Maximum consensus estimation plays a critically important role in several robust fitting problems in computer vision. Currently, the most prevalent algorithms for consensus maximization draw from the class of randomiz...
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Maximum consensus estimation plays a critically important role in several robust fitting problems in computer vision. Currently, the most prevalent algorithms for consensus maximization draw from the class of randomized hypothesize-and-verify algorithms, which are cheap but can usually deliver only rough approximate solutions. On the other extreme, there are exact algorithms which are exhaustive search in nature and can be costly for practical-sized inputs. This paper fills the gap between the two extremes by proposing deterministic algorithms to approximately optimize the maximum consensus criterion. Our work begins by reformulating consensus maximization with linear complementarity constraints. Then, we develop two novel algorithms: one based on non-smooth penalty method with a Frank-Wolfe style optimization scheme, the other based on the Alternating Direction Method of Multipliers (ADMM). Both algorithms solve convex subproblems to efficiently perform the optimization. We demonstrate the capability of our algorithms to greatly improve a rough initial estimate, such as those obtained using least squares or a randomized algorithm. Compared to the exact algorithms, our approach is much more practical on realistic input sizes. Further, our approach is naturally applicable to estimation problems with geometric residuals. Matlab code and demo program for our methods can be downloaded from https://***/FQcxpi.
In this paper, numerical results for a fourth-order nonlinear wave equation of Kirchhoff type with a viscoelastic term are established. First, the existence and uniqueness of a solution is proved by applying the Faedo...
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In this paper, numerical results for a fourth-order nonlinear wave equation of Kirchhoff type with a viscoelastic term are established. First, the existence and uniqueness of a solution is proved by applying the Faedo-Galerkin method and the weak compact method. Next, an algorithm to the initial boundary value problem for a nonlinear evolution equation of fourth order is studied where the spatial-variable discretization and time-variable discretization are constructed to approximate derivatives by the difference schemes. Finally, the numerical results are shown to present the errors of proposed algorithm. Simulations of the approximate solution and the exact solution are also visualized.
In genome/transcriptome assembly and similar scenarios, we are usually given millions of fragments and ready to assemble them into longer contigs by first aligning them to a reference sequence. Since one fragment may ...
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Community detection is one way to reduce the complexity of analyzing networks, especially with their rapid growth. Dividing networks into communities can help analysts and experts to understand the behavior and functi...
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Community detection is one way to reduce the complexity of analyzing networks, especially with their rapid growth. Dividing networks into communities can help analysts and experts to understand the behavior and function of the networks. Also, besides the community structure, finding the influential nodes to spread infor-mation in the networks is a critical issue for researchers. Community detection is a challenging topic in network science and, various methods have been proposed for that. Many methods that find community structure use modularity as a measure to qualify the strength of community structure. These methods try to find community structures based on maximizing modularity. Modularity maximization is an NP-hard problem. One of the ap-proaches that could solve such problems is approximate algorithms. Identifying the influential nodes which has many applications in complex networks can also be used in community detection. Therefore to maximize the modularity, in this paper, we first try to identify influential nodes, and then by estimating their influence domain, the communities are detected. We used scale-free networks concepts to prove the approximate factor. Experi-ments on real-world networks show that the proposed algorithm can compete with the state-of-the-art methods in community detection algorithms. In addition, our proposed method also identifies the most influential node within each community.
Given a graph G with n nodes, and two nodes u, v is an element of G, the CoSimRank value s(u, v) quantifies the similarity between u and v based on graph topology. Compared to SimRank, CoSimRank is shown to be more ac...
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ISBN:
(纸本)9783030908881;9783030908874
Given a graph G with n nodes, and two nodes u, v is an element of G, the CoSimRank value s(u, v) quantifies the similarity between u and v based on graph topology. Compared to SimRank, CoSimRank is shown to be more accurate and effective in many real-world applications including synonym expansion, lexicon extraction, and entity relatedness in knowledge graphs. The computation of all pairwise CoSimRanks in G is highly expensive and challenging. Existing solutions all focus on devising approximate algorithms for the computation of all pairwise CoSimRanks. To attain a desired absolute accuracy guarantee epsilon, the state-of-the-art approximate algorithm for computing all pairwise CoSimRanks requires O(n(3) log(2)(ln(1/epsilon))) time, which is prohibitively expensive even epsilon is large. In this paper, we propose RPCS, a fast randomized algorithm for computing all pairwise CoSimRank values. The basic idea of RPCS is to approximate the n x n matrix multiplications in CoSimRank computation via random projection. Theoretically, RPCS runs in O(n(2) ln(n)/epsilon(2) ln(1/epsilon)) time and meanwhile ensures an absolute error of at most epsilon in each CoSimRank value in G with a high probability. Extensive experiments using six real graphs demonstrate that RPCS is more than up to orders of magnitude faster than the state of the art. In particular, on a million-edge Twitter graph, RPCS answers the epsilon-approximate (epsilon = 0.1) all pairwise CoSimRank query within 4 h, using a single commodity server, while existing solutions fail to terminate within a day.
Facility Relocation (FR), which is an effort to reallocate the placement of facilities to adapt to the changes of urban planning and population distribution, has remarkable impact on many application areas. Existing s...
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ISBN:
(纸本)9781450384469
Facility Relocation (FR), which is an effort to reallocate the placement of facilities to adapt to the changes of urban planning and population distribution, has remarkable impact on many application areas. Existing solutions to the FR problem either focus on relocating one facility (i.e., 1-FR) or fail to guarantee the result quality on relocating k > 1 facilities (i.e., k-FR). As k-FR problem is NP-hard and is not submodular or non-decreasing, traditional hill-climb approximate algorithm cannot be directly applied. In light of that, we propose to transform k-FR into another facility placement problem, which is submodular and non-decreasing. We theoretically prove that the optimal solution of both problems are equivalent. Accordingly, we are able to present the first approximate solution towards the k-FR, namely FR2FP. Our extensive comparison over both FR2FP and the state-of-the-art heuristic solution shows that FR2FP, although provides approximation guarantee, cannot necessarily given superior results to the heuristic solution. The comparison motivates and, more importantly, directs us to present an advanced approximate solution, namely FR2FP-ex. Extensive experimental study over both real-world and synthetic datasets have verified that, FR2FP-ex demonstrates the best result quality. In addition, we also exactly unveil the scenarios when the state-of-the-art heuristic would fail to provide satisfied results in practice.
Network function virtualization (NFV) is introduced to effectively deliver end-to-end network services for the emerging Internet of Things (IoT), multiaccess edge computing, and 5G communication techniques. In NFV, th...
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Network function virtualization (NFV) is introduced to effectively deliver end-to-end network services for the emerging Internet of Things (IoT), multiaccess edge computing, and 5G communication techniques. In NFV, the network service request can be accommodated in the form of a service function chain (SFC). The SFC will have to reserve abundant resources, such as link bandwidth, service functions, and computation in the physical network to meet the demands of customers. Minimizing the cost from the resource reservation in NFV remains challenging, even though a few works in the literature proposed cost-optimization methodologies with assumptions to guarantee their correctness. In this article, we comprehensively investigate how to minimize the cost when delivering network services as SFCs with provable bounds and fewer assumptions. We formally define the problem of minimum cost service function chaining and embedding (MC-SFCE) and propose an algorithm, namely, cost factor-based SFCE optimization with shortcut (COFO-SC), for MC-SFCE. Novel mathematical analysis is provided to demonstrate the correctness of our approaches and related bounds. Our extensive simulations and analysis also show that the proposed COFO-SC outperforms the schemes directly extended from the existing work.
Gaussian kernel support vector machine recursive feature elimination (GKSVM-RFE) is a method for feature ranking in a nonlinear way. However, GKSVM-RFE suffers from the issue of high computational complexity, which hi...
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Gaussian kernel support vector machine recursive feature elimination (GKSVM-RFE) is a method for feature ranking in a nonlinear way. However, GKSVM-RFE suffers from the issue of high computational complexity, which hinders its applications. This paper investigates the issue of computational complexity in GKSVM-RFE, and proposes two fast versions for GKSVM-RFE, called fast GKSVM-RFE (FGKSVM-RFE), to speed up the procedure of recursive feature elimination in GKSVM-RFE. For this purpose, we design two kinds of ranking scores based on the first-order and second-order approximate schemes by introducing approximate Gaussian kernels. In iterations, FGKSVM-RFE fast calculates approximate ranking scores according to approximate schemes and ranks features based on approximate ranking scores. Experimental results reveal that our proposed methods can faster perform feature ranking than GKSVM-RFE and have compared performance to GKSVM-RFE.
The behavior of the welding pool plays an important role in determining the quality of the weld, and the surface behavior of the welding pool contains some important information as feedback to adjust welding parameter...
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The behavior of the welding pool plays an important role in determining the quality of the weld, and the surface behavior of the welding pool contains some important information as feedback to adjust welding parameters. In order to study the dynamic characteristics of the molten pool surface in the TIG welding process with the filler wire, a grid structure laser measurement platform, based on the principle of surface reflection, was designed to observe the molten pool surface in this work. CCD was used to record the imaging on the projection screen. A new three-dimensional reconstruction algorithm was proposed for calculation of the welding pool surface. This algorithm analyzes the image which is captured by the CCD to restore the three-dimensional topography of the fixed-point wire-filled TIG welding pool, so as to obtain the three-dimensional topography evolution the during welding process. The difference between the obtained weld pool height and the experimental results is very small.
We consider the NP-hard integer three-index axial assignment problem. Strategies for combining feasible solutions of the problem are investigated. Combining can be used as a supplement to heuristic or approximate solu...
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We consider the NP-hard integer three-index axial assignment problem. Strategies for combining feasible solutions of the problem are investigated. Combining can be used as a supplement to heuristic or approximate solution algorithms instead of the generally accepted step of choosing the record among the feasible solutions found. The results of computational experiments are presented that demonstrate the promising nature of the approach proposed.
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