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Deep Neural Network Optimization Based on binary method for Handling Multi-Class Problems

IEEE ACCESS 2024年 12卷 46881-46890页

作者： Liu, Yuqi Yang, Sibo Bao, Yuan Dalian Maritime Univ Marine Engn Coll Dalian 116026 Peoples R China Dalian Maritime Univ Sch Sci Dalian 116026 Peoples R China Xinyang Normal Univ Sch Math & Stat Xinyang Peoples R China

In this paper, we conceive a new kind of output layer design in deep neural networks for the multi-class problems. The traditional output layer is set by the one-to-one method. For the one-to-one method, the output layer neuron number is the same as the class number. And the ideal output for the j-th class sample is e(j) , where e(j) is j-th unit vector. However, one-to-one method requires too many output neurons, which will increase the number of weights connecting the last-hidden and the output layers. Furthermore, during the process of network training, computation time and cost will greatly increase. We design the binary method for the output layer: Let the class number be k (k >= 3), and 2(a-1) < k <= 2(a) (a = inverted right perpendicularlog2(k)inverted left perpendicular) , then the output layer neuron number is a and the ideal output is designed by binary method. Obviously, the binary method uses less output nodes than the traditional one-to-one method. On this foundation, the number of hidden-output weights will also decrease. On the other hand, while training the deep neural network, the learning efficiency will also be significantly improved. Numerical experiments show that binary method has better classification performance and calculation speed than one-to-one method on the datasets.

关键词： Deep neural networks one-to-one method binary method multi-class problems

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Combined heat and power economic dispatch problem with binary method using flower pollination algorithm and differential evolution

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ELECTRICAL ENGINEERING 2023年第4期105卷 2161-2168页

作者： Mellal, Mohamed Arezki Khitous, Marwa Zemmouri, Meriem MHamed Bougara Univ Fac Technol LMSS Boumerdes Algeria

Nowadays, the need for electrical energy became crucial in the world. The co-generation plants, which simultaneously produce electrical and heat energies, are one of the alternative solutions to supply people and industry with both energies. The present work addresses the cost minimization of the nonconvex combined heat and power dispatch problem (CHPED). The nonconvex operating region is handled using the binary method, and the optimization problem is solved using two nature-inspired algorithms, namely the flower pollination algorithm (FPA) and the differential evolution (DE). Penalty functions are adopted to handle all the operating constraints, units' limits, and demands. The results obtained compare the algorithms and those of the literature. It is observed that the fuel cost obtained by the flower pollination algorithm (FPA) is less than the one obtained by the differential evolution (DE) and the particle swarm optimization (PSO).

关键词： Co-generations plants Optimization binary method Flower pollination algorithm Differential evolution

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Patch antenna design using the gA and the binary method for dual-band applications

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JOURNAL OF ELECTROMAGNETIC WAVES AND APPLICATIONS 2020年第12期34卷 1691-1704页

作者： Lee, Wontaek Jung, Mingook Kim, Tae-Hyung Yook, Jong-Gwan Yoo, Jeonghoon Yonsei Univ Dept Mech Engn Seoul South Korea Yonsei Univ Dept Elect & Elect Engn Seoul South Korea

This study proposes an innovative patch antenna design for multi-band operation and high radiation efficiency. The design target is the structural shape of a patch and a ground plane. The operating range of patch antenna is set to both the 5G band (3.4-3.7 GHz) and the Bluetooth range (2.4-2.48 GHz). The design process follows two steps, the genetic algorithm (GA) and the binary method. Although the GA has been widely used for patch antenna design, however, it is hard to improve the performance only using the GA due to its restriction on design constraints. Therefore, this study proposes the successive application of the binary method after the GA to derive a unique topological shape of a patch antenna. The application of the binary method enables the design constraint for bandwidth enhancement. Design results are verified through experimental measurements using fabricated antennas.

关键词： Patch antenna genetic algorithm binary method dual-band topological shape experimental verification

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A binary Characterization method for Shape Convexity and Applications

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APPLIED MATHEMATICAL MODELLING 2023年第1期122卷 780-795页

作者： Luo, Shousheng Chen, Jinfeng Xiao, Yunhai Tai, Xue-Cheng Zhejiang Normal Univ Coll Math Med Jinhua 321004 Zhejiang Peoples R China Henan Univ Sch Math & Stat Kaifeng 475000 Peoples R China Henan Univ Ctr Appl Math Henan Prov Kaifeng 475000 Peoples R China Hong Kong Baptist Univ Dept Math Hong Kong Peoples R China

Convexity prior is one of the main cues for human vision and shape completion with im-portant applications in image processing and computer vision. This paper provides a com-putable characterization method for shape convexity, and illustrates its applications in im-age segmentation and convex hull computation. We prove that the convexity of a region is equivalent to a series of quadratic inequality constraints on its indicator function. By incor-porating this result, models are proposed for image segmentation with convexity prior and convex hull computation of clean and noisy data sets, respectively. Then, these models are summarized into a unified optimization problem on binary function(s) with the quadratic inequality constraints. Numerical method is proposed by linearizing the quadratic con-straints. The linearization problem is solved by a proximal alternating direction method of multipliers, the convergence of which is guaranteed under some proper conditions. Nu-merical experiments demonstrate the efficiency and effectiveness of the proposed methods for image segmentation and convex hull computation.& COPY;2023 Elsevier Inc. All rights reserved.

关键词： Convexity prior Object(s) segmentation binary method Convex hull computation Proximal alternating direction method of multipliers

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Coalgebras for binary methods: Properties of bisimulations and invariants

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RAIRO-INFORMATIQUE THEORIQUE ET APPLICATIONS-THEORETICAL INFORMATICS AND APPLICATIONS 2001年第1期35卷 83-111页

作者： Tews, H Tech Univ Dresden Inst Theoret Informat D-01062 Dresden Germany Univ Nijmegen Nijmegen Netherlands

Coalgebras for endofunctors C --> C can be used to model classes of object-oriented languages. However, binary methods do not fit directly into this approach. This paper proposes an extension of the coalgebraic framework, namely the use of extended polynomial functors C-op x C --> C. This extension allows the incorporation of binary methods into coalgebraic class specifications. The paper also discusses how to define bisimulation and invariants for coalgebras of extended polynomial functors and proves many standard results.

关键词： binary method coalgebra bisimulation invariant object-orientation

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Shorter addition chain for smooth integers using decomposition method

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2011年第11期88卷 2222-2232页

作者： Mohamed, M. A. Said, M. R. Md Atan, K. A. Mohd Zulkarnain, Z. Ahmad Univ Putra Malaysia Inst Math Res Serdang 43400 Malaysia Univ Putra Malaysia Fac Comp Sci & Informat Technol Serdang 43400 Malaysia

An efficient computation of scalar multiplication in elliptic curve cryptography can be achieved by reducing the original problem into a chain of additions and doublings. Finding the shortest addition chain is an NP-problem. To produce the nearest possible shortest chain, various methods were introduced and most of them depends on the representation of a positive integer n into a binary form. Our method works out the given n by twice decomposition, first into its prime powers and second, for each prime into a series of 2's from which a set of rules based on addition and doubling is defined. Since prime factorization is computationally a hard problem, this method is only suitable for smooth integers. As an alternative, the need to decompose n can be avoided by choosing n of the form p(1)(e1) p(2)(e2) ... p(r)(er). This shall not compromise the security of ECC since its does not depend on prime factorization problem. The result shows a significant improvement over existing methods especially when n grows very large.

关键词： elliptic curve cryptography scalar multiplication binary method non-adjacent form complementary recoding

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A sampling framework for incorporating quantitative mass spectrometry data in protein interaction analysis

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BMC BIOINFORMATICS 2013年第1期14卷 1-9页

作者： Tucker, George Loh, Po-Ru Berger, Bonnie MIT Dept Math Cambridge MA 02139 USA MIT Comp Sci & Artificial Intelligence Lab Cambridge MA 02139 USA

Background: Comprehensive protein-protein interaction (PPI) maps are a powerful resource for uncovering the molecular basis of genetic interactions and providing mechanistic insights. Over the past decade, high-throughput experimental techniques have been developed to generate PPI maps at proteome scale, first using yeast two-hybrid approaches and more recently via affinity purification combined with mass spectrometry (AP-MS). Unfortunately, data from both protocols are prone to both high false positive and false negative rates. To address these issues, many methods have been developed to post-process raw PPI data. However, with few exceptions, these methods only analyze binary experimental data (in which each potential interaction tested is deemed either observed or unobserved), neglecting quantitative information available from AP-MS such as spectral counts. Results: We propose a novel method for incorporating quantitative information from AP-MS data into existing PPI inference methods that analyze binary interaction data. Our approach introduces a probabilistic framework that models the statistical noise inherent in observations of co-purifications. Using a sampling-based approach, we model the uncertainty of interactions with low spectral counts by generating an ensemble of possible alternative experimental outcomes. We then apply the existing method of choice to each alternative outcome and aggregate results over the ensemble. We validate our approach on three recent AP-MS data sets and demonstrate performance comparable to or better than state-of-the-art methods. Additionally, we provide an in-depth discussion comparing the theoretical bases of existing approaches and identify common aspects that may be key to their performance. Conclusions: Our sampling framework extends the existing body of work on PPI analysis using binary interaction data to apply to the richer quantitative data now commonly available through AP-MS assays. This framework is quite general,

关键词： Matrix Model Spectral Count binary method Sampling Framework Protein Complex Prediction

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Simultaneous estimation of quantile regression functions using B-splines and total variation penalty

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2019年 133卷 228-244页

作者： Jhong, Jae-Hwan Koo, Ja-Yong Korea Univ Dept Stat Seoul 02841 South Korea

We consider the problem of simultaneously estimating a finite number of quantile functions with B-splines and the total variation penalty. For the implementation of simultaneous quantile function estimators, we develop a new coordinate descent algorithm taking into account a special structure of the total variation penalty determined by B-spline coefficients. The entire paths of solution paths for several quantile function estimators and tuning parameters can be efficiently computed using the coordinate descent algorithm. We also consider non-crossing quantile function estimators having additional constraints at the knots of spline functions. Numerical studies using both simulated and real data sets are provided to illustrate the performance of the proposed method. For a theoretical result, we prove that the proposed the quantile regression function estimators achieve the minimax rate under regularity conditions. (C) 2018 Elsevier B.V. All rights reserved.

关键词： binary method Coordinate descent algorithm Minimax rate Non-crossing Total variation Weighted quantile

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ANALYSIS OF SLIDING WINDOW TECHNIQUES FOR EXPONENTIATION

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 1995年第10期30卷 17-24页

作者： KOC, CK Department of Electrical & Computer Engineering Oregon State University Corvallis OR 97331 U.S.A.

The m-ary method for computing x(E) partitions the bits of the integer E into words of constant length, and then performs as many multiplications as there are nonzero words. Variable length partitioning strategies have been suggested to reduce the number of nonzero words, and thus, the total number of multiplications. Algorithms for exponentiation using such partitioning strategies are termed sliding window techniques. In this paper, we give algorithmic descriptions of two recently proposed sliding window techniques, and calculate the average number of multiplications by modeling the partitioning process as a Markov chain;We tabulate the optimal values of the partitioning parameters, and show that the sliding window algorithms require up to 8% fewer multiplications than the m-ary method.

关键词： ANALYSIS OF ALGORITHMS EXPONENTIATION binary method M-ARY method MARKOV CHAIN

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A fast optimal parallel algorithm for a short addition chain

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JOURNAL OF SUPERCOMPUTING 2018年第1期74卷 324-333页

作者： Bahig, Hazem M. Ain Shams Univ Div Comp Sci Dept Math Fac Sci Cairo Egypt Hail Univ Comp Sci & Engn Coll Hail Saudi Arabia

Given a natural number e, an addition chain for e is a finite sequence of numbers having the following properties: (1) the first number is one, (2) every element is the sum of two earlier elements, and (3) the given number occurs at the end of the sequence. We introduce a fast optimal algorithm to generate a chain of short length for the number e of n-bits. The algorithm is based on the right-left binary strategy and barrel shifter circuit. The algorithm uses processors and runs in time under exclusive read exclusive write parallel random access machine.

关键词： Short chain Parallel algorithm binary method Parallel random access machine

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