Locality-Sensitive Hashing with Margin Based Feature Selection

We propose a learning method with feature selection for Locality-Sensitive Hashing. Locality-Sensitive Hashing converts feature vectors into bit arrays. These bit arrays can be used to perform similarity searches and personal authentication. The proposed method uses bit arrays longer than those used in the end for similarity and other searches and by learning selects the bits that will be used. We demonstrated this method can effectively perform optimization for cases such as fingerprint images with a large number of labels and extremely few data that share the same labels, as well as verifying that it is also effective for natural images, handwritten digits, and speech features.Comment: 9 pages, 6 figures, 3 table

HDIdx: High-Dimensional Indexing for Efficient Approximate Nearest Neighbor Search

Fast Nearest Neighbor (NN) search is a fundamental challenge in large-scale data processing and analytics, particularly for analyzing multimedia contents which are often of high dimensionality. Instead of using exact NN search, extensive research efforts have been focusing on approximate NN search algorithms. In this work, we present "HDIdx", an efficient high-dimensional indexing library for fast approximate NN search, which is open-source and written in Python. It offers a family of state-of-the-art algorithms that convert input high-dimensional vectors into compact binary codes, making them very efficient and scalable for NN search with very low space complexity

Hashing for Similarity Search: A Survey

Similarity search (nearest neighbor search) is a problem of pursuing the data items whose distances to a query item are the smallest from a large database. Various methods have been developed to address this problem, and recently a lot of efforts have been devoted to approximate search. In this paper, we present a survey on one of the main solutions, hashing, which has been widely studied since the pioneering work locality sensitive hashing. We divide the hashing algorithms two main categories: locality sensitive hashing, which designs hash functions without exploring the data distribution and learning to hash, which learns hash functions according the data distribution, and review them from various aspects, including hash function design and distance measure and search scheme in the hash coding space

Fast Exact Search in Hamming Space with Multi-Index Hashing

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

Hyperplane Arrangements and Locality-Sensitive Hashing with Lift

Locality-sensitive hashing converts high-dimensional feature vectors, such as image and speech, into bit arrays and allows high-speed similarity calculation with the Hamming distance. There is a hashing scheme that maps feature vectors to bit arrays depending on the signs of the inner products between feature vectors and the normal vectors of hyperplanes placed in the feature space. This hashing can be seen as a discretization of the feature space by hyperplanes. If labels for data are given, one can determine the hyperplanes by using learning algorithms. However, many proposed learning methods do not consider the hyperplanes' offsets. Not doing so decreases the number of partitioned regions, and the correlation between Hamming distances and Euclidean distances becomes small. In this paper, we propose a lift map that converts learning algorithms without the offsets to the ones that take into account the offsets. With this method, the learning methods without the offsets give the discretizations of spaces as if it takes into account the offsets. For the proposed method, we input several high-dimensional feature data sets and studied the relationship between the statistical characteristics of data, the number of hyperplanes, and the effect of the proposed method.Comment: 9 pages, 7 figure