algorithms are based on unsupervised learning, and their retrieval performance is mostly unsatisfactory without fully utilizing label information. Although most SGD-based algorithms aim to preserve the label information via online hash function learning, the relaxation process is adopted to update the hash functions, which contradicts with the recent advances in offline hashing where discrete optimizations are adopted directly, such as Discrete Graph Hashing @cite_19 and Discrete Supervised Hashing @cite_16 . In this paper, we are the first to investigate OH with discrete optimizations, which have shown superior performance compared with the quantization-based schemes.