761547
Finite Element Surface Fitting for Bridge Management
We propose a new finite element surface fitting method which can handle very large databases. This method uses finite element discretization to find an approximation of a smooth function which minimizes a sum of data residuals and second derivatives under some constraints on data. The finite element discretization derives a large scale constrained quadratic program, which can be reformulated as a system of piecewise linear equations. We develop a preconditioned Newton method to solve the system efficiently. We apply this method to form surfaces over Aomori Region in Japan by geographic databases, such that every bridge became associated with environmental information.
16295262
A preconditioning proximal newton method for nondifferentiable convex optimization
We propose a proximal Newton method for solving nondifferentiable convex optimization. This method combines the generalized Newton method with Rockafellar’s proximal point algorithm. At each step, the proximal point is found approximately and the regularization matrix is preconditioned to overcome inexactness of this approximation. We show that such a preconditioning is possible within some accuracy and the second-order differentiability properties of the Moreau-Yosida regularization are invariant with respect to this preconditioning. Based upon these, superlinear convergence is established under a semismoothness condition.
33892015
A Multiple-Criteria Quadratic Programming Approach to Network Intrusion Detection
The early and reliable detection and deterrence of malicious attacks, both from external and internal sources are a crucial issue for today’s e-business. There are various methods available today for intrusion detection; however, every method has its limitations and new approaches should still be explored. The objectives of this study are twofold: one is to discuss the formulation of Multiple Criteria Quadratic Programming (MCQP) approach, and to investigate the applicability of the quadratic classification method to the intrusion detection problem. The demonstration of successful Multiple Criteria Quadratic Programming application in intrusion detection can add another option to network security toolbox. The classification results are examined by cross-validation and improved by an ensemble method. The results demonstrated that MCQP is excellent and stable. Furthermore, the outcome of MCQP can be improved by the ensemble method.
8507685
Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities
The smoothing Newton method for solving a system of nonsmooth equations F(x) = 0, which may arise from the nonlinear complementarity problem, the variational inequality problem or other problems, can be regarded as a variant of the smoothing method. At the kth step, the nonsmooth function F is approximated by a smooth function f(.,∈ κ ), and the derivative of f(.,∈ κ ) at x k is used as the Newton iterative matrix. The merits of smoothing methods and smoothing Newton methods are global convergence and convenience in handling. In this paper, we show that the smoothing Newton method is also superlinearly convergent if F is semismooth at the solution and f satisfies a Jacobian consistency property. We show that most common smooth functions, such as the Gabriel-More function, have this property. As an application, we show that for box constrained variational inequalities if the involved function is P- uniform, the iteration sequence generated by the smoothing Newton method will converge to the unique solution of the problem globally and superlinearly (quadratically).
19172237
A verification method for solutions of nonsmooth equations
This paper proposes a verification method for the existence of solutions of nonsmooth equations. We generalize the Krawczyk operator to nonsmooth equations by using the mean-value theorem for nonsmooth functions. We establish a semi-local convergence theorem for the generalized Newton method for nonsmooth equations. The proposed method is a combination of the generalized Krawczyk operator and the semi-local convergence theorem.ZusammenfassungDieser Artikel schlägt eine Methode zur Verifizierung der Existenz von Lösungen nicht-differenzierbarer Gleichungen vor. Wir verallgemeinern den Krawczyk-Operator auf nicht-differenzierbare Gleichungen indem wir den Mittelwertsatz für nicht-differenzierbare Funktionen benutzen. Wir entwickeln einen semilokalen Konvergenzsatz für das verallgemeinerte Newton-Verfahren, angewendet auf nicht-differenzierbare Gleichungen. Die vorgeschlagene Methode ist eine Kombination aus dem verallgemeinerten Krawczyk-Operator und dem semi-lokalen Konvergenzsatz.
41168099
A note on Roman domination in graphs
Let G=(V,E) be a simple graph. A subset [email protected]?V is a dominating set of G, if for any vertex [email protected]?V-S, there exists a vertex [email protected]?S such that [email protected]?E. The domination number of G, @c(G), equals the minimum cardinality of a dominating set. A Roman dominating function on graph G=(V,E) is a function f:V->{0,1,2} satisfying the condition that every vertex v for which f(v)=0 is adjacent to at least one vertex u for which f(u)=2. The weight of a Roman dominating function is the value f(V)[email protected]?"v"@?"Vf(v). The Roman domination number of a graph G, denoted by @c"R(G), equals the minimum weight of a Roman dominating function on G. In this paper, for any integer k(2=
12374753
Efficient Method for Geometric Attribute Estimation
A new method is proposed to estimate the discrete geometric attributes, such as normal vector and curvature. The method contains two steps: points sampling and 4D Shepard interpolation. In the first step, we extract points from point cloud and estimate the attribute of the sampled points. During the second step, we interpolate a global 4D Shepard surface over these sampled points and compute the attribute of each point in point cloud. This method is very effective for using a new global surface model. It benefits many applications such as segmentation, feature extraction, data preprocessing and etc. Application examples are given to verify the proposed method.
3226359
Segmentation, Registration, and Deformation Analysis of 3D MR Images of Mice
We demonstrate our mouse MR image and shape analysis pipeline. The long term goal of our work is the description of structural shape variations in normal, genetically identical mice and the subsequent detection of pathological phenotypes in genetically modified mice. The pipeline begins with the acquisition and reconstruction of high resolution MR images of mice. Regions of the images containing organs under study are enhanced via edge-preserving smoothing and mouse organs are segmented using a deformable mesh model. Images are registered using a multi-resolution approach and displacement fields are used to calculate local volume changes. Detailed descriptions and results for each step of the pipeline are presented.
3763580
Extracting Features from Web Search Returned Hits for Hierarchical Classification
17670948
A General Framework for Biclustering Gene Expression Data
A large number of biclustering methods have been proposed to detect patterns in gene expression data. All these methods try to find some type of biclusters but no one can discover all the types of patterns in the data. Furthermore, researchers have to design new algorithms in order to find new types of biclusters/patterns that interest biologists. In this paper, we propose a novel approach for biclustering that, in general, can be used to discover all computable patterns in gene expression data. The method is based on the theory of Kolmogorov complexity. More precisely, we use Kolmogorov complexity to measure the randomness of submatrices as the merit of biclusters because randomness naturally consists in a lack of regularity, which is a common property of all types of patterns. On the basis of algorithmic probability measure, we develop a Markov Chain Monte Carlo algorithm to search for biclusters. Our method can also be easily extended to solve the problems of conventional clustering and checkerboard type biclustering. The preliminary experiments on simulated as well as real data show that our approach is very versatile and promising.