Transformation-Based Fuzzy Rule Interpolation Using Interval Type-2 Fuzzy Sets*Algorithms* **2017**, *10*(3), 91; doi:10.3390/a10030091 - 15 August 2017**Abstract **

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In support of reasoning with sparse rule bases, fuzzy rule interpolation (FRI) offers a helpful inference mechanism for deriving an approximate conclusion when a given observation has no overlap with any rule in the existing rule base. One of the recent and popular

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In support of reasoning with sparse rule bases, fuzzy rule interpolation (FRI) offers a helpful inference mechanism for deriving an approximate conclusion when a given observation has no overlap with any rule in the existing rule base. One of the recent and popular FRI approaches is the scale and move transformation-based rule interpolation, known as T-FRI in the literature. It supports both interpolation and extrapolation with multiple multi-antecedent rules. However, the difficult problem of defining the precise-valued membership functions required in the representation of fuzzy rules, or of the observations, restricts its applications. Fortunately, this problem can be alleviated through the use of type-2 fuzzy sets, owing to the fact that the membership functions of such fuzzy sets are themselves fuzzy, providing a more flexible means of modelling. This paper therefore, extends the existing T-FRI approach using interval type-2 fuzzy sets, which covers the original T-FRI as its specific instance. The effectiveness of this extension is demonstrated by experimental investigations and, also, by a practical application in comparison to the state-of-the-art alternative approach developed using rough-fuzzy sets.
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Local Community Detection Based on Small Cliques*Algorithms* **2017**, *10*(3), 90; doi:10.3390/a10030090 - 11 August 2017**Abstract **

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Community detection aims to find dense subgraphs in a network. We consider the problem of finding a community locally around a seed node both in unweighted and weighted networks. This is a faster alternative to algorithms that detect communities that cover the whole

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Community detection aims to find dense subgraphs in a network. We consider the problem of finding a community locally around a seed node both in unweighted and weighted networks. This is a faster alternative to algorithms that detect communities that cover the whole network when actually only a single community is required. Further, many overlapping community detection algorithms use local community detection algorithms as basic building block. We provide a broad comparison of different existing strategies of expanding a seed node greedily into a community. For this, we conduct an extensive experimental evaluation both on synthetic benchmark graphs as well as real world networks. We show that results both on synthetic as well as real-world networks can be significantly improved by starting from the largest clique in the neighborhood of the seed node. Further, our experiments indicate that algorithms using scores based on triangles outperform other algorithms in most cases. We provide theoretical descriptions as well as open source implementations of all algorithms used.
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On the Existence of Solutions of Nonlinear Fredholm Integral Equations from Kantorovich’s Technique*Algorithms* **2017**, *10*(3), 89; doi:10.3390/a10030089 - 2 August 2017**Abstract **

The well-known Kantorovich technique based on majorizing sequences is used to analyse the convergence of Newton’s method when it is used to solve nonlinear Fredholm integral equations. In addition, we obtain information about the domains of existence and uniqueness of a solution for

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The well-known Kantorovich technique based on majorizing sequences is used to analyse the convergence of Newton’s method when it is used to solve nonlinear Fredholm integral equations. In addition, we obtain information about the domains of existence and uniqueness of a solution for these equations. Finally, we illustrate the above with two particular Fredholm integral equations.
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On the Lagged Diffusivity Method for the Solution of Nonlinear Finite Difference Systems*Algorithms* **2017**, *10*(3), 88; doi:10.3390/a10030088 - 2 August 2017**Abstract **

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In this paper, we extend the analysis of the Lagged Diffusivity Method for nonlinear, non-steady reaction-convection-diffusion equations. In particular, we describe how the method can be used to solve the systems arising from different discretization schemes, recalling some results on the convergence of

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In this paper, we extend the analysis of the Lagged Diffusivity Method for nonlinear, non-steady reaction-convection-diffusion equations. In particular, we describe how the method can be used to solve the systems arising from different discretization schemes, recalling some results on the convergence of the method itself. Moreover, we also analyze the behavior of the method in case of problems presenting boundary layers or blow-up solutions.
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Auxiliary Model Based Multi-Innovation Stochastic Gradient Identification Algorithm for Periodically Non-Uniformly Sampled-Data Hammerstein Systems*Algorithms* **2017**, *10*(3), 84; doi:10.3390/a10030084 - 31 July 2017**Abstract **

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Due to the lack of powerful model description methods, the identification of Hammerstein systems based on the non-uniform input-output dataset remains a challenging problem. This paper introduces a time-varying backward shift operator to describe periodically non-uniformly sampled-data Hammerstein systems, which can simplify the

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Due to the lack of powerful model description methods, the identification of Hammerstein systems based on the non-uniform input-output dataset remains a challenging problem. This paper introduces a time-varying backward shift operator to describe periodically non-uniformly sampled-data Hammerstein systems, which can simplify the structure of the lifted models using the traditional lifting technique. Furthermore, an auxiliary model-based multi-innovation stochastic gradient algorithm is presented to estimate the parameters involved in the linear and nonlinear blocks. The simulation results confirm that the proposed algorithm is effective and can achieve a high estimation performance.
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Evolutionary Optimization for Robust Epipolar-Geometry Estimation and Outlier Detection*Algorithms* **2017**, *10*(3), 87; doi:10.3390/a10030087 - 27 July 2017**Abstract **

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In this paper, a robust technique [-5]based on a genetic algorithm is proposed for estimating two-view epipolar-geometry of uncalibrated perspective stereo images from putative correspondences containing a high percentage of outliers. The advantages of this technique are three-fold: (i) replacing random search with

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In this paper, a robust technique [-5]based on a genetic algorithm is proposed for estimating two-view epipolar-geometry of uncalibrated perspective stereo images from putative correspondences containing a high percentage of outliers. The advantages of this technique are three-fold: (i) replacing random search with evolutionary search applying new strategies of encoding and guided sampling; (ii) robust and fast estimation of the epipolar geometry via detecting a more-than-enough set of inliers without making any assumptions about the probability distribution of the residuals; (iii) determining the inlier-outlier threshold based on the uncertainty of the estimated model. The proposed method was evaluated both on synthetic data and real images. The results were compared with the most popular techniques from the state-of-the-art, including RANSAC (random sample consensus), MSAC, MLESAC, Cov-RANSAC, LO-RANSAC, StaRSAC, Multi-GS RANSAC and least median of squares (LMedS). Experimental results showed that the proposed approach performed better than other methods regarding the accuracy of inlier detection and epipolar-geometry estimation, as well as the computational efficiency for datasets majorly contaminated by outliers and noise.
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An Improved MOEA/D with Optimal DE Schemes for Many-Objective Optimization Problems*Algorithms* **2017**, *10*(3), 86; doi:10.3390/a10030086 - 26 July 2017**Abstract **

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MOEA/D is a promising multi-objective evolutionary algorithm based on decomposition, and it has been used to solve many multi-objective optimization problems very well. However, there is a class of multi-objective problems, called many-objective optimization problems, but the original MOEA/D cannot solve them well.

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MOEA/D is a promising multi-objective evolutionary algorithm based on decomposition, and it has been used to solve many multi-objective optimization problems very well. However, there is a class of multi-objective problems, called many-objective optimization problems, but the original MOEA/D cannot solve them well. In this paper, an improved MOEA/D with optimal differential evolution (oDE) schemes is proposed, called MOEA/D-oDE, aiming to solve many-objective optimization problems. Compared with MOEA/D, MOEA/D-oDE has two distinguishing points. On the one hand, MOEA/D-oDE adopts a newly-introduced decomposition approach to decompose the many-objective optimization problems, which combines the advantages of the weighted sum approach and the Tchebycheff approach. On the other hand, a kind of combination mechanism for DE operators is designed for finding the best child solution so as to do the a posteriori computing. In our experimental study, six continuous test instances with 4–6 objectives comparing NSGA-II (nondominated sorting genetic algorithm II) and MOEA/D as accompanying experiments are applied. Additionally, the final results indicate that MOEA/D-oDE outperforms NSGA-II and MOEA/D in almost all cases, particularly in those problems that have complicated Pareto shapes and higher dimensional objectives, where its advantages are more obvious.
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A New Meta-Heuristics of Optimization with Dynamic Adaptation of Parameters Using Type-2 Fuzzy Logic for Trajectory Control of a Mobile Robot*Algorithms* **2017**, *10*(3), 85; doi:10.3390/a10030085 - 26 July 2017**Abstract **

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Fuzzy logic is a soft computing technique that has been very successful in recent years when it is used as a complement to improve meta-heuristic optimization. In this paper, we present a new variant of the bio-inspired optimization algorithm based on the self-defense

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Fuzzy logic is a soft computing technique that has been very successful in recent years when it is used as a complement to improve meta-heuristic optimization. In this paper, we present a new variant of the bio-inspired optimization algorithm based on the self-defense mechanisms of plants in the nature. The optimization algorithm proposed in this work is based on the predator-prey model originally presented by Lotka and Volterra, where two populations interact with each other and the objective is to maintain a balance. The system of predator-prey equations use four variables (α, β, λ, δ) and the values of these variables are very important since they are in charge of maintaining a balance between the pair of equations. In this work, we propose the use of Type-2 fuzzy logic for the dynamic adaptation of the variables of the system. This time a fuzzy controller is in charge of finding the optimal values for the model variables, the use of this technique will allow the algorithm to have a higher performance and accuracy in the exploration of the values.
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Fuzzy Fireworks Algorithm Based on a Sparks Dispersion Measure*Algorithms* **2017**, *10*(3), 83; doi:10.3390/a10030083 - 21 July 2017**Abstract **

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The main goal of this paper is to improve the performance of the Fireworks Algorithm (FWA). To improve the performance of the FWA we propose three modifications: the first modification is to change the stopping criteria, this is to say, previously, the number

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The main goal of this paper is to improve the performance of the Fireworks Algorithm (FWA). To improve the performance of the FWA we propose three modifications: the first modification is to change the stopping criteria, this is to say, previously, the number of function evaluations was utilized as a stopping criteria, and we decided to change this to specify a particular number of iterations; the second and third modifications consist on introducing a dispersion metric (dispersion percent), and both modifications were made with the goal of achieving dynamic adaptation of the two parameters in the algorithm. The parameters that were controlled are the explosion amplitude and the number of sparks, and it is worth mentioning that the control of these parameters is based on a fuzzy logic approach. To measure the impact of these modifications, we perform experiments with 14 benchmark functions and a comparative study shows the advantage of the proposed approach. We decided to call the proposed algorithms Iterative Fireworks Algorithm (IFWA) and two variants of the Dispersion Percent Iterative Fuzzy Fireworks Algorithm (DPIFWA-I and DPIFWA-II, respectively).
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Optimization of Intelligent Controllers Using a Type-1 and Interval Type-2 Fuzzy Harmony Search Algorithm*Algorithms* **2017**, *10*(3), 82; doi:10.3390/a10030082 - 20 July 2017**Abstract **

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This article focuses on the dynamic parameter adaptation in the harmony search algorithm using Type-1 and interval Type-2 fuzzy logic. In particular, this work focuses on the adaptation of the parameters of the original harmony search algorithm. At present there are several types

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This article focuses on the dynamic parameter adaptation in the harmony search algorithm using Type-1 and interval Type-2 fuzzy logic. In particular, this work focuses on the adaptation of the parameters of the original harmony search algorithm. At present there are several types of algorithms that can solve complex real-world problems with uncertainty management. In this case the proposed method is in charge of optimizing the membership functions of three benchmark control problems (water tank, shower, and mobile robot). The main goal is to find the best parameters for the membership functions in the controller to follow a desired trajectory. Noise experiments are performed to test the efficacy of the method.
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Low-Resource Cross-Domain Product Review Sentiment Classification Based on a CNN with an Auxiliary Large-Scale Corpus*Algorithms* **2017**, *10*(3), 81; doi:10.3390/a10030081 - 19 July 2017**Abstract **

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The literature [-5]contains several reports evaluating the abilities of deep neural networks in text transfer learning. To our knowledge, however, there have been few efforts to fully realize the potential of deep neural networks in cross-domain product review sentiment classification. In this paper,

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The literature [-5]contains several reports evaluating the abilities of deep neural networks in text transfer learning. To our knowledge, however, there have been few efforts to fully realize the potential of deep neural networks in cross-domain product review sentiment classification. In this paper, we propose a two-layer convolutional neural network (CNN) for cross-domain product review sentiment classification (LM-CNN-LB). Transfer learning research into product review sentiment classification based on deep neural networks has been limited by the lack of a large-scale corpus; we sought to remedy this problem using a large-scale auxiliary cross-domain dataset collected from Amazon product reviews. Our proposed framework exhibits the dramatic transferability of deep neural networks for cross-domain product review sentiment classification and achieves state-of-the-art performance. The framework also outperforms complex engineered features used with a non-deep neural network method. The experiments demonstrate that introducing large-scale data from similar domains is an effective way to resolve the lack of training data. The LM-CNN-LB trained on the multi-source related domain dataset outperformed the one trained on a single similar domain.
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A Hybrid Algorithm for Optimal Wireless Sensor Network Deployment with the Minimum Number of Sensor Nodes*Algorithms* **2017**, *10*(3), 80; doi:10.3390/a10030080 - 18 July 2017**Abstract **

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Wireless sensor network (WSN) applications are rapidly growing and are widely used in various disciplines. Deployment is one of the key issues to be solved in WSNs, since the sensor nodes’ positioning affects highly the system performance. An optimal WSN deployment should maximize

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Wireless sensor network (WSN) applications are rapidly growing and are widely used in various disciplines. Deployment is one of the key issues to be solved in WSNs, since the sensor nodes’ positioning affects highly the system performance. An optimal WSN deployment should maximize the collection of the desired interest phenomena, guarantee the required coverage and connectivity, extend the network lifetime, and minimize the network cost in terms of energy consumption. Most of the research effort in this area aims to solve the deployment issue, without minimizing the network cost by reducing unnecessary working nodes in the network. In this paper, we propose a deployment approach based on the gradient method and the Simulated Annealing algorithm to solve the sensor deployment problem with the minimum number of sensor nodes. The proposed algorithm is able to heuristically optimize the number of sensors and their positions in order to achieve the desired application requirements.
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Design of an Optimized Fuzzy Classifier for the Diagnosis of Blood Pressure with a New Computational Method for Expert Rule Optimization*Algorithms* **2017**, *10*(3), 79; doi:10.3390/a10030079 - 14 July 2017**Abstract **

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A neuro fuzzy hybrid model (NFHM) is proposed as a new artificial intelligence method to classify blood pressure (BP). The NFHM uses techniques such as neural networks, fuzzy logic and evolutionary computation, and in the last case genetic algorithms (GAs) are used. The

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A neuro fuzzy hybrid model (NFHM) is proposed as a new artificial intelligence method to classify blood pressure (BP). The NFHM uses techniques such as neural networks, fuzzy logic and evolutionary computation, and in the last case genetic algorithms (GAs) are used. The main goal is to model the behavior of blood pressure based on monitoring data of 24 h per patient and based on this to obtain the trend, which is classified using a fuzzy system based on rules provided by an expert, and these rules are optimized by a genetic algorithm to obtain the best possible number of rules for the classifier with the lowest classification error. Simulation results are presented to show the advantage of the proposed model.
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An Efficient Algorithm for the Separable Nonlinear Least Squares Problem*Algorithms* **2017**, *10*(3), 78; doi:10.3390/a10030078 - 10 July 2017**Abstract **

The nonlinear least squares problem $mi{n}_{y,z}\parallel A\left(y\right)z+b\left(y\right)\parallel $ , where $A\left(y\right)$ is a full-rank $(N+\ell )\times N$ matrix, $y\in {\mathbf{R}}^{}$

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The nonlinear least squares problem $mi{n}_{y,z}\parallel A\left(y\right)z+b\left(y\right)\parallel $ , where $A\left(y\right)$ is a full-rank $(N+\ell )\times N$ matrix, $y\in {\mathbf{R}}^{n}$ , $z\in {\mathbf{R}}^{N}$ and $b\left(y\right)\in {\mathbf{R}}^{N+\ell}$ with $\ell \ge n$ , can be solved by first solving a reduced problem $mi{n}_{y}\parallel f\left(y\right)\parallel $ to find the optimal value ${y}^{*}$ of *y*, and then solving the resulting linear least squares problem $mi{n}_{z}\parallel A\left({y}^{*}\right)z+b\left({y}^{*}\right)\parallel $ to find the optimal value ${z}^{*}$ of *z*. We have previously justified the use of the reduced function $f\left(y\right)={C}^{T}\left(y\right)b\left(y\right)$ , where $C\left(y\right)$ is a matrix whose columns form an orthonormal basis for the nullspace of ${A}^{T}\left(y\right)$ , and presented a quadratically convergent Gauss–Newton type method for solving $mi{n}_{y}\parallel {C}^{T}\left(y\right)b\left(y\right)\parallel $ based on the use of QR factorization. In this note, we show how LU factorization can replace the QR factorization in those computations, halving the associated computational cost while also providing opportunities to exploit sparsity and thus further enhance computational efficiency.
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New Methodology to Approximate Type-Reduction Based on a Continuous Root-Finding Karnik Mendel Algorithm*Algorithms* **2017**, *10*(3), 77; doi:10.3390/a10030077 - 5 July 2017**Abstract **

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Interval Type-2 fuzzy systems allow the possibility of considering uncertainty in models based on fuzzy systems, and enable an increase of robustness in solutions to applications, but also increase the complexity of the fuzzy system design. Several attempts have been previously proposed to

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Interval Type-2 fuzzy systems allow the possibility of considering uncertainty in models based on fuzzy systems, and enable an increase of robustness in solutions to applications, but also increase the complexity of the fuzzy system design. Several attempts have been previously proposed to reduce the computational cost of the type-reduction stage, as this process requires a lot of computing time because it is basically a numerical approximation based on sampling, and the computational cost is proportional to the number of samples, but also the error is inversely proportional to the number of samples. Several works have focused on reducing the computational cost of type-reduction by developing strategies to reduce the number of operations. The first type-reduction method was proposed by Karnik and Mendel (KM), and then was followed by its enhanced version called EKM. Then continuous versions were called CKM and CEKM, and there were variations of this and also other types of variations that eliminate the type-reduction process reducing the computational cost to a Type-1 defuzzification, such as the Nie-Tan versions and similar enhancements. In this work we analyzed and proposed a variant of CEKM by viewing this process as solving a root-finding problem, in this way taking advantage of existing numerical methods to solve the type-reduction problem, the main objective being eliminating the type-reduction process and also providing a continuous solution of the defuzzification.
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A Genetic Algorithm Using Triplet Nucleotide Encoding and DNA Reproduction Operations for Unconstrained Optimization Problems*Algorithms* **2017**, *10*(3), 76; doi:10.3390/a10030076 - 30 June 2017**Abstract **

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As one of the evolutionary heuristics methods, genetic algorithms (GAs) have shown a promising ability to solve complex optimization problems. However, existing GAs still have difficulties in finding the global optimum and avoiding premature convergence. To further improve the search efficiency and convergence

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As one of the evolutionary heuristics methods, genetic algorithms (GAs) have shown a promising ability to solve complex optimization problems. However, existing GAs still have difficulties in finding the global optimum and avoiding premature convergence. To further improve the search efficiency and convergence rate of evolution algorithms, inspired by the mechanism of biological DNA genetic information and evolution, we present a new genetic algorithm, called GA-TNE+DRO, which uses a novel triplet nucleotide coding scheme to encode potential solutions and a set of new genetic operators to search for globally optimal solutions. The coding scheme represents potential solutions as a sequence of triplet nucleotides and the DNA reproduction operations mimic the DNA reproduction process more vividly than existing DNA-GAs. We compared our algorithm with several existing GA and DNA-based GA algorithms using a benchmark of eight unconstrained optimization functions. Our experimental results show that the proposed algorithm can converge to solutions much closer to the global optimal solutions in a much lower number of iterations than the existing algorithms. A complexity analysis also shows that our algorithm is computationally more efficient than the existing algorithms.
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Variable Selection Using Adaptive Band Clustering and Physarum Network*Algorithms* **2017**, *10*(3), 73; doi:10.3390/a10030073 - 27 June 2017**Abstract **

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Variable selection is a key step for eliminating redundant information in spectroscopy. Among various variable selection methods, the physarum network (PN) is a newly-introduced and efficient one. However, the whole spectrum has to be equally divided into sub-spectral bands in PN. These division

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Variable selection is a key step for eliminating redundant information in spectroscopy. Among various variable selection methods, the physarum network (PN) is a newly-introduced and efficient one. However, the whole spectrum has to be equally divided into sub-spectral bands in PN. These division criteria limit the selecting ability and prediction performance. In this paper, we transform the spectrum division problem into a clustering problem and solve the problem by using an affinity propagation (AP) algorithm, an adaptive clustering method, to find the optimized number of sub-spectral bands and the number of wavelengths in each sub-spectral band. Experimental results show that combining AP and PN together can achieve similar prediction accuracy with much less wavelength than what PN alone can achieve.
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The Isomorphic Version of Brualdi’s and Sanderson’s Nestedness*Algorithms* **2017**, *10*(3), 74; doi:10.3390/a10030074 - 27 June 2017**Abstract **

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The discrepancy BR for an m × n 0, 1-matrix from Brualdi and Sanderson in 1998 is defined as the minimum number of 1 s that need to be shifted in each row to the left to achieve its Ferrers matrix, i.e., each

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The discrepancy BR for an m × n 0, 1-matrix from Brualdi and Sanderson in 1998 is defined as the minimum number of 1 s that need to be shifted in each row to the left to achieve its Ferrers matrix, i.e., each row consists of consecutive 1 s followed by consecutive 0 s. For ecological bipartite networks, BR describes a nested set of relationships. Since two different labelled networks can be isomorphic, but possess different discrepancies due to different adjacency matrices, we define a metric determining the minimum discrepancy in an isomorphic class. We give a reduction to k ≤ n minimum weighted perfect matching problems. We show on 289 ecological matrices (given as a benchmark by Atmar and Patterson in 1995) that classical discrepancy can underestimate the nestedness by up to 30%.
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Thresholds of the Inner Steps in Multi-Step Newton Method*Algorithms* **2017**, *10*(3), 75; doi:10.3390/a10030075 - 27 June 2017**Abstract **

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We investigate the efficiency of multi-step Newton method (the classical Newton method in which the first derivative is re-evaluated periodically after *m* steps) for solving nonlinear equations, $F\left(x\right)=0,\phantom{\rule{4pt}{0ex}}F:D\subseteq {R}^{n}\to {R}^{n}$

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We investigate the efficiency of multi-step Newton method (the classical Newton method in which the first derivative is re-evaluated periodically after *m* steps) for solving nonlinear equations, $F\left(x\right)=0,\phantom{\rule{4pt}{0ex}}F:D\subseteq {R}^{n}\to {R}^{n}$ . We highlight the following property of multi-step Newton method with respect to some other Newton-type method: for a given *n*, there exist thresholds of *m*, that is an interval $({m}_{i},{m}_{s})$ , such that for *m* inside of this interval, the efficiency index of multi-step Newton method is better than that of other Newton-type method. We also search for optimal values of *m*.
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Hierarchical Gradient Similarity Based Video Quality Assessment Metric*Algorithms* **2017**, *10*(3), 72; doi:10.3390/a10030072 - 23 June 2017**Abstract **

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Video quality assessment (VQA) plays an important role in video applications for quality evaluation and resource allocation. It aims to evaluate video quality in a way that is consistent with human perception. In this letter, a hierarchical gradient similarity based VQA metric is

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Video quality assessment (VQA) plays an important role in video applications for quality evaluation and resource allocation. It aims to evaluate video quality in a way that is consistent with human perception. In this letter, a hierarchical gradient similarity based VQA metric is proposed inspired by the structure of the primate visual cortex, in which visual information is processed through sequential visual areas. These areas are modeled with the corresponding measures to evaluate the overall perceptual quality. Experimental results on the LIVE database show that the proposed VQA metric significantly outperforms most of the state-of-the-art VQA metrics.
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