Pairwise Hamming Distance Research Articles

Analysing Equilibrium States for Population Diversity

Population diversity is crucial in evolutionary algorithms as it helps with global exploration and facilitates the use of crossover. Despite many runtime analyses showing advantages of population diversity, we have no clear picture of how diversity evolves over time. We study how the population diversity of (μ+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\mu +1)$$\\end{document} algorithms, measured by the sum of pairwise Hamming distances, evolves in a fitness-neutral environment. We give an exact formula for the drift of population diversity and show that it is driven towards an equilibrium state. Moreover, we bound the expected time for getting close to the equilibrium state. We find that these dynamics, including the location of the equilibrium, are unaffected by surprisingly many algorithmic choices. All unbiased mutation operators with the same expected number of bit flips have the same effect on the expected diversity. Many crossover operators have no effect at all, including all binary unbiased, respectful operators. We review crossover operators from the literature and identify crossovers that are neutral towards the evolution of diversity and crossovers that are not.

Dimensionality Reduction for Categorical Data

Categorical attributes are those that can take a discrete set of values, e.g., colours. This work is about compressing vectors over categorical attributes to low-dimension discrete vectors. The current hash-based methods compressing vectors over categorical attributes to low-dimension discrete vectors do not provide any guarantee on the Hamming distances between the compressed representations. Here we present FSketch to create sketches for sparse categorical data and an estimator to estimate the pairwise Hamming distances among the uncompressed data only from their sketches. We claim that these sketches can be used in the usual data mining tasks in place of the original data without compromising the quality of the task. For that, we ensure that the sketches also are categorical, sparse, and the Hamming distance estimates are reasonably precise. Both the sketch construction and the Hamming distance estimation algorithms require just a single-pass; furthermore, changes to a data point can be incorporated into its sketch in an efficient manner. The compressibility depends upon how sparse the data is and is independent of the original dimension -- making our algorithm attractive for many real-life scenarios. Our claims are backed by rigorous theoretical analysis of the properties of FSketch and supplemented by extensive comparative evaluations with related algorithms on some real-world datasets. We show that FSketch is significantly faster, and the accuracy obtained by using its sketches are among the top for the standard unsupervised tasks of RMSE, clustering and similarity search.

Permutation-Based Block Code for Short Packet Communication Systems.

This paper presents an approach to the construction of block error-correcting code for data transmission systems with short packets. The need for this is driven by the necessity of information interaction between objects of machine-type communication network with a dynamically changing structure and unique system of commands or alerts for each network object. The codewords of a code are permutations with a given minimum pairwise Hamming distance. The purpose of the study is to develop a statistical method for constructing a code, in contrast to known algebraic methods, and to investigate the code size. An algorithm for generating codewords has been developed. It can be implemented both by enumeration of the full set of permutations, and by enumeration of a given number of randomly selected permutations. We have experimentally determined the dependencies of the average and the maximum values of the code size on the size of a subset of permutations used for constructing the code. A technique for computing approximation quadratic polynomials for the determined code size dependencies has been developed. These polynomials and their corresponding curves estimate the size of a code generated from a subset of random permutations of such a size that a statistically significant experiment cannot be performed. The results of implementing the developed technique for constructing a code based on permutations of lengths 7 and 11 have been presented. The prediction relative error of the code size did not exceed the value of 0.72% for permutation length 11, code distance 9, random permutation subset size 50,000, and permutation statistical study range limited by 5040.

Finding Diverse Trees, Paths, and More

Mathematical modeling is a standard approach to solve many real-world problems and diversity of solutions is an important issue, emerging in applying solutions obtained from mathematical models to real-world problems. Many studies have been devoted to finding diverse solutions. Baste et al. (Algorithms 2019, IJCAI 2020) recently initiated the study of computing diverse solutions of combinatorial problems from the perspective of fixed-parameter tractability. They considered problems of finding r solutions that maximize some diversity measures (the minimum or sum of the pairwise Hamming distances among them) and gave some fixed-parameter tractable algorithms for the diverse version of several well-known problems, such as Vertex Cover, Feedback Vertex Set, d-Hitting Set}, and problems on bounded-treewidth graphs. In this work, we further investigate the (fixed-parameter) tractability of problems of finding diverse spanning trees, paths, and several subgraphs. In particular, we show that, given a graph G and an integer r, the problem of computing r spanning trees of G maximizing the sum of the pairwise Hamming distances among them can be solved in polynomial time. To the best of the authors' knowledge, this is the first polynomial-time solvable case for finding diverse solutions of unbounded size.

Algorithms for all‐pairs Hamming distance based similarity

AbstractAll‐pairs distance computation for a collection of strings is a computation‐intensive task with important applications in bioinformatics, in particular, in distance‐based phylogenetic analysis techniques. Even if the computationally efficient Hamming distance is used for this purpose, the quadratic number of sequence pairs may be challenging. We propose a number of practical algorithms for efficient pairwise Hamming distance computation under a given distance threshold. The techniques are based on such concepts as pivot‐based similarity search in metric spaces, pigeonhole principle for approximate string matching, cache‐friendly data arrangement, bit‐parallelism, and others. We experimentally show that our solutions are often about an order of magnitude faster than the average‐case linear‐time LCP based clusters method proposed recently, both in real and synthetic benchmarks.

An Automatic Convolutional Neural Network Optimization Using a Diversity-Guided Genetic Algorithm

Hyperparameters and architecture greatly influence the performance of convolutional neural networks (CNNs); therefore, their optimization is important to obtain the desired results. One of the state-of-the-art methods to achieve this is the use of neuroevolution that utilizes a genetic algorithm (GA) to optimize a CNN. However, the GA is often trapped into a local optimum resulting in premature convergence. In this study, we propose an approach called the “diversity-guided genetic algorithm-convolutional neural network (DGGA-CNN)” that uses adaptive parameter control and random injection to facilitate the search process by exploration and exploitation while preserving the population diversity. The alternation between exploration and exploitation is guided by using an average pairwise Hamming distance. Moreover, the DGGA fully handles the architecture of the CNN by using a novel finite state machine (FSM) combined with three novel mutation mechanisms that are specifically created for architecture chromosomes. Tests conducted on suggestion mining and twitter airline datasets reveal that the DGGA-CNN performs well with valid architectures and a comparison with other methods demonstrates its capability and efficiency.

Abstract 2683: Ductal carcinoma in situ is a multiclonal disease

Abstract Introduction. Ductal carcinoma in situ (DCIS) of the breast has a limited propensity to progress to invasive breast cancer. However, due to a lack of markers that predict the risk of progression to invasive cancer, many DCIS patients may receive unnecessary surgery. Here, we explore whether the multiclonal intratumoral heterogeneity commonly observed in invasive breast cancers is also present in the precursor DCIS, and whether it differs between pure DCIS (without concurrent invasion) and mixed DCIS (with concurrent invasion). Methods. A total of 19 tumors (10 pure, 9 mixed) were analyzed. Based on whole exome sequencing, tumor-specific mutation panels were identified and contained a median of 60 point mutations per tumor (range: 35-80). From each tumor, 3-4 histologic sections were obtained, with a mean distance between slides of 1.26cm (range: 0.34-6.0cm). Individual DCIS ducts were microdissected from the sections using selective ultraviolet radiation fractionation (SURF); median number of ducts per tumor was 23 (range: 10-50). For each duct, the tumor specific mutation panel was assayed using targeted deep sequencing (median depth: 9,000x). Clonal deconvolution within each tumor was performed using the software package CloneFinder. Individual glands were classified as multiclonal if they contained 2 or more tumor subclones. In addition, the following evolutionary measures were computed for each tumor: (i) clone diversity as the mean pairwise Hamming distance between all ducts; (ii) clonal mixing as the number of clones that were present in more than one section. Comparisons between pure and mixed cases were performed using a two-sided Wilcoxon rank sum test. Results. All DCIS lesions were multiclonal. The number of subclones per tumor ranged from 2 to 9 overall, with a median of 5 and 6 subclones in pure and mixed DCIS, respectively (p-value for difference=.1). The median fraction of multiclonal glands per tumor was higher in mixed vs. pure DCIS (10% vs. 0%; p=.03). Median subclone diversity was higher in mixed vs. pure DCIS (1.48 vs. 1.04; p=.03), and the fraction of mixing subclones trended higher in mixed DCIS (median: 63%, range: 38-100%) compared to pure DCIS (median: 37%, range: 0-80%; p=.1). Subclones were spatially extensive: 18/19 tumors had at least one subclone that spanned across the analyzed sections, covering a mean distance of 2.5cm. Conclusions. All analyzed DCIS cases were multiclonal and individual subclones were found to span large regions of the tumor. Despite small sample sizes we found differences between pure and mixed DCIS. In particular, mixed DCIS harbored a higher fraction of multiclonal glands and a higher subclone diversity between individual ducts. Our findings characterize the evolutionary dynamics of breast cancer initiation and may provide evolutionary markers that distinguish indolent (pure) and progressive (mixed) disease. As such, this line of work has the potential to risk-stratify DCIS lesions. Citation Format: Marc D. Ryser, Inmaculada C. Sorribes, Matthew Greenwald, Allison Hall, Diego Mallo, Lorraine M. King, Timothy Hardman, Lunden Simpson, Carlo C. Maley, Jeffrey R. Marks, Darryl Shibata, E. Shelley Hwang. Ductal carcinoma in situ is a multiclonal disease [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr 2683.

FPT Algorithms for Diverse Collections of Hitting Sets

In this work, we study the d-Hitting Set and Feedback Vertex Set problems through the paradigm of finding diverse collections of r solutions of size at most k each, which has recently been introduced to the field of parameterized complexity. This paradigm is aimed at addressing the loss of important side information which typically occurs during the abstraction process that models real-world problems as computational problems. We use two measures for the diversity of such a collection: the sum of all pairwise Hamming distances, and the minimum pairwise Hamming distance. We show that both problems are fixed-parameter tractable in k + r for both diversity measures. A key ingredient in our algorithms is a (problem independent) network flow formulation that, given a set of ‘base’ solutions, computes a maximally diverse collection of solutions. We believe that this could be of independent interest.

Constructing permutation arrays using partition and extension

We give new lower bounds for M(n, d), for various positive integers n and d with $$n>d$$, where M(n, d) is the largest number of permutations on n symbols with pairwise Hamming distance at least d. Large sets of permutations on n symbols with pairwise Hamming distance d are needed for constructing error correcting permutation codes, which have been proposed for power-line communications. Our technique, partition and extension, is universally applicable to constructing such sets for all n and all d, $$d<n$$. We describe three new techniques, sequential partition and extension, parallel partition and extension, and a modified Kronecker product operation, which extend the applicability of partition and extension in different ways. We describe how partition and extension gives improved lower bounds for $$M(n,n-1)$$ using mutually orthogonal Latin squares (MOLS). We present efficient algorithms for computing new partitions: an iterative greedy algorithm and an algorithm based on integer linear programming. These algorithms yield partitions of positions (or symbols) used as input to our partition and extension techniques. We report many new lower bounds for M(n, d) found using these techniques for n up to 600.

Telugu Word Image Retrieval using Deep learning Convolutional Neural Networks

Telugu word image retrieval (TWIR) is a still challenging task due to the structure complexity of Telugu word image. An efficient TWIR system can be implemented by a holistic representation of word image that comprises of every possible extracted feature. Further, it is also required to retrieve more relevant word images even there is a noisy query word image. Here, it is proposed an efficient TWIR system that utilizes deep learning convolutional neural networks (DL-CNN) to extract the feature map from the query and database word images. In addition, principal component analysis (PCA) is employed to compute the principal features form the feature map and pairwise hamming distance is considered as a similarity metric to retrieve most relevant Telugu word images from the database. Extensive simulation analysis disclosed that proposed TIWR system obtained a superior performance over conventional TIWR systems in terms of mean average precision (mAP) and mean average recall (mAR).

A new coding-based algorithm for finding closest pair of vectors

Given n vectors x0,x1,…,xn−1 in {0,1}m, how to find two vectors whose pairwise Hamming distance is minimum? This problem is known as the Closest Pair Problem. If these vectors are generated uniformly at random except two of them are correlated with Pearson-correlation coefficient ρ, then the problem is called the Light Bulb Problem. In this work, we propose a novel coding-based scheme for the Closest Pair Problem. We design both randomized and deterministic algorithms, which achieve the best-known running time when the length of input vectors m is small and the minimum distance is very small compared to m. Specifically, the running time of our randomized algorithm is O(nlog2⁡n⋅2cm⋅poly(m)) and the running time of our deterministic algorithm is O(nlog⁡n⋅2c′m⋅poly(m)), where c and c′ are constants depending only on the (relative) distance of the closest pair. When applied to the Light Bulb Problem, our result yields state-of-the-art deterministic running time when the Pearson-correlation coefficient ρ is very large. Specifically, when ρ≥0.9933, our deterministic algorithm runs faster than the previously best deterministic algorithm (Alman, SOSA 2019).

Encoding pairwise Hamming distances of Local Binary Patterns for visual smoke recognition

To achieve scale invariance, existing methods based on multi-scale local binary patterns (LBP) usually concatenate histograms of LBP codes from different scales. Direct concatenation of histograms is very simple and computationally efficient, but it cannot well model the spatial relationship of LBP codes across scales. Aiming at modeling scale-level variations of LBP codes, we measure and encode the relationship between a pair of LBP codes at the same position from two scales. Gaussian filters are applied to generate the scale space of an image, and original LBP codes are extracted on each scale. The Hamming distance between a pair of LBP codes is used to measure variations of LBP codes across scales. To incorporate the scale-level variations of LBPs into codes, we encode the Hamming distance measures in the same way as LBP to generate a novel code, called Pairwise Comparing Local Binary Patterns (PCLBP). To achieve rotation invariance, LBP and PCLBP codes are aligned to the direction with the maximum magnitude of local differences between a center pixel and its neighbors. To improve reliability of the alignments, we also propose a circular Gaussian smoothing method to remove noise in local differences. Finally, we concatenate the histograms of aligned PCLBP and LBP codes to obtain rotation and scale invariant descriptors for smoke classification. Extensive experiments show that our method obviously outperforms existing LBP variants on smoke datasets, and also achieves outstanding performance on other datasets.

Fast phylogenetic inference from typing data

BackgroundMicrobial typing methods are commonly used to study the relatedness of bacterial strains. Sequence-based typing methods are a gold standard for epidemiological surveillance due to the inherent portability of sequence and allelic profile data, fast analysis times and their capacity to create common nomenclatures for strains or clones. This led to development of several novel methods and several databases being made available for many microbial species. With the mainstream use of High Throughput Sequencing, the amount of data being accumulated in these databases is huge, storing thousands of different profiles. On the other hand, computing genetic evolutionary distances among a set of typing profiles or taxa dominates the running time of many phylogenetic inference methods. It is important also to note that most of genetic evolution distance definitions rely, even if indirectly, on computing the pairwise Hamming distance among sequences or profiles. ResultsWe propose here an average-case linear-time algorithm to compute pairwise Hamming distances among a set of taxa under a given Hamming distance threshold. This article includes both a theoretical analysis and extensive experimental results concerning the proposed algorithm. We further show how this algorithm can be successfully integrated into a well known phylogenetic inference method, and how it can be used to speedup querying local phylogenetic patterns over large typing databases.

Cross-View Retrieval via Probability-Based Semantics-Preserving Hashing

For efficiently retrieving nearest neighbors from large-scale multiview data, recently hashing methods are widely investigated, which can substantially improve query speeds. In this paper, we propose an effective probability-based semantics-preserving hashing (SePH) method to tackle the problem of cross-view retrieval. Considering the semantic consistency between views, SePH generates one unified hash code for all observed views of any instance. For training, SePH first transforms the given semantic affinities of training data into a probability distribution, and aims to approximate it with another one in Hamming space, via minimizing their Kullback-Leibler divergence. Specifically, the latter probability distribution is derived from all pair-wise Hamming distances between to-be-learnt hash codes of the training data. Then with learnt hash codes, any kind of predictive models like linear ridge regression, logistic regression, or kernel logistic regression, can be learnt as hash functions in each view for projecting the corresponding view-specific features into hash codes. As for out-of-sample extension, given any unseen instance, the learnt hash functions in its observed views can predict view-specific hash codes. Then by deriving or estimating the corresponding output probabilities with respect to the predicted view-specific hash codes, a novel probabilistic approach is further proposed to utilize them for determining a unified hash code. To evaluate the proposed SePH, we conduct extensive experiments on diverse benchmark datasets, and the experimental results demonstrate that SePH is reasonable and effective.

Constructing permutation arrays from groups

Let M(n, d) be the maximum size of a permutation array on n symbols with pairwise Hamming distance at least d. We use various combinatorial, algebraic, and computational methods to improve lower bounds for M(n, d). We compute the Hamming distances of affine semilinear groups and projective semilinear groups, and unions of cosets of AGL(1, q) and PGL(2, q) with Frobenius maps to obtain new, improved lower bounds for M(n, d). We give new randomized algorithms. We give better lower bounds for M(n, d) also using new theorems concerning the contraction operation. For example, we prove a quadratic lower bound for $$M(n,n-2)$$ for all $$n\equiv 2 \pmod 3$$ such that $$n+1$$ is a prime power.

Extending permutation arrays: improving MOLS bounds

A permutation array (PA) A is a set of permutations on $$Z_n=\{0,1,\dots ,n-1\}$$Zn={0,1,ź,n-1}, for some n. A PA A has pairwise Hamming distance at least d, if for every pair of permutations $$\sigma $$ź and $$\tau $$ź in A, there are at least d integers i in $$Z_n$$Zn such that $$\sigma (i)\ne \tau (i)$$ź(i)źź(i). Let M(n, d) denote the maximum number of permutations in any PA with pairwise Hamming distance at least d. Recently considerable effort has been devoted to improving known lower bounds for M(n, d) for all $$n>d>3$$n>d>3. We give a partition and extension operation that enables the production of a new PA $$A'$$Aź for $$M(n+1,d)$$M(n+1,d) from an existing PA A for $$M(n,d-1)$$M(n,d-1). In particular, this operation allows for improvements for PA's for $$M(q+1,q)$$M(q+1,q) for powers of prime numbers q, as well as for many other choices of n and d, where n is not a power of a prime. Finally, for prime numbers p, the partition and extension technique provides an asymptotically better lower bound for $$M(p+1,p)$$M(p+1,p) than that given by current knowledge about mutually orthogonal Latin squares. We prove a new asymptotic lower bound for the set of primes p, namely, $$M(p+1,p)\ge p^{1.5}/2-O(p)$$M(p+1,p)źp1.5/2-O(p).

Exploiting hidden structure in selecting dimensions that distinguish vectors

The NP-hard Distinct Vectors problem asks to delete as many columns as possible from a matrix such that all rows in the resulting matrix are still pairwise distinct. Our main result is that, for binary matrices, there is a complexity dichotomy for Distinct Vectors based on the maximum (H) and the minimum (h) pairwise Hamming distance between matrix rows: Distinct Vectors can be solved in polynomial time if H≤2⌈h/2⌉+1, and is NP-complete otherwise. Moreover, we explore connections of Distinct Vectors to hitting sets, thereby providing several fixed-parameter tractability and intractability results also for general matrices.

Generating constant weight binary codes

The determination of bounds for A(n, d, w), the maximum possible number of binary vectors of length n, weight w, and pairwise Hamming distance no less than d, is a classic problem in coding theory. Such sets of vectors have many applications. A description is given of how the problem can be used in a first-year undergraduate computational mathematics class as a challenging alternative to more traditional problems, and thus provide motivation for programming with loops and arrays, and the investigation of computational efficiency. Some new results, obtained by a fast implementation of a lexicographic approach, are also presented.

Performance Analysis and Code Design for Minimum Hamming Distance Fusion in Wireless Sensor Networks

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Distributed classification fusion using error-correcting codes (DCFECC) has recently been proposed for wireless sensor networks operating in a harsh environment. It has been shown to have a considerably better capability against unexpected sensor faults than the optimal likelihood fusion. In this paper, we analyze the performance of a DCFECC code with minimum Hamming distance fusion. No assumption on identical distribution for local observations, as well as common marginal distribution for the additive noises of the wireless links, is made. In addition, sensors are allowed to employ their own local classification rules. Upper bounds on the probability of error that are valid for any finite number of sensors are derived based on large deviations technique. A necessary and sufficient condition under which the minimum Hamming distance fusion error vanishes as the number of sensors tends to infinity is also established. With the necessary and sufficient condition and the upper error bounds, the relation between the fault-tolerance capability of a DCFECC code and its pair-wise Hamming distances is characterized, and can be used together with any code search criterion in finding the code with the desired fault-tolerance capability. Based on the above results, we further propose a code search criterion of much less complexity than the minimum Hamming distance fusion error criterion adopted earlier by the authors. This makes the code construction with acceptable fault-tolerance capability for a network with over a hundred of sensors practical. Simulation results show that the code determined based on the new criterion of much less complexity performs almost identically to the best code that minimizes the minimum Hamming distance fusion error. Also simulated and discussed are the performance trends of the codes searched based on the new simpler criterion with respect to the network size and the number of hypotheses. </para>

Pairs of codes with prescribed Hamming distances and coincidences

The main problem of coding theory is to construct codes with large Hamming-distances between the code-words. In this work we describe a fast algorithm for generating pairs of q-ary codes with prescribed pairwise Hamming-distances and coincidences (for a letter s ? {0,1,...,q ? 1}, the number of s-coincidences between codewords a and b is the number of letters s in the same positions both in a and b). The method is a generalization of a method for constructing set-systems with prescribed intersection sizes (Grolmusz (2002) Constructing set-systems with prescribed intersection sizes. J Algorithms 44:321---337), where only the case q = 2 and s = 1 was examined. As an application, we show that the modular version of the classical Delsarte-inequality does not hold for odd, non-prime power composite moduli.