There is growing interest in representing image data and feature descriptors using compact binary codes for fast near neighbor search. Although binary codes are motivated by their use as direct indices (addresses) into a hash table, codes longer than 32 bits are not being used as such, as it was thought to be ineffective. We introduce a rigorous way to build multiple hash tables on binary code substrings that enables exact k-nearest neighbor search in Hamming space. The approach is storage efficient and straightforward to implement. Theoretical analysis shows that the algorithm exhibits sub-linear run-time behavior for uniformly distributed codes. Empirical results show dramatic speedups over a linear scan baseline for datasets of up to one billion codes of 64, 128, or 256 bits.
@cite_46: Similarity search, namely, finding approximate nearest neighborhoods, is the core of many large scale machine learning or vision applications. Recently, many research results demonstrate that hashing with compact codes can achieve promising performance for large scale similarity search. However, most of the previous hashing methods with compact codes only model and optimize the search accuracy. Search time, which is an important factor for hashing in practice, is usually not addressed explicitly. In this paper, we develop a new scalable hashing algorithm with joint optimization of search accuracy and search time simultaneously. Our method generates compact hash codes for data of general formats with any similarity function. We evaluate our method using diverse data sets up to 1 million samples (e.g., web images). Our comprehensive results show the proposed method significantly outperforms several state-of-the-art hashing approaches.
@cite_14: The Internet contains billions of images, freely available online. Methods for efficiently searching this incredibly rich resource are vital for a large number of applications. These include object recognition, computer graphics, personal photo collections, online image search tools. In this paper, our goal is to develop efficient image search and scene matching techniques that are not only fast, but also require very little memory, enabling their use on standard hardware or even on handheld devices. Our approach uses recently developed machine learning techniques to convert the Gist descriptor (a real valued vector that describes orientation energies at different scales and orientations within an image) to a compact binary code, with a few hundred bits per image. Using our scheme, it is possible to perform real-time searches with millions from the Internet using a single large PC and obtain recognition results comparable to the full descriptor. Using our codes on high quality labeled images from the LabelMe database gives surprisingly powerful recognition results using simple nearest neighbor techniques.
@cite_23: Hashing based Approximate Nearest Neighbor (ANN) search has attracted much attention due to its fast query time and drastically reduced storage. However, most of the hashing methods either use random projections or extract principal directions from the data to derive hash functions. The resulting embedding suffers from poor discrimination when compact codes are used. In this paper, we propose a novel data-dependent projection learning method such that each hash function is designed to correct the errors made by the previous one sequentially. The proposed method easily adapts to both unsupervised and semi-supervised scenarios and shows significant performance gains over the state-of-the-art methods on two large datasets containing up to 1 million points.
One way to tackle @math -neighbor search is to use a hash table populated with the binary codes @math , and examine all hash buckets whose indices are within @math bits of a query @math ( , @cite_14 ). For binary codes of @math bits, the number of distinct hash buckets to examine is As shown in Fig. (top), @math grows very rapidly with @math . Thus, this approach is only practical for small radii or short code lengths. Some vision applications restrict search to exact matches ( @math ) or a small search radius ( @cite_46 @cite_23 ), but in most cases of interest the desired search radius is larger than is currently feasible ( see Fig. (bottom)).