Algorithms, Volume 8, Issue 4 (December 2015) – 24 articles , Pages 799-1218

This paper is dedicated to the study of continuous Newton’s method, which is a generic differential equation whose associated flow tends to the zeros of a given polynomial. Firstly, we analyze some numerical features related to the root-finding methods obtained after applying different numerical methods for solving initial value problems. The relationship between the step size and the order of convergence is particularly considered. We have analyzed both the cases of a constant and non-constant step size in the procedure of integration. We show that working with a non-constant step, the well-known Chebyshev-Halley family of iterative methods for solving nonlinear scalar equations is obtained. Full article

In this paper, by using the smoothing Fischer-Burmeister function, we present a new smoothing conjugate gradient method for solving the nonlinear nonsmooth complementarity problems. The line search which we used guarantees the descent of the method. Under suitable conditions, the new smoothing conjugate gradient method is proved globally convergent. Finally, preliminary numerical experiments show that the new method is efficient. Full article

Big data are everywhere as high volumes of varieties of valuable precise and uncertain data can be easily collected or generated at high velocity in various real-life applications. Embedded in these big data are rich sets of useful information and knowledge. To mine these big data and to discover useful information and knowledge, we present a data analytic algorithm in this article. Our algorithm manages, queries, and processes uncertain big data in cloud environments. More specifically, it manages transactions of uncertain big data, allows users to query these big data by specifying constraints expressing their interests, and processes the user-specified constraints to discover useful information and knowledge from the uncertain big data. As each item in every transaction in these uncertain big data is associated with an existential probability value expressing the likelihood of that item to be present in a particular transaction, computation could be intensive. Our algorithm uses the MapReduce model on a cloud environment for effective data analytics on these uncertain big data. Experimental results show the effectiveness of our data analytic algorithm for managing, querying, and processing uncertain big data in cloud environments. Full article

Generative algorithms for random graphs have yielded insights into the structure and evolution of real-world networks. Most networks exhibit a well-known set of properties, such as heavy-tailed degree distributions, clustering and community formation. Usually, random graph models consider only structural information, but many real-world networks also have labelled vertices and weighted edges. In this paper, we present a generative model for random graphs with discrete vertex labels and numeric edge weights. The weights are represented as a set of Beta Mixture Models (BMMs) with an arbitrary number of mixtures, which are learned from real-world networks. We propose a Bayesian Variational Inference (VI) approach, which yields an accurate estimation while keeping computation times tractable. We compare our approach to state-of-the-art random labelled graph generators and an earlier approach based on Gaussian Mixture Models (GMMs). Our results allow us to draw conclusions about the contribution of vertex labels and edge weights to graph structure. Full article

In Long Term Evolution-Advanced (LTE-A) networks, Device-to-device (D2D) communications can be utilized to enhance the performance of multicast services by leveraging D2D relays to serve nodes with worse channel conditions within a cluster. For traditional D2D relay schemes, D2D links with poor channel condition may be the bottleneck of system sum data rate. In this paper, to optimize the throughput of D2D communications, we introduce an iterative combinatorial auction algorithm for efficient D2D relay selection. In combinatorial auctions, the User Equipments (UEs) that fails to correctly receive multicast data from eNodeB (eNB) are viewed as bidders that compete for D2D relays, while the eNB is treated as the auctioneer. We also give properties of convergency and low-complexity and present numerical simulations to verify the efficiency of the proposed algorithm. Full article

Efficiency is generally the most important aspect to take into account when choosing an iterative method to approximate a solution of an equation, but is not the only aspect to consider in the iterative process. Another important aspect to consider is the accessibility of the iterative process, which shows the domain of starting points from which the iterative process converges to a solution of the equation. So, we consider a family of iterative processes with a higher efficiency index than Newton’s method. However, this family of proecsses presents problems of accessibility to the solution x * . From a local study of the convergence of this family, we perform an optimization study of the accessibility and obtain iterative processes with better accessibility than Newton’s method. Full article

In this paper, a family of Steffensen-type methods of optimal order of convergence with two parameters is constructed by direct Newtonian interpolation. It satisfies the conjecture proposed by Kung and Traub (J. Assoc. Comput. Math. 1974, 21, 634–651) that an iterative method based on m evaluations per iteration without memory would arrive at the optimal convergence of order 2^m-1 . Furthermore, the family of Steffensen-type methods of super convergence is suggested by using arithmetic expressions for the parameters with memory but no additional new evaluation of the function. Their error equations, asymptotic convergence constants and convergence orders are obtained. Finally, they are compared with related root-finding methods in the numerical examples. Full article

Lung cancer continues to rank as the leading cause of cancer deaths worldwide. One of the most promising techniques for early detection of cancerous cells relies on sputum cell analysis. This was the motivation behind the design and the development of a new computer aided diagnosis (CAD) system for early detection of lung cancer based on the analysis of sputum color images. The proposed CAD system encompasses four main processing steps. First is the preprocessing step which utilizes a Bayesian classification method using histogram analysis. Then, in the second step, mean shift segmentation is applied to segment the nuclei from the cytoplasm. The third step is the feature analysis. In this step, geometric and chromatic features are extracted from the nucleus region. These features are used in the diagnostic process of the sputum images. Finally, the diagnosis is completed using an artificial neural network and support vector machine (SVM) for classifying the cells into benign or malignant. The performance of the system was analyzed based on different criteria such as sensitivity, specificity and accuracy. The evaluation was carried out using Receiver Operating Characteristic (ROC) curve. The experimental results demonstrate the efficiency of the SVM classifier over other classifiers, with 97% sensitivity and accuracy as well as a significant reduction in the number of false positive and false negative rates. Full article

We present a local convergence analysis of an eighth order three step methodin order to approximate a locally unique solution of nonlinear equation in a Banach spacesetting. In an earlier study by Sharma and Arora (2015), the order of convergence wasshown using Taylor series expansions and hypotheses up to the fourth order derivative oreven higher of the function involved which restrict the applicability of the proposed scheme. However, only first order derivative appears in the proposed scheme. In order to overcomethis problem, we proposed the hypotheses up to only the first order derivative. In this way,we not only expand the applicability of the methods but also propose convergence domain. Finally, where earlier studies cannot be applied, a variety of concrete numerical examplesare proposed to obtain the solutions of nonlinear equations. Our study does not exhibit thistype of problem/restriction. Full article

Near-infrared spectroscopy (NIRS) enables the non-invasive measurement of changes in hemodynamics and oxygenation in tissue. Changes in light-coupling due to movement of the subject can cause movement artifacts (MAs) in the recorded signals. Several methods have been developed so far that facilitate the detection and reduction of MAs in the data. However, due to fixed parameter values (e.g., global threshold) none of these methods are perfectly suitable for long-term (i.e., hours) recordings or were not time-effective when applied to large datasets. We aimed to overcome these limitations by automation, i.e., data adaptive thresholding specifically designed for long-term measurements, and by introducing a stable long-term signal reconstruction. Our new technique (“acceleration-based movement artifact reduction algorithm”, AMARA) is based on combining two methods: the “movement artifact reduction algorithm” (MARA, Scholkmann et al. Phys. Meas. 2010, 31, 649–662), and the “accelerometer-based motion artifact removal” (ABAMAR, Virtanen et al. J. Biomed. Opt. 2011, 16, 087005). We describe AMARA in detail and report about successful validation of the algorithm using empirical NIRS data, measured over the prefrontal cortex in adolescents during sleep. In addition, we compared the performance of AMARA to that of MARA and ABAMAR based on validation data. Full article

Data on molecular interactions is increasing at a tremendous pace, while the development of solid methods for analyzing this network data is still lagging behind. This holds in particular for the field of comparative network analysis, where one wants to identify commonalities between biological networks. Since biological functionality primarily operates at the network level, there is a clear need for topology-aware comparison methods. We present a method for global network alignment that is fast and robust and can flexibly deal with various scoring schemes taking both node-to-node correspondences as well as network topologies into account. We exploit that network alignment is a special case of the well-studied quadratic assignment problem (QAP). We focus on sparse network alignment, where each node can be mapped only to a typically small subset of nodes in the other network. This corresponds to a QAP instance with a symmetric and sparse weight matrix. We obtain strong upper and lower bounds for the problem by improving a Lagrangian relaxation approach and introduce the open source software tool Natalie 2.0, a publicly available implementation of our method. In an extensive computational study on protein interaction networks for six different species, we find that our new method outperforms alternative established and recent state-of-the-art methods. Full article

Graph-based semi-supervised classification heavily depends on a well-structured graph. In this paper, we investigate a mixture graph and propose a method called semi-supervised classification based on mixture graph (SSCMG). SSCMG first constructs multiple k nearest neighborhood (kNN) graphs in different random subspaces of the samples. Then, it combines these graphs into a mixture graph and incorporates this graph into a graph-based semi-supervised classifier. SSCMG can preserve the local structure of samples in subspaces and is less affected by noisy and redundant features. Empirical study on facial images classification shows that SSCMG not only has better recognition performance, but also is more robust to input parameters than other related methods. Full article

In this article, we investigate the Minimum Cardinality Segmentation Problem (MCSP), an NP-hard combinatorial optimization problem arising in intensity-modulated radiation therapy. The problem consists in decomposing a given nonnegative integer matrix into a nonnegative integer linear combination of a minimum cardinality set of binary matrices satisfying the consecutive ones property. We show how to transform the MCSP into a combinatorial optimization problem on a weighted directed network and we exploit this result to develop an integer linear programming formulation to exactly solve it. Computational experiments show that the lower bounds obtained by the linear relaxation of the considered formulation improve upon those currently described in the literature and suggest, at the same time, new directions for the development of future exact solution approaches to the problem. Full article

An application of iterative methods for computing the Moore–Penrose inverse in balancing chemical equations is considered. With the aim to illustrate proposed algorithms, an improved high order hyper-power matrix iterative method for computing generalized inverses is introduced and applied. The improvements of the hyper-power iterative scheme are based on its proper factorization, as well as on the possibility to accelerate the iterations in the initial phase of the convergence. Although the effectiveness of our approach is confirmed on the basis of the theoretical point of view, some numerical comparisons in balancing chemical equations, as well as on randomly-generated matrices are furnished. Full article

In this paper, we address the problem of detecting and tracking targets with a low signal-to-noise ratio (SNR) by exploiting hybrid differential evolution (HDE) in the particle filter track-before-detect (PF-TBD) context. Firstly, we introduce the Bayesian PF-TBD method and its weaknesses. Secondly, the HDE algorithm is regarded as a novel particle updating strategy, which is proposed to optimize the performance of the PF-TBD algorithm. Thirdly, we combine the systematic resampling approach to enhance the performance of the proposed algorithm. Then, an improved PF-TBD algorithm based on the HDE method is proposed. Experiment results indicate that the proposed method has better performance in detecting and tracking than previous algorithms when the targets have a low SNR. Full article

As one of the most popular and well-recognized clustering methods, fuzzy C-means (FCM) clustering algorithm is the basis of other fuzzy clustering analysis methods in theory and application respects. However, FCM algorithm is essentially a local search optimization algorithm. Therefore, sometimes, it may fail to find the global optimum. For the purpose of getting over the disadvantages of FCM algorithm, a new version of the krill herd (KH) algorithm with elitism strategy, called KHE, is proposed to solve the clustering problem. Elitism tragedy has a strong ability of preventing the krill population from degrading. In addition, the well-selected parameters are used in the KHE method instead of originating from nature. Through an array of simulation experiments, the results show that the KHE is indeed a good choice for solving general benchmark problems and fuzzy clustering analyses. Full article

Arc fault is one of the most critical reasons for electrical fires. Due to the diversity, randomness and concealment of arc faults in low-voltage circuits, it is difficult for general methods to protect all loads from series arc faults. From the analysis of many series arc faults, a large number of high frequency signals generated in circuits are found. These signals are easily affected by Gaussian noise which is difficult to be eliminated as a result of frequency aliasing. Thus, a novel detection algorithm is developed to accurately detect series arc faults in this paper. Initially, an autoregressive model of the mixed high frequency signals is modelled. Then, autoregressive bispectrum analysis is introduced to analyze common series arc fault features. The phase information of arc fault signal is preserved using this method. The influence of Gaussian noise is restrained effectively. Afterwards, several features including characteristic frequency, fluctuation of phase angles, diffused distribution and incremental numbers of bispectrum peaks are extracted for recognizing arc faults. Finally, least squares support vector machine is used to accurately identify series arc faults from the load states based on these frequency features of bispectrum. The validity of the algorithm is experimentally verified obtaining arc fault detection rate above 97%. Full article

In designing wireless sensor networks (WSNs), it is important to reduce energy dissipation and prolong network lifetime. Clustering of nodes is one of the most effective approaches for conserving energy in WSNs. Cluster formation protocols generally consider the heterogeneity of sensor nodes in terms of energy difference of nodes but ignore the different transmission ranges of them. In this paper, we propose an effective data acquisition clustered protocol using compressive sensing (EDACP-CS) for heterogeneous WSNs that aims to conserve the energy of sensor nodes in the presence of energy and transmission range heterogeneity. In EDACP-CS, cluster heads are selected based on the distance from the base station and sensor residual energy. Simulation results show that our protocol offers a much better performance than the existing protocols in terms of energy consumption, stability, network lifetime, and throughput. Full article

In this work, we have developed a fourth order Newton-like method based on harmonic mean and its multi-step version for solving system of nonlinear equations. The new fourth order method requires evaluation of one function and two first order Fréchet derivatives for each iteration. The multi-step version requires one more function evaluation for each iteration. The proposed new scheme does not require the evaluation of second or higher order Fréchet derivatives and still reaches fourth order convergence. The multi-step version converges with order 2r+4, where r is a positive integer and r ≥ 1. We have proved that the root α is a point of attraction for a general iterative function, whereas the proposed new schemes also satisfy this result. Numerical experiments including an application to 1-D Bratu problem are given to illustrate the efficiency of the new methods. Also, the new methods are compared with some existing methods. Full article

Spread Spectrum (SPSP) Communication is the theoretical basis of Direct Sequence Spread Spectrum (DSSS) transceiver technology. Spreading code, modulation, demodulation, carrier synchronization and code synchronization in SPSP communications are the core parts of DSSS transceivers. This paper focuses on the code synchronization problem in SPSP communications. A novel code synchronization algorithm based on segment correlation is proposed. The proposed algorithm can effectively deal with the informational misjudgment caused by the unreasonable data acquisition times. This misjudgment may lead to an inability of DSSS receivers to restore transmitted signals. Simulation results show the feasibility of a DSSS transceiver design based on the proposed code synchronization algorithm. Finally, the communication functions of the DSSS transceiver based on the proposed code synchronization algorithm are implemented on Field Programmable Gate Array (FPGA). Full article

In this work, we propose a new distance measure for comparing two protein structures based on their contact map representations. We show that our novel measure, which we refer to as the maximum contact map overlap (max-CMO) metric, satisfies all properties of a metric on the space of protein representations. Having a metric in that space allows one to avoid pairwise comparisons on the entire database and, thus, to significantly accelerate exploring the protein space compared to no-metric spaces. We show on a gold standard superfamily classification benchmark set of 6759 proteins that our exact k-nearest neighbor (k-NN) scheme classifies up to 224 out of 236 queries correctly and on a larger, extended version of the benchmark with 60; 850 additional structures, up to 1361 out of 1369 queries. Our k-NN classification thus provides a promising approach for the automatic classification of protein structures based on flexible contact map overlap alignments. Full article

We present a semilocal convergence study of Newton-type methods on a generalized Banach space setting to approximate a locally unique zero of an operator. Earlier studies require that the operator involved is Fréchet differentiable. In the present study we assume that the operator is only continuous. This way we extend the applicability of Newton-type methods to include fractional calculus and problems from other areas. Moreover, under the same or weaker conditions, we obtain weaker sufficient convergence criteria, tighter error bounds on the distances involved and an at least as precise information on the location of the solution. Special cases are provided where the old convergence criteria cannot apply but the new criteria can apply to locate zeros of operators. Some applications include fractional calculus involving the Riemann-Liouville fractional integral and the Caputo fractional derivative. Fractional calculus is very important for its applications in many applied sciences. Full article

Subnetwork mining is an essential issue in the analysis of biological, social and communication networks. Recent applications require the simultaneous mining of several networks on the same or a similar vertex set. That is, one searches for subnetworks fulfilling different properties in each input network. We study the case that the input consists of a directed graph D and an undirected graph G on the same vertex set, and the sought pattern is a path P in D whose vertex set induces a connected subgraph of G. In this context, three concrete problems arise, depending on whether the existence of P is questioned or whether the length of P is to be optimized: in that case, one can search for a longest path or (maybe less intuitively) a shortest one. These problems have immediate applications in biological networks and predictable applications in social, information and communication networks. We study the classic and parameterized complexity of the problem, thus identifying polynomial and NP-complete cases, as well as fixed-parameter tractable and W[1]-hard cases. We also propose two enumeration algorithms that we evaluate on synthetic and biological data. Full article

The sign least mean square with reweighted L1-norm constraint (SLMS-RL1) algorithm is an attractive sparse channel estimation method among Gaussian mixture model (GMM) based algorithms for use in impulsive noise environments. The channel sparsity can be exploited by SLMS-RL1 algorithm based on appropriate reweighted factor, which is one of key parameters to adjust the sparse constraint for SLMS-RL1 algorithm. However, to the best of the authors’ knowledge, a reweighted factor selection scheme has not been developed. This paper proposes a Monte-Carlo (MC) based reweighted factor selection method to further strengthen the performance of SLMS-RL1 algorithm. To validate the performance of SLMS-RL1 using the proposed reweighted factor, simulations results are provided to demonstrate that convergence speed can be reduced by increasing the channel sparsity, while the steady-state MSE performance only slightly changes with different GMM impulsive-noise strengths. Full article