Search

A similar waveform search plays a crucial role in seismology for detecting seismic events, such as small earthquakes and low-frequency events. However, the high computational costs associated with waveform cross-correlation calculations represent bottlenecks during the analysis of long, continuous records obtained from numerous stations. In this study, we developed a deep-learning network to obtain 64-bit hash codes containing information on seismic waveforms. Using this network, we performed a similar waveform search for ∼35 million moving windows developed for the 30 min waveforms recorded continuously at 10 MHz sampling rates using 16 acoustic emission transducers during a laboratory hydraulic fracturing experiment. The sampling points of each channel corresponded to those of the 5.8-yr records obtained from typical seismic observations at 100 Hz sampling rates. Of the 35 million windows, we searched for windows with small average Hamming distances among the hash codes of 16 channel waveforms against template hash codes of 6057 events that were catalogued using conventional autoprocessing techniques. The calculation of average Hamming distances is 1430–1530 times faster than that of the corresponding network correlation. This hashing-based template matching enabled the detection of 23   462 additional events. We also demonstrated the feasibility of the hashing-based autocorrelation analysis, where similar event pairs were extracted without templates, by calculating the average Hamming distances for all possible pairs of the ∼35 million windows. This calculation required only 15.5 h under 120 thread parallelization. This deep hashing approach significantly reduced the required memory compared with locality-sensitive hashing approaches based on random permutations, enabling similar waveform searching on a large-scale data set. [ABSTRACT FROM AUTHOR]

In this paper we show that the largest possible size of a subset of F q n avoiding right angles, that is, distinct vectors x , y , z such that x − z and y − z are perpendicular to each other is at most O (n q − 2). This improves on the previously best known bound due to Naslund [13] and refutes a conjecture of Ge and Shangguan [11]. A lower bound of n q / 3 is also presented. It is also shown that a subset of F q n avoiding triangles with all right angles can have size at most O (n 2 q − 2). Furthermore, asymptotically tight bounds are given for the largest possible size of a subset A ⊆ F q n for which x − y is not self-orthogonal for any distinct x , y ∈ A. The exact answer is determined for q = 3 and n ≡ 2 (mod 3). Our methods can also be used to bound the maximum possible size of a binary code where no two codewords have Hamming distance divisible by a fixed prime q. Our lower- and upper bounds are asymptotically tight and both are sharp in infinitely many cases. [ABSTRACT FROM AUTHOR]

Multi-view subspace clustering, which partitions multi-view data into their respective underlying subspaces, has achieved the remarkable clustering performance by extracting abundant complementary information from data of different views. However, existing subspace clustering methods almost suffer from very heavy computational burden that restricts their capacity on computational efficiency for large-scale datasets. Recently, hashing/binary code learning has attracted intensive attentions due to fast Hamming distance computation and much less storage requirement, but existing related research does not explore underlying subspace clustering structure well that widely exists in real-world data. In order to handle the both issues, in this paper, we propose a multi-view subspace clustering method named Hashing Multi-view Sparse Subspace Learning (HMSSL). HMSSL incorporates multi-view binary code learning and binary sparse subspace learning with a "thin" dictionary into a unified framework. HMSSL encodes multi-view real-valued features in the original space into compact common binary codes in the Hamming space for fast Hamming distance computation by multi-view binary code learning and learns the binary sparse subspace representation matrix for exploring the underlying subspace clustering structure efficiently and effectively by binary sparse subspace learning with a "thin" dictionary matrix. All the columns of the dictionary matrix are randomly and uniformly sampled from all the columns of the compact common binary code matrix. We design an effective binary optimization algorithm based on alternating direction multiplier method and analyze its time complexity. Extensive experiments performed on six benchmark multi-view datasets demonstrate the effectiveness of HMSSL in comparison with ten state-of-the-art baselines in this field. [ABSTRACT FROM AUTHOR]

We study codes with parameters of $q$ -ary shortened Hamming codes, i.e., $(n=(q^{m}-q)/(q-1), q^{n-m}, 3)_{q}$. Firstly, we prove the fact mentioned in 1998 by Brouwer et al. that such codes are optimal, generalizing it to a bound for multifold packings of radius-1 balls, with a corollary for multiple coverings. In particular, we show that the punctured Hamming code is an optimal $q$ -fold packing with minimum distance 2. Secondly, for every admissible length starting from $n=20$ , we show the existence of 4-ary codes with parameters of shortened 1-perfect codes that cannot be obtained by shortening a 1-perfect code. [ABSTRACT FROM AUTHOR]

Hashing technology can support large-scale recommendation very effectively due to its advantages of low storage cost and high recommendation efficiency. However, existing hashing-based recommendation methods often suffer from item cold-start problem. This is because they simply consider the user-item interaction and the single content information of the items, but the full interaction history is not always available and the single auxiliary information may be missing. To solve this issue, in this paper we propose a Binary Multi-modal Matrix Factorization (BMMF) method. First, we propose an efficient consensus multi-modal mapping to transform the heterogeneous multi-modal features to the unified factors by exploiting the complementarity of multiple modalities. Then, binary matrix factorization is simultaneously performed on the multi-modal features of the items and past user preferences to learn the compact binary codes of the users/items in a common Hamming space. In addition, inspired by the observation that similar instances often have similar binary codes within a short Hamming distance, we formulate a semantic structure regularization term to preserve the similarities of the items during the binary embedding process. Finally, we develop an effective Discrete Coordinate Descent (DCD) approach to tackle the formulated discrete hash optimization problem directly. Experiments on three publicly available real-world datasets demonstrate the superiority of the proposed method against the state-of-the-art methods. Our source codes and testing datasets are available at https://github.com/pcm1217/BMMF. [ABSTRACT FROM AUTHOR]

The image-text cross-modal retrieval task, which aims to retrieve the relevant image from text and vice versa, is now attracting widespread attention. To quickly respond to the large-scale task, we propose an Unsupervised Deep Relative Neighbor Relationship Preserving Cross-Modal Hashing (DRNPH) to achieve cross-modal retrieval in the common Hamming space, which has the advantages of storage and efficiency. To fulfill the nearest neighbor search in the Hamming space, we demand to reconstruct both the original intra- and inter-modal neighbor matrix according to the binary feature vectors. Thus, we can compute the neighbor relationship among different modal samples directly based on the Hamming distances. Furthermore, the cross-modal pair-wise similarity preserving constraint requires the similar sample pair have an identical Hamming distance to the anchor. Therefore, the similar sample pairs own the same binary code, and they have minimal Hamming distances. Unfortunately, the pair-wise similarity preserving constraint may lead to an imbalanced code problem. Therefore, we propose the cross-modal triplet relative similarity preserving constraint, which demands the Hamming distances of similar pairs should be less than those of dissimilar pairs to distinguish the samples' ranking orders in the retrieval results. Moreover, a large similarity marginal can boost the algorithm's noise robustness. We conduct the cross-modal retrieval comparative experiments and ablation study on two public datasets, MIRFlickr and NUS-WIDE, respectively. The experimental results show that DRNPH outperforms the state-of-the-art approaches in various image-text retrieval scenarios, and all three proposed constraints are necessary and effective for boosting cross-modal retrieval performance. [ABSTRACT FROM AUTHOR]

Background: Protein–protein interaction (PPI) is vital for life processes, disease treatment, and drug discovery. The computational prediction of PPI is relatively inexpensive and efficient when compared to traditional wet-lab experiments. Given a new protein, one may wish to find whether the protein has any PPI relationship with other existing proteins. Current computational PPI prediction methods usually compare the new protein to existing proteins one by one in a pairwise manner. This is time consuming. Results: In this work, we propose a more efficient model, called deep hash learning protein-and-protein interaction (DHL-PPI), to predict all-against-all PPI relationships in a database of proteins. First, DHL-PPI encodes a protein sequence into a binary hash code based on deep features extracted from the protein sequences using deep learning techniques. This encoding scheme enables us to turn the PPI discrimination problem into a much simpler searching problem. The binary hash code for a protein sequence can be regarded as a number. Thus, in the pre-screening stage of DHL-PPI, the string matching problem of comparing a protein sequence against a database with M proteins can be transformed into a much more simpler problem: to find a number inside a sorted array of length M. This pre-screening process narrows down the search to a much smaller set of candidate proteins for further confirmation. As a final step, DHL-PPI uses the Hamming distance to verify the final PPI relationship. Conclusions: The experimental results confirmed that DHL-PPI is feasible and effective. Using a dataset with strictly negative PPI examples of four species, DHL-PPI is shown to be superior or competitive when compared to the other state-of-the-art methods in terms of precision, recall or F1 score. Furthermore, in the prediction stage, the proposed DHL-PPI reduced the time complexity from O (M 2) to O (M log M) for performing an all-against-all PPI prediction for a database with M proteins. With the proposed approach, a protein database can be preprocessed and stored for later search using the proposed encoding scheme. This can provide a more efficient way to cope with the rapidly increasing volume of protein datasets. [ABSTRACT FROM AUTHOR]

Hashing has been widely applied to the large-scale approximate nearest neighbor search problem owing to its high efficiency and low storage requirement. Most investigations concentrate on learning hashing methods in a centralized setting. However, in existing big data systems, data is often stored across different nodes. In some situations, data is even collected in a distributed manner. A straightforward way to solve this problem is to aggregate all the data into the fusion center to obtain the search result (aggregating method). However, this strategy is not feasible because of the prohibitive communication cost. Although a few distributed hashing methods have been proposed to reduce this cost, they only focus on designing a distributed algorithm for a specific global optimization objective without considering scalability. Moreover, existing distributed hashing methods aim at finding a distributed solution to hashing, meanwhile avoiding accuracy loss, rather than improving accuracy. To address these challenges, we propose a Scalable Distributed Hashing (SDisH) model in which most existing hashing methods can be extended to process distributed data with no changes. Furthermore, to improve accuracy, we utilize the search radius as a global variable across different nodes to achieve a global optimum search result for every iteration. In addition, a voting algorithm is presented based on the results produced by multiple iterations to further reduce search errors. Theoretical analyses of communication, computation, and accuracy demonstrate the superiority of the proposed model. Numerical simulations on three large-scale and two relatively small benchmark datasets also show that the SDisH model achieves up to 44.75% and 10.23% accuracy gains compared to the aggregating method and state-of-the-art distributed hashing methods, respectively. [ABSTRACT FROM AUTHOR]

Recommendation efficiency and data sparsity problems have been regarded as two challenges of improving performance for online recommendation. Most of the previous related work focus on improving recommendation accuracy instead of efficiency. In this paper, we propose a Deep Pairwise Hashing (DPH) to map users and items to binary vectors in Hamming space, where a user's preference for an item can be efficiently calculated by Hamming distance, which significantly improves the efficiency of online recommendation. To alleviate data sparsity and cold-start problems, the user-item interactive information and item content information are unified to learn effective representations of items and users. Specifically, we first pre-train robust item representation from item content data by a Denoising Auto-encoder instead of other deterministic deep learning frameworks; then we finetune the entire framework by adding a pairwise loss objective with discrete constraints; moreover, DPH aims to minimize a pairwise ranking loss that is consistent with the ultimate goal of recommendation. Finally, we adopt the alternating optimization method to optimize the proposed model with discrete constraints. Extensive experiments on three different datasets show that DPH can significantly advance the state-of-the-art frameworks regarding data sparsity and item cold-start recommendation. [ABSTRACT FROM AUTHOR]

Approximate Nearest Neighbor(ANN) search is the core problem in many large-scale machine learning and computer vision applications such as multimodal retrieval. Hashing is becoming increasingly popular, since it can provide efficient similarity search and compact data representations suitable for handling such large-scale ANN search problems. Most hashing algorithms concentrate on learning more effective projection functions. However, the accuracy loss in the quantization step has been ignored and barely studied. In this paper, we analyse the importance of various projected dimensions, distribute them into several groups and quantize them with two types of values which can both better preserve the neighborhood structure among data. One is Variable Integer-based Quantization (VIQ) that quantizes each projected dimension with integer values. The other is Variable Codebook-based Quantization (VCQ) that quantizes each projected dimension with corresponding codebook values. We conduct experiments on five common public data sets containing up to one million vectors. The results show that the proposed VCQ and VIQ algorithms can both achieve much higher accuracy than state-of-the-art quantization methods. Furthermore, although VCQ performs better than VIQ, ANN search with VIQ provides much higher search efficiency. [ABSTRACT FROM AUTHOR]

The core of cross-modal hashing methods is to map high dimensional features into binary hash codes, which can then efficiently utilize the Hamming distance metric to enhance retrieval efficiency. Recent development emphasizes the advantages of the unsupervised cross-modal hashing technique, since it only relies on relevant information of the paired data, making it more applicable to real-world applications. However, two problems, that is intro-modality correlation and inter-modality correlation, still have not been fully considered. Intra-modality correlation describes the complex overall concept of a single modality and provides semantic relevance for retrieval tasks, while inter-modality correction refers to the relationship between different modalities. From our observation and hypothesis, the dependency relationship within the modality and between different modalities can be constructed at the object level, which can further improve cross-modal hashing retrieval accuracy. To this end, we propose a Visual-textful Correlation Graph Hashing (OVCGH) approach to mine the fine-grained object-level similarity in cross-modal data while suppressing noise interference. Specifically, a novel intra-modality correlation graph is designed to learn graph-level representations of different modalities, obtaining the dependency relationship of the image region to image region and the tag to tag in an unsupervised manner. Then, we design a visual-text dependency building module that can capture correlation semantic information between different modalities by modeling the dependency relationship between image object region and text tag. Extensive experiments on two widely used datasets verify the effectiveness of our proposed approach. [ABSTRACT FROM AUTHOR]

Diameter perfect codes form a natural generalization for perfect codes. They are based on the code-anticode bound which generalizes the sphere-packing bound. The code-anticode bound was proved by Delsarte for distance-regular graphs and it holds for some other metrics too. In this paper we prove the bound for non-binary constant-weight codes with the Hamming metric and characterize the diameter perfect codes and the maximum size anticodes for these codes. We distinguish between six families of non-binary diameter constant-weight codes and four families of maximum size non-binary constant-weight anticodes. Each one of these families of diameter perfect codes raises some different questions. We consider some of these questions and leave lot of ground for further research. Finally, as a consequence, some $t$ -intersecting families related to the well-known Erdös-Ko-Rado theorem, are constructed. [ABSTRACT FROM AUTHOR]

Let A (n , d) be the size of the maximum binary code of length n and minimum Hamming distance d. A (n , d , w) is defined similarly for binary code with constant weight w. Obviously, finding the value of A (n , d) is equivalent to finding the maximum independent set of the d − 1 th-power of n -dimensional hypercube. Based on this, this paper obtains that A (3 m , 2 m) = 4 , A (m (m + 1) 2 , 2 m − 2 , m) = m + 1 , A (2 m + 1 − 2 , 2 m − 1) = 2 m + 1 , and explores the structure of the maximum code of length 2 m + 2 and minimum Hamming distance 2 m + 1 , where m is an integer. [ABSTRACT FROM AUTHOR]

A fundamental problem in coding theory is to find the values of A (n , d) , i.e., the A (n , d) is the size of the maximum binary code set of length n and minimum Hamming distance d. And A (n , d) can also be viewed as the size of maximum independent set of d − 1 t h -power of the n -dimensional hypercube Q n. In order to further understand and study this problem, we study the distribution of the maximum clique and the structure of the point of Q n d for d ≤ 5. [ABSTRACT FROM AUTHOR]

Image representation and approximate query is always a research challenge and is affected greatly by the dimension and size of images. Since hash-based methods and binary encodings in combination with other techniques, such as kernel tricks, a longer binary code and mapping vectors rotation, can maintain a linear query time and query accuracy, they have been used in this area broadly. This paper develops principal component analysis hashing (PCAH) and unequal length of binary coding to divide images into more categories, denoted as PCA-MD, to improve accuracy of the representation and lookup of images. This paper firstly proves that the eigenvector mapping is locality sensitive, which is the basis for more classes division. For the anisotropy of the eigenvectors, PCA-MD utilizes an unequal length of binary coding and fewer eigenvectors, rather than an equal code, to divide the images mapped on every eigenvector to more categories. Moreover, L1-norm distance is applied to measure the distances of images to avoid the enormous computation of Euclidean distance. Theoretical analysis and extensive experimental results demonstrate that the PCA-MD has a higher query performance and a slight longer run time than the state-of-the-art approaches based on the Hamming distance. This in turn verifies that PCAH is a locality sensitive hash and that partitioning into more categories rather than only two categories is reasonable. [ABSTRACT FROM AUTHOR]

Hashing methods have been widely used in Approximate Nearest Neighbor (ANN) search for big data due to low storage requirements and high search efficiency. These methods usually map the ANN search for big data into the $k$ -Nearest Neighbor ($k$ NN) search problem in Hamming space. However, Hamming distance calculation ignores the bit-level distinction, leading to confusing ranking. In order to further increase search accuracy, various bit-level weights have been proposed to rank hash codes in weighted Hamming space. Nevertheless, existing ranking methods in weighted Hamming space are almost based on exhaustive linear scan, which is time consuming and not suitable for large datasets. Although Multi-Index hashing that is a sub-linear search method has been proposed, it relies on Hamming distance rather than weighted Hamming distance. To address this issue, we propose an exact $k$ NN search approach with Multiple Tables in Weighted Hamming space named WHMT, in which the distribution of bit-level weights is incorporated into the multi-index building. By WHMT, we can get the optimal candidate set for exact $k$ NN search in weighted Hamming space without exhaustive linear scan. Experimental results show that WHMT can achieve dramatic speedup up to 69.8 times over linear scan baseline without losing accuracy in weighted Hamming space. [ABSTRACT FROM AUTHOR]

Symbol-pair codes were introduced by Cassuto and Blaum in 2010 to protect pair errors in symbol-pair read channels. Recently Yaakobi, Bruck and Siegel (2016) generalized this notion to b-symbol codes in order to consider consecutive b errors for a prescribed integer b ≥ 2, and they gave constructions and decoding algorithms. Cyclic codes were considered by various authors as candidates for symbol-pair codes and they established minimum distance bounds on (certain) cyclic codes. In this paper we use algebraic curves over finite fields in order to obtain tight lower and upper bounds on b-symbol Hamming weights of arbitrary cyclic codes over Fq. Here b ≥ 2 is an arbitrary prescribed positive integer and Fq is an arbitrary finite field. We also present a stability theorem for an arbitrary cyclic code C of dimension k and length n: the b-symbol Hamming weight enumerator of C is the same as the k-symbol Hamming weight enumerator of C if k ≤ b ≤ n−1. Moreover, we give improved tight lower and upper bounds on b-symbol Hamming weights of some cyclic codes related to irreducible cyclic codes. Throughout the paper the length n is coprime to q. [ABSTRACT FROM AUTHOR]

We obtain a characterization on self-orthogonality for a given binary linear code in terms of the number of column vectors in its generator matrix, which extends the result of Bouyukliev et al. (2006). As an application, we give an algorithmic method to embed a given binary k-dimensional linear code C (k = 3,4) into a self-orthogonal code of the shortest length which has the same dimension k and minimum distance d' ≥ d(C). For k > 4, we suggest a recursive method to embed a k -dimensional linear code to a self-orthogonal code. We also give new explicit formulas for the minimum distances of optimal self-orthogonal codes for any length n with dimension 4 and any length n ≢ 6, 13,14,21,22,28,29 (mod 31) with dimension 5. [ABSTRACT FROM AUTHOR]

Let 𝔽 p m be a finite field with pm elements for an odd prime p and a positive integer m. In this paper, we aim to construct non-binary quantum codes from repeated root cyclic and negacyclic codes of length 4ps over 𝔽 p m . To achieve this, first we discuss the structure of all maximum distance separable (MDS) cyclic and negacyclic codes of length 4ps over 𝔽 p m and their Euclidean and Hermitian duals. Further, we establish a necessary and sufficient condition for these codes to contain their duals. Finally, many new and quantum MDS codes are obtained with the help of CSS and Hermitian constructions from dual containing cyclic and negacyclic codes. [ABSTRACT FROM AUTHOR]

Time series similarity search is an essential operation in time series data mining and has received much higher interest along with the growing popularity of time series data. Although many algorithms to solve this problem have been investigated, there is a challenging demand for supporting similarity search in a fast and accurate way. In this paper, we present a novel approach, TS2BC, to perform time series similarity search efficiently and effectively. TS2BC uses binary code to represent time series and measures the similarity under the Hamming Distance. Our method is able to represent original data compactly and can handle shifted time series and work with time series of different lengths. Moreover, it can be performed with reasonably low complexity due to the efficiency of calculating the Hamming Distance. We extensively compare TS2BC with state-of-the-art algorithms in classification framework using 61 online datasets. Experimental results show that TS2BC achieves better or comparative performance than other the state-of-the-art in accuracy and is much faster than most existing algorithms. Furthermore, we propose an approximate version of TS2BC to speed up the query procedure and test its efficiency by experiment. [ABSTRACT FROM AUTHOR]

Background: In molecular epidemiology, comparison of intra-host viral variants among infected persons is frequently used for tracing transmissions in human population and detecting viral infection outbreaks. Application of Ultra-Deep Sequencing (UDS) immensely increases the sensitivity of transmission detection but brings considerable computational challenges when comparing all pairs of sequences. We developed a new population comparison method based on convex hulls in hamming space. We applied this method to a large set of UDS samples obtained from unrelated cases infected with hepatitis C virus (HCV) and compared its performance with three previously published methods. Results: The convex hull in hamming space is a data structure that provides information on: (1) average hamming distance within the set, (2) average hamming distance between two sets; (3) closeness centrality of each sequence; and (4) lower and upper bound of all the pairwise distances among the members of two sets. This filtering strategy rapidly and correctly removes 96.2% of all pairwise HCV sample comparisons, outperforming all previous methods. The convex hull distance (CHD) algorithm showed variable performance depending on sequence heterogeneity of the studied populations in real and simulated datasets, suggesting the possibility of using clustering methods to improve the performance. To address this issue, we developed a new clustering algorithm, k-hulls, that reduces heterogeneity of the convex hull. This efficient algorithm is an extension of the k-means algorithm and can be used with any type of categorical data. It is 6.8-times more accurate than k-mode, a previously developed clustering algorithm for categorical data. Conclusions: CHD is a fast and efficient filtering strategy for massively reducing the computational burden of pairwise comparison among large samples of sequences, and thus, aiding the calculation of transmission links among infected individuals using threshold-based methods. In addition, the convex hull efficiently obtains important summary metrics for intra-host viral populations. [ABSTRACT FROM AUTHOR]

Due to the wide applications in consumer electronics, data storage systems and communication systems, cyclic codes have been an interesting research topic in coding theory. In this paper, let p be a prime with p ≥ 7. We determine the Hamming distances of all repeated-root cyclic codes of length 5 p s over F q , where q = p m and both s and m are positive integers. Furthermore, we find all MDS cyclic codes of length 5 p s and take quantum synchronizable codes from repeated-root cyclic codes of length 5 p s . By comparing the minimum distances of 5 p s -length repeated-root cyclic codes to BCH codes of close lengths, we illustrated that quantum synchronizable codes constructed from repeated-root cyclic codes have in general better performance in correcting Pauli errors than those from BCH codes. [ABSTRACT FROM AUTHOR]

In a real-world cloud server, a speech signal is prone to suffer various attacks, such as malicious muting and tampering. In such a context, the privacy security of the speech owner will not be guaranteed. In order to achieve content authentication of encrypted speech in the cloud server, an efficient encrypted speech authentication method based on uniform subband spectrum variance and perceptual hashing is proposed. Firstly, the original speech is scrambled by Henon mapping to construct an encrypted speech library in the cloud, through extracting uniform subband spectrum variance of the encrypted speech and constructing a hashing sequence to generate a hashing template of the cloud. In this way, a one-to-one correspondence between the encrypted speech and the hashing sequence is built. Secondly, the authentication digest of encrypted speech is extracted according to the inquiry result. Finally, the authentication digest and the hashing sequence in the cloud are matched by the Hamming distance algorithm. The experimental results demonstrate that the proposed method has great security and efficiency, and it can directly extract the authentication digest from encrypted speech. The authentication digest not only has good discrimination and robustness, but it accurately locates the tampered area for malicious substitution and mute attacks. [ABSTRACT FROM AUTHOR]

In this work, we study the problem of list decoding of insertions and deletions. We present a Johnson-type upper bound on the maximum list size. The bound is meaningful only when insertions occur. Our bound implies that there are binary codes of rate $\Omega (1)$ that are list-decodable from a 0.707-fraction of insertions. For any $\tau _{\mathsf {I}} \geq 0$ and $\tau _{\mathsf {D}} \in [0,1)$ , there exist $q$ -ary codes of rate $\Omega (1)$ that are list-decodable from a $\tau _{\mathsf {I}}$ -fraction of insertions and $\tau _{\mathsf {D}}$ -fraction of deletions, where $q$ depends only on $\tau _{\mathsf {I}}$ and $\tau _{\mathsf {D}}$. We also provide efficient encoding and decoding algorithms for list-decoding from $\tau _{\mathsf {I}}$ -fraction of insertions and $\tau _{\mathsf {D}}$ -fraction of deletions for any $\tau _{\mathsf {I}} \geq 0$ and $\tau _{\mathsf {D}} \in [0,1)$. Based on the Johnson-type bound, we derive a Plotkin-type upper bound on the code size in the Levenshtein metric. [ABSTRACT FROM AUTHOR]

The weight spectra of MDS codes of length n and dimension k over arbitrary alphabets are studied. For all q-ary MDS codes of dimension k and length ${n}\ne {q}+{k}-1 $ containing the zero codeword, it is shown that all k weights from n to ${n}-{k}+1 $ are realized. The weight spectrum in the remaining case ${n}={q}+{k}-1 $ is also determined. Additionally, we prove that all binary MDS codes are equivalent to linear MDS codes. The proofs are combinatorial, and self contained. [ABSTRACT FROM AUTHOR]

An additive quaternary [n,k,d]-code (length n, quaternary dimension k, minimum distance d) is a 2k-dimensional F2-vector space of n-tuples with entries in F2 ⊕ F2 (the 2-dimensional vector space over F2) with minimum Hamming distance d. We determine the optimal parameters of additive quaternary codes of dimension k ≤ 3. The most challenging case is dimension k = 2.5. We prove that an additive quaternary [n,2.5,d]-code where d < n−1 exists if and only if 3(n−d) ≥ ⌈d/2⌉ + ⌈d/4⌉ + ⌈d/8⌉. In particular, we construct new optimal 2.5-dimensional additive quaternary codes. As a by-product, we give a direct proof for the fact that a binary linear [3m,5,2e]2-code for e < m−1 exists if and only if the Griesmer bound 3(m−e) ≥e/2⌉ + ⌈e/4⌉ + ⌈e/8⌉ is satisfied. [ABSTRACT FROM AUTHOR]

Hashing techniques have been widely used for large-scale image retrieval because of its low storage cost and high query speed. Hashing maps similar data onto binary codes with a smaller Hamming distance, which is essentially a discrete optimization problem with constraints. Recently, several discrete hashing methods have begun focusing on minimizing the discrete loss between hash codes and continuous values but ignoring the hidden structure among data points in the original space. Following these efforts, we propose a locality-constrained discrete graph hashing (LCH) method that attempts to minimize the similarity distance of the data points in the original space by softening the hash codes' hard constraint into two spaces: the discrete constraint space and the bit-balanced, bit-uncorrected constraint space. Furthermore, both spaces maintain the neighbourhood structure of the data points in the original space, and the best hash codes are found by minimizing the similarity distance between the two spaces. This is consistent with the nature of hashing for similarity preservation. Experiments on four real image datasets show that LCH obtains superior search accuracy over state-of-the-art hashing methods. [ABSTRACT FROM AUTHOR]

Nearest neighbor search is a basic and recurring proximity problem that has been studied for several decades. The goal is to preprocess a dataset of points so that we can quickly report the closet point(s) to any query point. Many recent applications of NNS involve datasets that are very large and dynamic, that is items of data items become available gradually. In this study, we propose a data structure for solving NNS for dynamic binary data where both query and dataset items are represented as binary strings. The proposed tree data structure, called the Hamming Weight Tree, is simple and as the names suggests, is based on partitioning the feature space of binary strings by exploiting the Hamming weights of the binary codes and their substrings. Given a Hamming Weight Tree of binary codes, we propose two search algorithms that accommodate nearest neighbor search for two different distance functions, the Hamming distance and the angular distance. Our empirical results show significant speedup in comparison with the best known large-scale solutions. [ABSTRACT FROM AUTHOR]

Despite the thrilling success achieved by existing binary descriptors, most of them are still in the mire of three limitations: 1) vulnerable to the geometric transformations; 2) incapable of preserving the manifold structure when learning binary codes; 3) NO guarantee to find the true match if multiple candidates happen to have the same Hamming distance to a given query. All these together make the binary descriptor less effective, given large-scale visual recognition tasks. In this paper, we propose a novel learning-based feature descriptor, namely Unsupervised Deep Binary Descriptor (UDBD), which learns transformation invariant binary descriptors via projecting the original data and their transformed sets into a joint binary space. Moreover, we involve a $\ell _{2,1}$ -norm loss term in the binary embedding process to gain simultaneously the robustness against data noises and less probability of mistakenly flipping bits of the binary descriptor, on top of it, a graph constraint is used to preserve the original manifold structure in the binary space. Furthermore, a weak bit mechanism is adopted to find the real match from candidates sharing the same minimum Hamming distance, thus enhancing matching performance. Extensive experimental results on public datasets show the superiority of UDBD in terms of matching and retrieval accuracy over state-of-the-arts. [ABSTRACT FROM AUTHOR]

Hashing could significantly accelerate large-scale image search by transforming the high-dimensional features into binary Hamming space, where efficient similarity search can be achieved with very fast Hamming distance computation and extremely low storage cost. As an important branch of hashing methods, multi-view hashing takes advantages of multiple features from different views for binary hash learning. However, existing multi-view hashing methods are either based on shallow models which fail to fully capture the intrinsic correlations of heterogeneous views, or unsupervised deep models which suffer from insufficient semantics and cannot effectively exploit the complementarity of view features. In this paper, we propose a novel Deep Collaborative Multi-view Hashing (DCMVH) method to deeply fuse multi-view features and learn multi-view hash codes collaboratively under a deep architecture. DCMVH is a new deep multi-view hash learning framework. It mainly consists of 1) multiple view-specific networks to extract hidden representations of different views, and 2) a fusion network to learn multi-view fused hash code. DCMVH associates different layers with instance-wise and pair-wise semantic labels respectively. In this way, the discriminative capability of representation layers can be progressively enhanced and meanwhile the complementarity of different view features can be exploited effectively. Finally, we develop a fast discrete hash optimization method based on augmented Lagrangian multiplier to efficiently solve the binary hash codes. Experiments on public multi-view image search datasets demonstrate our approach achieves substantial performance improvement over state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Recently, some infinite families of binary minimal and optimal linear codes were constructed from simplicial complexes by Hyun et al. Inspired by their work, we present two new constructions of codes over the ring $\mathbb {F}_{2}+u\mathbb {F}_{2}$ by employing simplicial complexes. When the simplicial complexes are all generated by a maximal element, we determine the Lee weight distributions of two classes of the codes over $\mathbb {F}_{2}+u\mathbb {F}_{2}$. Our results show that the codes have few Lee weights. Via the Gray map, we obtain an infinite family of binary codes meeting the Griesmer bound and a class of binary distance optimal codes. [ABSTRACT FROM AUTHOR]

Aiming at the problem of fast certification for a constrained iris in the same category caused by the unstable iris features caused by the change of the iris acquisition environment and shooting status under lightweight training samples, a one-to-one fast certification algorithm for constrained unsteady-state iris based on the scale change stable feature and multi-algorithm voting is proposed. Scale change stable features are found by constructing an isometric differential Gaussian space, and a local binary pattern algorithm with extended statistics (ES-LBP), the Haar wavelet with over threshold detection and the Gabor filter algorithm with immune particle swarm optimization (IPSO) are used to represent the stable features as binary feature codes. Iris certification is performed by the Hamming distance. According to the certification results of three algorithms, the final result is obtained by multi-algorithm voting. Experiments with the JLU and CASIA iris libraries under the iris prerequisite conditions show that the correct recognition rate of this algorithm can reach a high level of 98% or more, indicating that this algorithm can improve the operation speed, accuracy and robustness of certification. [ABSTRACT FROM AUTHOR]

Thanks to its storage and computation efficiency, hashing as a kind of nearest neighbor search method can facilitate massive data processing in recent vision and learning studies. Particularly, deep supervised hashing methods have significantly improved the retrieval performance compared with non-deep supervised hashing methods. However, most existing deep supervised hashing methods approximate the similarity between two images with the hamming distance between the outputs of the same hash function, i.e., the symmetric strategy. Consequently, it is typically time-consuming to train these symmetric hashing methods, and these methods can hardly take full advantage of the supervised information in the large-scale database. In this paper, we propose a novel discriminative deep m etric learning approach for a symmetric d iscrete h ashing (ADMH) approach for supervised hashing learning. ADMH integrates an asymmetric strategy with a deep metric learning method to learn the hash function for the query images and the discrete hash codes for database images directly. More specifically, we train a deep neural network to extract the features of the query images. Subsequently, we introduce a metric learning scheme for learning the discrete discriminative hash codes of the database images directly. Finally, the feature learning procedure for generating the hash codes of the query images and the discrete coding procedure for generating the hash codes of the database images are integrated into an end-to-end learning framework. Extensive experiments on various benchmark datasets show that the proposed asymmetric deep hashing method outperforms the existing hashing methods. [ABSTRACT FROM AUTHOR]

Most existing hashing methods resort to binary codes for large scale similarity search, owing to the high efficiency of computation and storage. However, binary codes lack enough capability in similarity preservation, resulting in less desirable performance. To address this issue, we propose Nonlinear Asymmetric Multi-Valued Hashing (NAMVH) supported by two distinct non-binary embeddings. Specifically, a real-valued embedding is used for representing the newly-coming query by an ideally nonlinear transformation. Besides, a multi-integer-embedding is employed for compressing the whole database, which is modeled by Binary Sparse Representation (BSR) with fixed sparsity. With these two non-binary embeddings, NAMVH preserves more precise similarities between data points and enables access to the incremental extension with database samples evolving dynamically. To perform meaningful asymmetric similarity computation for efficient semantic search, these embeddings are jointly learnt by preserving the pairwise label-based similarity. Technically, this results in a mixed integer programming problem, which is efficiently solved by a well-designed alternative optimization method. Extensive experiments on seven large scale datasets demonstrate that our approach not only outperforms the existing binary hashing methods in search accuracy, but also retains their query and storage efficiency. [ABSTRACT FROM AUTHOR]

In this paper, we consider q -ary codes of length n and minimum Hamming distance d , which have two weights w 1 and w 2. These codes are denoted by (n , d , { w 1 , w 2 }) q codes. Let A q (n , d , { w 1 , w 2 }) denote the largest possible number of codewords in an (n , d , { w 1 , w 2 }) q code and we simply write A (n , d , { w 1 , w 2 }) for A 2 (n , d , { w 1 , w 2 }). Some upper bounds on A q (n , d , { w 1 , w 2 }) are given. The equivalences between binarytwo-weight codes and special combinatorial configurations with certain properties are established and then new upper bounds on A (n , d , { w 1 , w 2 }) are derived. For w 1 , w 2 ∈ { 2 , 3 , 4 } , optimal constructions of (n , d , { w 1 , w 2 }) 2 codes are presented. The exact value of A (n , d , { 2 , 3 }) is completely determined for all n and d. We determine the exact value of A (n , d , { 2 , 4 }) for any positive integer n ≡ 2 , 4 (mod 6) and d ∈ { 3 , 4 }. The exact value of A (n , d , { 3 , 4 }) is determined for any integer n and d ∈ { 6 , 7 } , or d = 5 and n ≡ 0 , 2 , 3 , 11 (mod 12). [ABSTRACT FROM AUTHOR]

Hashing methods are used to perform the approximate nearest neighbor search due to the low storage for binary codes and the fast computation of Hamming distance. However, in most of the hashing methods, the learning process of hash functions has high cost in both time and storage. To overcome this issue, in this paper, a fast online unsupervised hashing method based on data sampling is proposed to learn the hypersphere-based hash functions from the streaming data. By maintaining a small-size data sample to efficiently preserve the properties of the streaming data, the hypersphere-based hash functions are learnt in an online fashion from the data sample and we can justify the hash functions by proving their theoretic properties. To further improve the search accuracy of our method, a new dimensionality reduction algorithm is proposed to learn the projection matrix from the data sample to construct a low-dimensional space. Then, the data sample is projected into the low-dimensional space, and our method can learn the hash functions online from the small-size projected data sample with low computational complexity and storage space. The experiments show that our method has a better search accuracy than other online hashing methods and runs faster in learning the hash functions. [ABSTRACT FROM AUTHOR]

Similarity-preserving hashing is a widely used method for nearest neighbor search in large-scale image retrieval tasks. Considerable research has been conducted on deep-network-based hashing approaches to improve the performance. However, the binary codes generated from deep networks may be not uniformly distributed over the Hamming space, which will greatly increase the retrieval time. To this end, we propose a deep-network-based multi-index hashing (MIH) for retrieval efficiency. We first introduce the MIH mechanism into the proposed deep architecture, which divides the binary codes into multiple substrings. Each substring corresponds to one hash table. Then, we add the two balanced constraints to obtain more uniformly distributed binary codes: 1) balanced substrings, where the Hamming distances of each substring are equal for any two binary codes and 2) balanced hash buckets, where the sizes of each bucket are equal. Extensive evaluations on several benchmark image retrieval data sets show that the learned balanced binary codes bring dramatic speedups and achieve comparable performance over the existing baselines. [ABSTRACT FROM AUTHOR]

In this paper, we propose an unsupervised feature learning method called deep binary descriptor with multi-quantization (DBD-MQ) for visual analysis. Existing learning-based binary descriptors such as compact binary face descriptor (CBFD) and DeepBit utilize the rigid sign function for binarization despite of data distributions, which usually suffer from severe quantization loss. In order to address the limitation, we propose a deep multi-quantization network to learn a data-dependent binarization in an unsupervised manner. More specifically, we design a K-Autoencoders (KAEs) network to jointly learn the parameters of feature extractor and the binarization functions under a deep learning framework, so that discriminative binary descriptors can be obtained with a fine-grained multi-quantization. As DBD-MQ simply allocates the same number of quantizers to each real-valued feature dimension ignoring the elementwise diversity of informativeness, we further propose a deep competitive binary descriptor with multi-quantization (DCBD-MQ) method to learn optimal allocation of bits with the fixed binary length in a competitive manner, where informative dimensions gain more bits for complete representation. Moreover, we present a similarity-aware binary encoding strategy based on the earth mover's distance of Autoencoders, so that elements that are quantized into similar Autoencoders will have smaller Hamming distances. Extensive experimental results on six widely-used datasets show that our DBD-MQ and DCBD-MQ outperform most state-of-the-art unsupervised binary descriptors. [ABSTRACT FROM AUTHOR]

Content-based histopathology image retrieval can be a useful technique for help in diagnosing various diseases. The process of retrieving images is often time-consuming and challenging due to the need for high-dimensional features when trying to model complex content. Hashing methods can therefore be employed to resolve the challenge by producing binary codes of different lengths. Deep hashing methods are frequently superior to traditional machine learning approaches but are affected by the size of training sets. In addition, back-propagation learning can further complicate the generation of binary values. Hence, this paper proposes a novel Siamese deep hashing model, named histopathology Siamese deep hashing (HSDH), for histopathology image retrieval. Two designed deep hashing models with shared weights and structures are used to generate hash codes. A Hamming distance layer is then applied to evaluate the similarity of the generated values. A highly effective loss function is also introduced that incorporates a modified version of the standard contrastive loss function with an error estimation term to improve both the training and retrieval phases. In the retrieval phase, the trained model compares a query image with all the training images and ranks the most similar images. According to the experimental results on two publicly available databases, BreakHis and Kather, the HSDH model outperforms other state-of-the-art hashing-based methods in histopathology image retrieval. [ABSTRACT FROM AUTHOR]

Highlights • Inspired by human perceptual attention study, the multiview features are used in the proposed segmentation framework. • The low-dimensional and smooth embedding over multiview features are learned by the proposed algorithm. • The image segmentation model is reformulated as a multiview semantic similarity computation at pixel-level. • Instead of alternating optimization algorithm, the spectral hashing model is used to solve optimization problem with less computational complexity. Abstract The image segmentation of finely detailed object in images is becoming increasingly important in various image applications. Herein, multiview features such as color, spatial features, texture, saliency, and depth are used to calculate the feature semantic that differentiates the image foreground and background at the pixel level. For different image type, the importance of every single image feature is various. We assume that combining multiple features will produce improved results compared to using any single feature and propose an unsupervised learning strategy to learn optimal feature projection to the final solution surface of binary segmentation. To reduce computational complexity, a hashing model is used to represent the projected feature using binary codes, as its hamming distance efficiently retrieves the pixel similarity. Comparative experiments using the current state-of-the-art unsupervised segmentation algorithms and a deep learning approach, i.e., a fully convolutional network, demonstrate the advantages of the proposed method. [ABSTRACT FROM AUTHOR]

Hashing is a promising approach for compact storage and efficient retrieval of big data. Compared to the conventional hashing methods using handcrafted features, emerging deep hashing approaches employ deep neural networks to learn both feature representations and hash functions, which have been proven to be more powerful and robust in real-world applications. Currently, most of the existing deep hashing methods construct pairwise or triplet-wise constraints to obtain similar binary codes between a pair of similar data points or relatively similar binary codes within a triplet. However, we argue that some critical local structures have not been fully exploited. So, this paper proposes a novel deep hashing method named local semantic-aware deep hashing with Hamming-isometric quantization (LSDH), aiming to make full use of local similarity in hash function learning. Specifically, the potential semantic relation is exploited to robustly preserve local similarity of data in the Hamming space. In addition to reducing the error introduced by binary quantizing, a Hamming-isometric objective is designed to maximize the consistency of similarity between the pairwise binary-like features and corresponding binary codes pair, which is shown to be able to improve the quality of binary codes. Extensive experimental results on several benchmark datasets, including three single-label datasets and one multi-label dataset, demonstrate that the proposed LSDH achieves better performance than the latest state-of-the-art hashing methods. [ABSTRACT FROM AUTHOR]

Abstract Let p be an odd prime, s , m be positive integers, γ , λ be nonzero elements of the finite field F p m such that γ p s = λ. In this paper, we show that, for any positive integer η , the Hamming distances of all repeated-root λ -constacyclic codes of length η p s can be determined by those of certain simple-root γ -constacyclic codes of length η. Using this result, Hamming distances of all constacyclic codes of length 4 p s are obtained. As an application, we identify all MDS λ -constacyclic codes of length 4 p s. [ABSTRACT FROM AUTHOR]

This paper generalizes the method proposed by Poulliat et al. for the determination of the optimal Galois field coefficients of a non-binary LDPC parity check constraint based on the binary image of the code. Optimal, or almost-optimal, parity check coefficients are given for check degree varying from 4 to 20 and Galois field varying from GF (64) up to GF (1024). For all given sets of coefficients, no codeword of Hamming weight two exists. A reduced complexity algorithm to compute the binary Hamming weight 3 of a parity check is proposed. When the number of sets of coefficients is too high for an exhaustive search and evaluation, a local greedy search is performed. Explicit tables of coefficients are given. The proposed sets of coefficients can effectively replace the random selection of coefficients often used in NB-LDPC construction. [ABSTRACT FROM AUTHOR]

Highlights • Both features and attributes are projected into orthogonal space. • Binary codes of different categories are orthogonal to each other. • All the Hamming distance of different classes are equal to half code length. • Both linear and deep models are implemented to show the performance. Abstract Hashing has been widely used in large-scale image retrieval. Supervised information such as semantic similarity and class label, and Convolutional Neural Network (CNN) has greatly improved the quality of hash codes and hash functions. However, due to the explosive growth of web data, existing hashing methods cannot well perform on emerging images of new classes. In this paper, we propose a novel hashing method based on orthogonal projection of both image and semantic attribute, which constrains the generated binary codes in orthogonal space should be orthogonal with each other when they belong to different classes, otherwise be same. This constraint guarantees that the generated hash codes from different categories have equal Hamming distance, which also makes the space more discriminative within limited code length. To improve the performance, we also extend our method with a deep model. Experiments of both our linear and deep model on three popular datasets show that our method can achieve competitive results, specially, the deep model can outperform all the listed state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

The study of subblock-constrained codes has recently gained attention due to their application in diverse fields. We present bounds on the size and asymptotic rate for two classes of subblock-constrained codes. The first class is binary constant subblock-composition codes (CSCCs), where each codeword is partitioned into equal sized subblocks, and every subblock has the same fixed weight. The second class is binary subblock energy-constrained codes (SECCs), where the weight of every subblock exceeds a given threshold. We present novel upper and lower bounds on the code sizes and asymptotic rates for the binary CSCCs and SECCs. For a fixed subblock length and small relative distance, we show that the asymptotic rate for CSCCs (respectively SECCs) is strictly lower than the corresponding rate for constant weight codes (CWCs) [respectively heavy weight codes (HWCs)]. Furthermore, for codes with high weight and low relative distance, we show that the asymptotic rate for CSCCs is strictly lower than that of SECCs, which contrasts with the fact that the asymptotic rate for the CWCs is equal to that of the HWCs. We also provide a correction to an earlier result by Chee et al. (2014) on the asymptotic CSCC rate. In addition, we present several numerical examples comparing the rates for the CSCCs and SECCs with those for the CWCs and HWCs. [ABSTRACT FROM AUTHOR]

This paper investigates fundamental properties of nonlinear binary codes by looking at the codebook matrix not row-wise (codewords), but column-wise. The family of weak flip codes is presented and shown to contain many beautiful properties. In particular the subfamily fair weak flip codes, which goes back to Shannon et al. and which was shown to achieve the error exponent with a fixed number of codewords $\mathsf {M}$ , can be seen as a generalization of linear codes to an arbitrary number of codewords. The fair weak flip codes are related to binary nonlinear Hadamard codes. Based on the column-wise approach to the codebook matrix, the $r$ -wise Hamming distance is introduced as a generalization to the well-known and widely used (pairwise) Hamming distance. It is shown that the minimum $r$ -wise Hamming distance satisfies a generalized $r$ -wise Plotkin bound. The $r$ -wise Hamming distance structure of the nonlinear fair weak flip codes is analyzed and shown to be superior to many codes. In particular, it is proven that the fair weak flip codes achieve the $r$ -wise Plotkin bound with equality for all $r$. In the second part of this paper, these insights are applied to a binary erasure channel with an arbitrary erasure probability 0 < $\delta$ < 1. An exact formula for the average error probability of an arbitrary (linear or nonlinear) code using maximum likelihood decoding is derived and shown to be expressible using only the $r$ -wise Hamming distance structure of the code. For a number of codewords $\mathsf {M}$ satisfying $\mathsf {M}\le 4$ and an arbitrary finite blocklength $n$ , the globally optimal codes (in the sense of minimizing the average error probability) are found. For $\mathsf {M}$ = 5 or $\mathsf {M}$ = 6 and an arbitrary finite blocklength $n$ , the optimal codes are conjectured. For larger $\mathsf {M}$ , observations regarding the optimal design are presented, e.g., that good codes have a large $r$ -wise Hamming distance structure for all $r$. Numerical results validate our code design criteria and show the superiority of our best found nonlinear weak flip codes compared with the best linear codes. [ABSTRACT FROM AUTHOR]