Online hashing has attracted extensive research attention when facing streaming data. Most online hashing methods, learning binary codes based on pairwise similarities of training instances, fail to capture the semantic relationship, and suffer from a poor generalization in large-scale applications due to large variations. In this paper, we propose to model the similarity distributions between the input data and the hashing codes, upon which a novel supervised online hashing method, dubbed as Similarity Distribution based Online Hashing (SDOH), is proposed, to keep the intrinsic semantic relationship in the produced Hamming space. Specifically, we first transform the discrete similarity matrix into a probability matrix via a Gaussian-based normalization to address the extremely imbalanced distribution issue. And then, we introduce a scaling Student t-distribution to solve the challenging initialization problem, and efficiently bridge the gap between the known and unknown distributions. Lastly, we align the two distributions via minimizing the Kullback-Leibler divergence (KL-diverence) with stochastic gradient descent (SGD), by which an intuitive similarity constraint is imposed to update hashing model on the new streaming data with a powerful generalizing ability to the past data. Extensive experiments on three widely-used benchmarks validate the superiority of the proposed SDOH over the state-of-the-art methods in the online retrieval task.
Recently, hashing based approximate nearest neighbor (ANN) search has attracted much attention. Extensive new algorithms have been developed and successfully applied to different applications. However, two critical problems are rarely mentioned. First, in real-world applications, the data often comes in a streaming fashion but most of existing hashing methods are batch based models. Second, when the dataset becomes huge, it is almost impossible to load all the data into memory to train hashing models. In this paper, we propose a novel approach to handle these two problems simultaneously based on the idea of data sketching. A sketch of one dataset preserves its major characters but with significantly smaller size. With a small size sketch, our method can learn hash functions in an online fashion, while needs rather low computational complexity and storage space. Extensive experiments on two large scale benchmarks and one synthetic dataset demonstrate the efficacy of the proposed method.  A sketch of a matrix A is another matrix B which is significantly smaller than A but still approximates it well. Finding such sketches efficiently is an important building block in modern algorithms for approximating, for example, the PCA of massive matrices. This task is made more challenging in the streaming model, where each row of the input matrix can only be processed once and storage is severely limited. In this paper we adapt a well known streaming algorithm for approximating item frequencies to the matrix sketching setting. The algorithm receives n rows of a large matrix A e ℜ n x m one after the other in a streaming fashion. It maintains a sketch B ℜ l x m containing only l This gives a streaming algorithm whose error decays proportional to 1 l using O(ml) space. For comparison, random-projection, hashing or sampling based algorithms produce convergence bounds proportional to 1 √l. Sketch updates per row in A require amortized O(ml) operations and the algorithm is perfectly parallelizable. Our experiments corroborate the algorithm's scalability and improved convergence rate. The presented algorithm also stands out in that it is deterministic, simple to implement and elementary to prove.