Search results for: projection
130 The Projection Methods for Computing the Pseudospectra of Large Scale Matrices
Authors: Zhengsheng Wang, Xiangyong Ji, Yong Du
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The projection methods, usually viewed as the methods for computing eigenvalues, can also be used to estimate pseudospectra. This paper proposes a kind of projection methods for computing the pseudospectra of large scale matrices, including orthogonalization projection method and oblique projection method respectively. This possibility may be of practical importance in applications involving large scale highly nonnormal matrices. Numerical algorithms are given and some numerical experiments illustrate the efficiency of the new algorithms.Keywords: Pseudospectra, eigenvalue, projection method, Arnoldi, IOM(q)
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1310129 Influence of Replacement Used Reference Coordinate System for Georeferencing of the Old Map of Europe
Authors: Jakub Havlicek, Jiri Cajthaml
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The article describes the effect of the replacement of the used reference coordinate system in the georeferencing of an old map of Europe. The map was georeferenced into three types of projection – the equal-area conic (original cartographic projection), cylindrical Plate Carrée and cylindrical Mercator map projection. The map was georeferenced by means of the affine and the second-order polynomial transformation. The resulting georeferenced raster datasets from the Plate Carrée and Mercator projection were projected into the equal-area conic projection by means of projection equations. The output is the comparison of drawn graphics, the magnitude of standard deviations for individual projections and types of transformation.Keywords: Georeferencing, reference coordinate system, transformation, standard deviation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1536128 Bidirectional Discriminant Supervised Locality Preserving Projection for Face Recognition
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Dimensionality reduction and feature extraction are of crucial importance for achieving high efficiency in manipulating the high dimensional data. Two-dimensional discriminant locality preserving projection (2D-DLPP) and two-dimensional discriminant supervised LPP (2D-DSLPP) are two effective two-dimensional projection methods for dimensionality reduction and feature extraction of face image matrices. Since 2D-DLPP and 2D-DSLPP preserve the local structure information of the original data and exploit the discriminant information, they usually have good recognition performance. However, 2D-DLPP and 2D-DSLPP only employ single-sided projection, and thus the generated low dimensional data matrices have still many features. In this paper, by combining the discriminant supervised LPP with the bidirectional projection, we propose the bidirectional discriminant supervised LPP (BDSLPP). The left and right projection matrices for BDSLPP can be computed iteratively. Experimental results show that the proposed BDSLPP achieves higher recognition accuracy than 2D-DLPP, 2D-DSLPP, and bidirectional discriminant LPP (BDLPP).Keywords: Face recognition, dimension reduction, locality preserving projection, discriminant information, bidirectional projection.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 672127 A Simulation Tool for Projection Mapping Based on Mapbox and Unity
Authors: Noriko Hanakawa, Masaki Obana
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A simulation tool is proposed for big-scale projection mapping events. The tool has four main functions based on Mapbox and Unity utilities. The first function is building three-dimensional models of real cities using Mapbox. The second function is movie projections to some buildings in real cities using Unity. The third is a movie sending function from a PC to a virtual projector. The fourth function is mapping movies with fitting buildings. The simulation tool was adapted to a real projection mapping event held in 2019. The event completed, but it faced a severe problem in the movie projection to the target building. Extra tents were set in front of the target building, and the tents became obstacles to the movie projection. The simulation tool developed herein could reconstruct the problems of the event. Therefore, if the simulation tool was developed before the 2019 projection mapping event, the problem of the tents being obstacles could have been avoided using the tool. Moreover, we confirmed that the simulation tool is useful for planning future projection mapping events to avoid various extra equipment obstacles, such as utility poles, planting trees, and monument towers.
Keywords: avoiding obstacles, projection mapping, projector position, real 3D map
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 704126 A New Seed Projection Method for Solving Shifted Systems with Multiple Right-Hand Sides
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In this paper, we propose a new seed projection method for solving shifted systems with multiple right-hand sides. This seed projection method uses a seed selection strategy. Numerical experiments are presented to show the efficiency of the newly method.
Keywords: shifted systems, multiple right-hand sides, seed projection.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1473125 Variable Step-Size Affine Projection Algorithm With a Weighted and Regularized Projection Matrix
Authors: Tao Dai, Andy Adler, Behnam Shahrrava
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This paper presents a forgetting factor scheme for variable step-size affine projection algorithms (APA). The proposed scheme uses a forgetting processed input matrix as the projection matrix of pseudo-inverse to estimate system deviation. This method introduces temporal weights into the projection matrix, which is typically a better model of the real error's behavior than homogeneous temporal weights. The regularization overcomes the ill-conditioning introduced by both the forgetting process and the increasing size of the input matrix. This algorithm is tested by independent trials with coloured input signals and various parameter combinations. Results show that the proposed algorithm is superior in terms of convergence rate and misadjustment compared to existing algorithms. As a special case, a variable step size NLMS with forgetting factor is also presented in this paper.
Keywords: Adaptive signal processing, affine projection algorithms, variable step-size adaptive algorithms, regularization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1621124 The Variable Step-Size Gauss-Seidel Pseudo Affine Projection Algorithm
Authors: F. Albu, C. Paleologu
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In this paper, a new pseudo affine projection (AP) algorithm based on Gauss-Seidel (GS) iterations is proposed for acoustic echo cancellation (AEC). It is shown that the algorithm is robust against near-end signal variations (including double-talk).Keywords: pseudo affine projection algorithm, acoustic echo cancellation, double-talk.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1417123 Data-Reusing Adaptive Filtering Algorithms with Adaptive Error Constraint
Authors: Young-Seok Choi
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We present a family of data-reusing and affine projection algorithms. For identification of a noisy linear finite impulse response channel, a partial knowledge of a channel, especially noise, can be used to improve the performance of the adaptive filter. Motivated by this fact, the proposed scheme incorporates an estimate of a knowledge of noise. A constraint, called the adaptive noise constraint, estimates an unknown information of noise. By imposing this constraint on a cost function of data-reusing and affine projection algorithms, a cost function based on the adaptive noise constraint and Lagrange multiplier is defined. Minimizing the new cost function leads to the adaptive noise constrained (ANC) data-reusing and affine projection algorithms. Experimental results comparing the proposed schemes to standard data-reusing and affine projection algorithms clearly indicate their superior performance.Keywords: Data-reusing, affine projection algorithm, error constraint, system identification.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1606122 A Family of Affine Projection Adaptive Filtering Algorithms With Selective Regressors
Authors: Mohammad Shams Esfand Abadi, Nader Hadizadeh Kashani, Vahid Mehrdad
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In this paper we present a general formalism for the establishment of the family of selective regressor affine projection algorithms (SR-APA). The SR-APA, the SR regularized APA (SR-RAPA), the SR partial rank algorithm (SR-PRA), the SR binormalized data reusing least mean squares (SR-BNDR-LMS), and the SR normalized LMS with orthogonal correction factors (SR-NLMS-OCF) algorithms are established by this general formalism. We demonstrate the performance of the presented algorithms through simulations in acoustic echo cancellation scenario.Keywords: Adaptive filter, affine projection, selective regressor.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1562121 Combination Scheme of Affine Projection Algorithm Filters with Complementary Order
Authors: Young-Seok Choi
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This paper proposes a complementary combination scheme of affine projection algorithm (APA) filters with different order of input regressors. A convex combination provides an interesting way to keep the advantage of APA having different order of input regressors. Consequently, a novel APA which has the rapid convergence and the reduced steady-state error is derived. Experimental results show the good properties of the proposed algorithm.
Keywords: Adaptive filter, affine projection algorithm, convex combination, input order.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1657120 A Projection Method Based on Extended Krylov Subspaces for Solving Sylvester Equations
Authors: Yiqin Lin, Liang Bao, Yimin Wei
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In this paper we study numerical methods for solving Sylvester matrix equations of the form AX +XBT +CDT = 0. A new projection method is proposed. The union of Krylov subspaces in A and its inverse and the union of Krylov subspaces in B and its inverse are used as the right and left projection subspaces, respectively. The Arnoldi-like process for constructing the orthonormal basis of the projection subspaces is outlined. We show that the approximate solution is an exact solution of a perturbed Sylvester matrix equation. Moreover, exact expression for the norm of residual is derived and results on finite termination and convergence are presented. Some numerical examples are presented to illustrate the effectiveness of the proposed method.
Keywords: Arnoldi process, Krylov subspace, Iterative method, Sylvester equation, Dissipative matrix.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1983119 Affine Projection Algorithm with Variable Data-Reuse Factor
Authors: ChangWoo Lee, Young Kow Lee, Sung Jun Ban, SungHoo Choi, Sang Woo Kim
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This paper suggests a new Affine Projection (AP) algorithm with variable data-reuse factor using the condition number as a decision factor. To reduce computational burden, we adopt a recently reported technique which estimates the condition number of an input data matrix. Several simulations show that the new algorithm has better performance than that of the conventional AP algorithm.
Keywords: Affine projection algorithm, variable data-reuse factor, condition number, convergence rate, misalignment.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1533118 Affine Projection Adaptive Filter with Variable Regularization
Authors: Young-Seok Choi
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We propose two affine projection algorithms (APA) with variable regularization parameter. The proposed algorithms dynamically update the regularization parameter that is fixed in the conventional regularized APA (R-APA) using a gradient descent based approach. By introducing the normalized gradient, the proposed algorithms give birth to an efficient and a robust update scheme for the regularization parameter. Through experiments we demonstrate that the proposed algorithms outperform conventional R-APA in terms of the convergence rate and the misadjustment error.Keywords: Affine projection, regularization, gradient descent, system identification.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1596117 3-D Reconstruction of Objects Using Digital Fringe Projection: Survey and Experimental Study
Authors: R. Talebi, A. Abdel-Dayem, J. Johnson
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Three-dimensional reconstruction of small objects has been one of the most challenging problems over the last decade. Computer graphics researchers and photography professionals have been working on improving 3D reconstruction algorithms to fit the high demands of various real life applications. Medical sciences, animation industry, virtual reality, pattern recognition, tourism industry, and reverse engineering are common fields where 3D reconstruction of objects plays a vital role. Both lack of accuracy and high computational cost are the major challenges facing successful 3D reconstruction. Fringe projection has emerged as a promising 3D reconstruction direction that combines low computational cost to both high precision and high resolution. It employs digital projection, structured light systems and phase analysis on fringed pictures. Research studies have shown that the system has acceptable performance, and moreover it is insensitive to ambient light. This paper presents an overview of fringe projection approaches. It also presents an experimental study and implementation of a simple fringe projection system. We tested our system using two objects with different materials and levels of details. Experimental results have shown that, while our system is simple, it produces acceptable results.Keywords: Digital fringe projection, 3D reconstruction, phase unwrapping, phase shifting.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5212116 Sparsity-Aware Affine Projection Algorithm for System Identification
Authors: Young-Seok Choi
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This work presents a new type of the affine projection (AP) algorithms which incorporate the sparsity condition of a system. To exploit the sparsity of the system, a weighted l1-norm regularization is imposed on the cost function of the AP algorithm. Minimizing the cost function with a subgradient calculus and choosing two distinct weighting for l1-norm, two stochastic gradient based sparsity regularized AP (SR-AP) algorithms are developed. Experimental results exhibit that the SR-AP algorithms outperform the typical AP counterparts for identifying sparse systems.Keywords: System identification, adaptive filter, affine projection, sparsity, sparse system.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1549115 A Straightforward Approach for Determining the Weights of Decision Makers Based on Angle Cosine and Projection Method
Authors: Qiang Yang, Ping-An Du
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Group decision making with multiple attribute has attracted intensive concern in the decision analysis area. This paper assumes that the contributions of all the decision makers (DMs) are not equal to the decision process based on different knowledge and experience in group setting. The aim of this paper is to develop a novel approach to determine weights of DMs in the group decision making problems. In this paper, the weights of DMs are determined in the group decision environment via angle cosine and projection method. First of all, the average decision of all individual decisions is defined as the ideal decision. After that, we define the weight of each decision maker (DM) by aggregating the angle cosine and projection between individual decision and ideal decision with associated direction indicator μ. By using the weights of DMs, all individual decisions are aggregated into a collective decision. Further, the preference order of alternatives is ranked in accordance with the overall row value of collective decision. Finally, an example in a chemical company is provided to illustrate the developed approach.Keywords: Angel cosine, ideal decision, projection method, weights of decision makers.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1848114 Steganalysis of Data Hiding via Halftoning and Coordinate Projection
Authors: Woong Hee Kim, Ilhwan Park
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Steganography is the art of hiding and transmitting data through apparently innocuous carriers in an effort to conceal the existence of the data. A lot of steganography algorithms have been proposed recently. Many of them use the digital image data as a carrier. In data hiding scheme of halftoning and coordinate projection, still image data is used as a carrier, and the data of carrier image are modified for data embedding. In this paper, we present three features for analysis of data hiding via halftoning and coordinate projection. Also, we present a classifier using the proposed three features.Keywords: Steganography, steganalysis, digital halftoning, data hiding.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1589113 Health Assessment of Electronic Products using Mahalanobis Distance and Projection Pursuit Analysis
Authors: Sachin Kumar, Vasilis Sotiris, Michael Pecht
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With increasing complexity in electronic systems there is a need for system level anomaly detection and fault isolation. Anomaly detection based on vector similarity to a training set is used in this paper through two approaches, one the preserves the original information, Mahalanobis Distance (MD), and the other that compresses the data into its principal components, Projection Pursuit Analysis. These methods have been used to detect deviations in system performance from normal operation and for critical parameter isolation in multivariate environments. The study evaluates the detection capability of each approach on a set of test data with known faults against a baseline set of data representative of such “healthy" systems.Keywords: Mahalanobis distance, Principle components, Projection pursuit, Health assessment, Anomaly.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1672112 New Wavelet-Based Superresolution Algorithm for Speckle Reduction in SAR Images
Authors: Mario Mastriani
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This paper describes a novel projection algorithm, the Projection Onto Span Algorithm (POSA) for wavelet-based superresolution and removing speckle (in wavelet domain) of unknown variance from Synthetic Aperture Radar (SAR) images. Although the POSA is good as a new superresolution algorithm for image enhancement, image metrology and biometric identification, here one will use it like a tool of despeckling, being the first time that an algorithm of super-resolution is used for despeckling of SAR images. Specifically, the speckled SAR image is decomposed into wavelet subbands; POSA is applied to the high subbands, and reconstruct a SAR image from the modified detail coefficients. Experimental results demonstrate that the new method compares favorably to several other despeckling methods on test SAR images.
Keywords: Projection, speckle, superresolution, synthetic aperture radar, thresholding, wavelets.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1602111 Comparison of Back-Projection with Non-Uniform Fast Fourier Transform for Real-Time Photoacoustic Tomography
Authors: Moung Young Lee, Chul Gyu Song
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Photoacoustic imaging is the imaging technology that combines the optical imaging and ultrasound. This provides the high contrast and resolution due to optical imaging and ultrasound imaging, respectively. We developed the real-time photoacoustic tomography (PAT) system using linear-ultrasound transducer and digital acquisition (DAQ) board. There are two types of algorithm for reconstructing the photoacoustic signal. One is back-projection algorithm, the other is FFT algorithm. Especially, we used the non-uniform FFT algorithm. To evaluate the performance of our system and algorithms, we monitored two wires that stands at interval of 2.89 mm and 0.87 mm. Then, we compared the images reconstructed by algorithms. Finally, we monitored the two hairs crossed and compared between these algorithms.Keywords: Back-projection, image comparison, non-uniform FFT, photoacoustic tomography.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1878110 Probabilistic Center Voting Method for Subsequent Object Tracking and Segmentation
Authors: Suryanto, Hyo-Kak Kim, Sang-Hee Park, Dae-Hwan Kim, Sung-Jea Ko
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In this paper, we introduce a novel algorithm for object tracking in video sequence. In order to represent the object to be tracked, we propose a spatial color histogram model which encodes both the color distribution and spatial information. The object tracking from frame to frame is accomplished via center voting and back projection method. The center voting method has every pixel in the new frame to cast a vote on whereabouts the object center is. The back projection method segments the object from the background. The segmented foreground provides information on object size and orientation, omitting the need to estimate them separately. We do not put any assumption on camera motion; the proposed algorithm works equally well for object tracking in both static and moving camera videos.
Keywords: center voting, back projection, object tracking, size adaptation, non-stationary camera tracking.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1658109 The Modified Eigenface Method using Two Thresholds
Authors: Yan Ma, ShunBao Li
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A new approach is adopted in this paper based on Turk and Pentland-s eigenface method. It was found that the probability density function of the distance between the projection vector of the input face image and the average projection vector of the subject in the face database, follows Rayleigh distribution. In order to decrease the false acceptance rate and increase the recognition rate, the input face image has been recognized using two thresholds including the acceptance threshold and the rejection threshold. We also find out that the value of two thresholds will be close to each other as number of trials increases. During the training, in order to reduce the number of trials, the projection vectors for each subject has been averaged. The recognition experiments using the proposed algorithm show that the recognition rate achieves to 92.875% whilst the average number of judgment is only 2.56 times.Keywords: Eigenface, Face Recognition, Threshold, Rayleigh Distribution, Feature Extraction
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1480108 A Descent-projection Method for Solving Monotone Structured Variational Inequalities
Authors: Min Sun, Zhenyu Liu
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In this paper, a new descent-projection method with a new search direction for monotone structured variational inequalities is proposed. The method is simple, which needs only projections and some function evaluations, so its computational load is very tiny. Under mild conditions on the problem-s data, the method is proved to converges globally. Some preliminary computational results are also reported to illustrate the efficiency of the method.Keywords: variational inequalities, monotone function, global convergence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1277107 Genetic Programming Based Data Projections for Classification Tasks
Authors: César Estébanez, Ricardo Aler, José M. Valls
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In this paper we present a GP-based method for automatically evolve projections, so that data can be more easily classified in the projected spaces. At the same time, our approach can reduce dimensionality by constructing more relevant attributes. Fitness of each projection measures how easy is to classify the dataset after applying the projection. This is quickly computed by a Simple Linear Perceptron. We have tested our approach in three domains. The experiments show that it obtains good results, compared to other Machine Learning approaches, while reducing dimensionality in many cases.
Keywords: Classification, genetic programming, projections.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1388106 Journals Subheadlines Text Extraction Using Wavelet Thresholding and New Projection Profile
Authors: Davod Zaravi, Habib Rostami, Alireza Malahzaheh, S. S. Mortazavi
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In this paper a new robust and efficient algorithm to automatic text extraction from colored book and journal cover sheets is proposed. First, we perform wavelet transform. Next for edge detecting from detail wavelet coefficient, we use dynamic threshold. By blurring approximate coefficients with alternative heuristic thresholding, achieve effective edge,. Afterward, with ROI technique get binary image. Finally text boxes would be extracted with new projection profile.
Keywords: Text extraction, colored cover sheet, wavelet threshold, region of interest.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1636105 Tomographic Images Reconstruction Simulation for Defects Detection in Specimen
Authors: Kedit J.
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This paper is the tomographic images reconstruction simulation for defects detection in specimen. The specimen is the thin cylindrical steel contained with low density materials. The defects in material are simulated in three shapes.The specimen image function will be transformed to projection data. Radon transform and its inverse provide the mathematical for reconstructing tomographic images from projection data. The result of the simulation show that the reconstruction images is complete for defect detection.Keywords: Tomography, Tomography Reconstruction, Radon Transform
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1417104 Restarted Generalized Second-Order Krylov Subspace Methods for Solving Quadratic Eigenvalue Problems
Authors: Liping Zhou, Liang Bao, Yiqin Lin, Yimin Wei, Qinghua Wu
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This article is devoted to the numerical solution of large-scale quadratic eigenvalue problems. Such problems arise in a wide variety of applications, such as the dynamic analysis of structural mechanical systems, acoustic systems, fluid mechanics, and signal processing. We first introduce a generalized second-order Krylov subspace based on a pair of square matrices and two initial vectors and present a generalized second-order Arnoldi process for constructing an orthonormal basis of the generalized second-order Krylov subspace. Then, by using the projection technique and the refined projection technique, we propose a restarted generalized second-order Arnoldi method and a restarted refined generalized second-order Arnoldi method for computing some eigenpairs of largescale quadratic eigenvalue problems. Some theoretical results are also presented. Some numerical examples are presented to illustrate the effectiveness of the proposed methods.Keywords: Quadratic eigenvalue problem, Generalized secondorder Krylov subspace, Generalized second-order Arnoldi process, Projection technique, Refined technique, Restarting.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1850103 The Implementation of the Javanese Lettered-Manuscript Image Preprocessing Stage Model on the Batak Lettered-Manuscript Image
Authors: Anastasia Rita Widiarti, Agus Harjoko, Marsono, Sri Hartati
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This paper presents the results of a study to test whether the Javanese character manuscript image preprocessing model that have been more widely applied, can also be applied to segment of the Batak characters manuscripts. The treatment process begins by converting the input image into a binary image. After the binary image is cleaned of noise, then the segmentation lines using projection profile is conducted. If unclear histogram projection is found, then the smoothing process before production indexes line segments is conducted. For each line image which has been produced, then the segmentation scripts in the line is applied, with regard of the connectivity between pixels which making up the letters that there is no characters are truncated. From the results of manuscript preprocessing system prototype testing, it is obtained the information about the system truth percentage value on pieces of Pustaka Batak Podani Ma AjiMamisinon manuscript ranged from 65% to 87.68% with a confidence level of 95%. The value indicates the truth percentage shown the initial processing model in Javanese characters manuscript image can be applied also to the image of the Batak characters manuscript.Keywords: Connected component, preprocessing manuscript image, projection profiles.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 915102 Topology Preservation in SOM
Authors: E. Arsuaga Uriarte, F. Díaz Martín
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The SOM has several beneficial features which make it a useful method for data mining. One of the most important features is the ability to preserve the topology in the projection. There are several measures that can be used to quantify the goodness of the map in order to obtain the optimal projection, including the average quantization error and many topological errors. Many researches have studied how the topology preservation should be measured. One option consists of using the topographic error which considers the ratio of data vectors for which the first and second best BMUs are not adjacent. In this work we present a study of the behaviour of the topographic error in different kinds of maps. We have found that this error devaluates the rectangular maps and we have studied the reasons why this happens. Finally, we suggest a new topological error to improve the deficiency of the topographic error.Keywords: Map lattice, Self-Organizing Map, topographic error, topology preservation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2990101 The Discovery and Application of Perspective Representation in Modern Italy
Authors: Matthias Stange
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In the early modern period, a different image of man began to prevail in Europe. The focus was on the self-determined human being and his abilities. At first, these developments could be seen in Italian painting and architecture, which again oriented itself to the concepts and forms of antiquity. For example, through the discovery of perspective representation by Brunelleschi or later the orthogonal projection by Alberti, after the ancient knowledge of optics had been forgotten in the Middle Ages. The understanding of reality in the Middle Ages was not focused on the sensually perceptible world, but was determined by ecclesiastical dogmas. The empirical part of this study examines the rediscovery and development of perspective. With the paradigm of antiquity, the figure of the architect was also recognised again - the cultural man trained theoretically and practically in numerous subjects, as Vitruvius describes him. In this context, the role of the architect, the influence on the painting of the Quattrocento as well as the influence on architectural representation in the Baroque period are examined. Baroque is commonly associated with the idea of illusionistic appearance as opposed to the tangible reality presented in the Renaissance. The study has shown that the central perspective projection developed by Filippo Brunelleschi enabled another understanding of seeing and the dissemination of painted images. Brunelleschi's development made it possible to understand the sight of nature as a reflection of what is presented to the viewer's eye. Alberti later shortened Brunelleschi's central perspective representation for practical use in painting. In early modern Italian architecture and painting, these developments apparently supported each other. The pictorial representation of architecture initially served the development of an art form before it became established in building practice itself.
Keywords: Alberti, Brunelleschi, Central perspective projection, Orthogonal projection, Quattrocento, Baroque.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 149