Search results for: deterministic-stochastic subspace system
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 8411

Search results for: deterministic-stochastic subspace system

8411 Self-Tuning Robot Control Based on Subspace Identification

Authors: Mathias Marquardt, Peter Dünow, Sandra Baßler

Abstract:

The paper describes the use of subspace based identification methods for auto tuning of a state space control system. The plant is an unstable but self balancing transport robot. Because of the unstable character of the process it has to be identified from closed loop input-output data. Based on the identified model a state space controller combined with an observer is calculated. The subspace identification algorithm and the controller design procedure is combined to a auto tuning method. The capability of the approach was verified in a simulation experiments under different process conditions.

Keywords: Auto tuning, balanced robot, closed loop identification, subspace identification.

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8410 Finite Element and Subspace Identification Approaches to Model Development of a Smart Acoustic Box with Experimental Verification

Authors: Tamara Nestorović, Jean Lefèvre, Stefan Ringwelski, Ulrich Gabbert

Abstract:

Two approaches for model development of a smart acoustic box are suggested in this paper: the finite element (FE) approach and the subspace identification. Both approaches result in a state-space model, which can be used for obtaining the frequency responses and for the controller design. In order to validate the developed FE model and to perform the subspace identification, an experimental set-up with the acoustic box and dSPACE system was used. Experimentally obtained frequency responses show good agreement with the frequency responses obtained from the FE model and from the identified model.

Keywords: Acoustic box, experimental verification, finite element model, subspace identification.

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8409 Blind Channel Estimation for Frequency Hopping System Using Subspace Based Method

Authors: M. M. Qasaymeh, M. A. Khodeir

Abstract:

Subspace channel estimation methods have been studied widely, where the subspace of the covariance matrix is decomposed to separate the signal subspace from noise subspace. The decomposition is normally done by using either the eigenvalue decomposition (EVD) or the singular value decomposition (SVD) of the auto-correlation matrix (ACM). However, the subspace decomposition process is computationally expensive. This paper considers the estimation of the multipath slow frequency hopping (FH) channel using noise space based method. In particular, an efficient method is proposed to estimate the multipath time delays by applying multiple signal classification (MUSIC) algorithm which is based on the null space extracted by the rank revealing LU (RRLU) factorization. As a result, precise information is provided by the RRLU about the numerical null space and the rank, (i.e., important tool in linear algebra). The simulation results demonstrate the effectiveness of the proposed novel method by approximately decreasing the computational complexity to the half as compared with RRQR methods keeping the same performance.

Keywords: Time Delay Estimation, RRLU, RRQR, MUSIC, LS-ESPRIT, LS-ESPRIT, Frequency Hopping.

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8408 A Text Clustering System based on k-means Type Subspace Clustering and Ontology

Authors: Liping Jing, Michael K. Ng, Xinhua Yang, Joshua Zhexue Huang

Abstract:

This paper presents a text clustering system developed based on a k-means type subspace clustering algorithm to cluster large, high dimensional and sparse text data. In this algorithm, a new step is added in the k-means clustering process to automatically calculate the weights of keywords in each cluster so that the important words of a cluster can be identified by the weight values. For understanding and interpretation of clustering results, a few keywords that can best represent the semantic topic are extracted from each cluster. Two methods are used to extract the representative words. The candidate words are first selected according to their weights calculated by our new algorithm. Then, the candidates are fed to the WordNet to identify the set of noun words and consolidate the synonymy and hyponymy words. Experimental results have shown that the clustering algorithm is superior to the other subspace clustering algorithms, such as PROCLUS and HARP and kmeans type algorithm, e.g., Bisecting-KMeans. Furthermore, the word extraction method is effective in selection of the words to represent the topics of the clusters.

Keywords: Subspace Clustering, Text Mining, Feature Weighting, Cluster Interpretation, Ontology

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8407 ISC–Intelligent Subspace Clustering, A Density Based Clustering Approach for High Dimensional Dataset

Authors: Sunita Jahirabadkar, Parag Kulkarni

Abstract:

Many real-world data sets consist of a very high dimensional feature space. Most clustering techniques use the distance or similarity between objects as a measure to build clusters. But in high dimensional spaces, distances between points become relatively uniform. In such cases, density based approaches may give better results. Subspace Clustering algorithms automatically identify lower dimensional subspaces of the higher dimensional feature space in which clusters exist. In this paper, we propose a new clustering algorithm, ISC – Intelligent Subspace Clustering, which tries to overcome three major limitations of the existing state-of-art techniques. ISC determines the input parameter such as є – distance at various levels of Subspace Clustering which helps in finding meaningful clusters. The uniform parameters approach is not suitable for different kind of databases. ISC implements dynamic and adaptive determination of Meaningful clustering parameters based on hierarchical filtering approach. Third and most important feature of ISC is the ability of incremental learning and dynamic inclusion and exclusions of subspaces which lead to better cluster formation.

Keywords: Density based clustering, high dimensional data, subspace clustering, dynamic parameter setting.

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8406 Restarted Generalized Second-Order Krylov Subspace Methods for Solving Quadratic Eigenvalue Problems

Authors: Liping Zhou, Liang Bao, Yiqin Lin, Yimin Wei, Qinghua Wu

Abstract:

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.

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8405 Krylov Model Order Reduction of a Thermal Subsea Model

Authors: J. Šindler, A. Suleng, T. Jelstad Olsen, P. Bárta

Abstract:

A subsea hydrocarbon production system can undergo planned and unplanned shutdowns during the life of the field. The thermal FEA is used to simulate the cool down to verify the insulation design of the subsea equipment, but it is also used to derive an acceptable insulation design for the cold spots. The driving factors of subsea analyses require fast responding and accurate models of the equipment cool down. This paper presents cool down analysis carried out by a Krylov subspace reduction method, and compares this approach to the commonly used FEA solvers. The model considered represents a typical component of a subsea production system, a closed valve on a dead leg. The results from the Krylov reduction method exhibits the least error and requires the shortest computational time to reach the solution. These findings make the Krylov model order reduction method very suitable for the above mentioned subsea applications.

Keywords: Model order reduction, Krylov subspace, subsea production system, finite element.

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8404 Video Data Mining based on Information Fusion for Tamper Detection

Authors: Girija Chetty, Renuka Biswas

Abstract:

In this paper, we propose novel algorithmic models based on information fusion and feature transformation in crossmodal subspace for different types of residue features extracted from several intra-frame and inter-frame pixel sub-blocks in video sequences for detecting digital video tampering or forgery. An evaluation of proposed residue features – the noise residue features and the quantization features, their transformation in cross-modal subspace, and their multimodal fusion, for emulated copy-move tamper scenario shows a significant improvement in tamper detection accuracy as compared to single mode features without transformation in cross-modal subspace.

Keywords: image tamper detection, digital forensics, correlation features image fusion

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8403 Damage Localization of Deterministic-Stochastic Systems

Authors: Yen-Po Wang, Ming-Chih Huang, Ming-Lian Chang

Abstract:

A scheme integrated with deterministic–stochastic subspace system identification and the method of damage localization vector is proposed in this study for damage detection of structures based on seismic response data. A series of shaking table tests using a five-storey steel frame has been conducted in National Center for Research on Earthquake Engineering (NCREE), Taiwan. Damage condition is simulated by reducing the cross-sectional area of some of the columns at the bottom. Both single and combinations of multiple damage conditions at various locations have been considered. In the system identification analysis, either full or partial observation conditions have been taken into account. It has been shown that the damaged stories can be identified from global responses of the structure to earthquakes if sufficiently observed. In addition to detecting damage(s) with respect to the intact structure, identification of new or extended damages of the as-damaged (ill-conditioned) counterpart has also been studied. The proposed scheme proves to be effective.

Keywords: Damage locating vectors, deterministic-stochastic subspace system, shaking table tests, system identification.

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8402 Gene Expression Data Classification Using Discriminatively Regularized Sparse Subspace Learning

Authors: Chunming Xu

Abstract:

Sparse representation which can represent high dimensional data effectively has been successfully used in computer vision and pattern recognition problems. However, it doesn-t consider the label information of data samples. To overcome this limitation, we develop a novel dimensionality reduction algorithm namely dscriminatively regularized sparse subspace learning(DR-SSL) in this paper. The proposed DR-SSL algorithm can not only make use of the sparse representation to model the data, but also can effective employ the label information to guide the procedure of dimensionality reduction. In addition,the presented algorithm can effectively deal with the out-of-sample problem.The experiments on gene-expression data sets show that the proposed algorithm is an effective tool for dimensionality reduction and gene-expression data classification.

Keywords: sparse representation, dimensionality reduction, labelinformation, sparse subspace learning, gene-expression data classification.

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8401 Global GMRES with Deflated Restarting for Families of Shifted Linear Systems

Authors: Jing Meng, Peiyong Zhu, Houbiao Li

Abstract:

Many problems in science and engineering field require the solution of shifted linear systems with multiple right hand sides and multiple shifts. To solve such systems efficiently, the implicitly restarted global GMRES algorithm is extended in this paper. However, the shift invariant property could no longer hold over the augmented global Krylov subspace due to adding the harmonic Ritz matrices. To remedy this situation, we enforce the collinearity condition on the shifted system and propose shift implicitly restarted global GMRES. The new method not only improves the convergence but also has a potential to simultaneously compute approximate solution for the shifted systems using only as many matrix vector multiplications as the solution of the seed system requires. In addition, some numerical experiments also confirm the effectiveness of our method.

Keywords: Shifted linear systems, global Krylov subspace, GLGMRESIR, GLGMRESIRsh, harmonic Ritz matrix, harmonic Ritz vector.

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8400 Performance Evaluation of Music and Minimum Norm Eigenvector Algorithms in Resolving Noisy Multiexponential Signals

Authors: Abdussamad U. Jibia, Momoh-Jimoh E. Salami

Abstract:

Eigenvector methods are gaining increasing acceptance in the area of spectrum estimation. This paper presents a successful attempt at testing and evaluating the performance of two of the most popular types of subspace techniques in determining the parameters of multiexponential signals with real decay constants buried in noise. In particular, MUSIC (Multiple Signal Classification) and minimum-norm techniques are examined. It is shown that these methods perform almost equally well on multiexponential signals with MUSIC displaying better defined peaks.

Keywords: Eigenvector, minimum norm, multiexponential, subspace.

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8399 A Propagator Method like Algorithm for Estimation of Multiple Real-Valued Sinusoidal Signal Frequencies

Authors: Sambit Prasad Kar, P.Palanisamy

Abstract:

In this paper a novel method for multiple one dimensional real valued sinusoidal signal frequency estimation in the presence of additive Gaussian noise is postulated. A computationally simple frequency estimation method with efficient statistical performance is attractive in many array signal processing applications. The prime focus of this paper is to combine the subspace-based technique and a simple peak search approach. This paper presents a variant of the Propagator Method (PM), where a collaborative approach of SUMWE and Propagator method is applied in order to estimate the multiple real valued sine wave frequencies. A new data model is proposed, which gives the dimension of the signal subspace is equal to the number of frequencies present in the observation. But, the signal subspace dimension is twice the number of frequencies in the conventional MUSIC method for estimating frequencies of real-valued sinusoidal signal. The statistical analysis of the proposed method is studied, and the explicit expression of asymptotic (large-sample) mean-squared-error (MSE) or variance of the estimation error is derived. The performance of the method is demonstrated, and the theoretical analysis is substantiated through numerical examples. The proposed method can achieve sustainable high estimation accuracy and frequency resolution at a lower SNR, which is verified by simulation by comparing with conventional MUSIC, ESPRIT and Propagator Method.

Keywords: Frequency estimation, peak search, subspace-based method without eigen decomposition, quadratic convex function.

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8398 Blind Channel Estimation Based on URV Decomposition Technique for Uplink of MC-CDMA

Authors: Pradya Pornnimitkul, Suwich Kunaruttanapruk, Bamrung Tau Sieskul, Somchai Jitapunkul

Abstract:

In this paper, we investigate a blind channel estimation method for Multi-carrier CDMA systems that use a subspace decomposition technique. This technique exploits the orthogonality property between the noise subspace and the received user codes to obtain channel of each user. In the past we used Singular Value Decomposition (SVD) technique but SVD have most computational complexity so in this paper use a new algorithm called URV Decomposition, which serve as an intermediary between the QR decomposition and SVD, replaced in SVD technique to track the noise space of the received data. Because of the URV decomposition has almost the same estimation performance as the SVD, but has less computational complexity.

Keywords: Channel estimation, MC-CDMA, SVD, URV.

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8397 Note to the Global GMRES for Solving the Matrix Equation AXB = F

Authors: Fatemeh Panjeh Ali Beik

Abstract:

In the present work, we propose a new projection method for solving the matrix equation AXB = F. For implementing our new method, generalized forms of block Krylov subspace and global Arnoldi process are presented. The new method can be considered as an extended form of the well-known global generalized minimum residual (Gl-GMRES) method for solving multiple linear systems and it will be called as the extended Gl-GMRES (EGl- GMRES). Some new theoretical results have been established for proposed method by employing Schur complement. Finally, some numerical results are given to illustrate the efficiency of our new method.

Keywords: Matrix equation, Iterative method, linear systems, block Krylov subspace method, global generalized minimum residual (Gl-GMRES).

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8396 Grid-based Supervised Clustering - GBSC

Authors: Pornpimol Bungkomkhun, Surapong Auwatanamongkol

Abstract:

This paper presents a supervised clustering algorithm, namely Grid-Based Supervised Clustering (GBSC), which is able to identify clusters of any shapes and sizes without presuming any canonical form for data distribution. The GBSC needs no prespecified number of clusters, is insensitive to the order of the input data objects, and is capable of handling outliers. Built on the combination of grid-based clustering and density-based clustering, under the assistance of the downward closure property of density used in bottom-up subspace clustering, the GBSC can notably reduce its search space to avoid the memory confinement situation during its execution. On two-dimension synthetic datasets, the GBSC can identify clusters with different shapes and sizes correctly. The GBSC also outperforms other five supervised clustering algorithms when the experiments are performed on some UCI datasets.

Keywords: supervised clustering, grid-based clustering, subspace clustering

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8395 Comparison of Multi-User Detectors of DS-CDMA System

Authors: Kavita Khairnar, Shikha Nema

Abstract:

DS-CDMA system is well known wireless technology. This system suffers from MAI (Multiple Access Interference) caused by Direct Sequence users. Multi-User Detection schemes were introduced to detect the users- data in presence of MAI. This paper focuses on linear multi-user detection schemes used for data demodulation. Simulation results depict the performance of three detectors viz-conventional detector, Decorrelating detector and Subspace MMSE (Minimum Mean Square Error) detector. It is seen that the performance of these detectors depends on the number of paths and the length of Gold code used.

Keywords: Cross Correlation Matrix, MAI, Multi-UserDetection, Multipath Effect.

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8394 A Novel Microarray Biclustering Algorithm

Authors: Chieh-Yuan Tsai, Chuang-Cheng Chiu

Abstract:

Biclustering aims at identifying several biclusters that reveal potential local patterns from a microarray matrix. A bicluster is a sub-matrix of the microarray consisting of only a subset of genes co-regulates in a subset of conditions. In this study, we extend the motif of subspace clustering to present a K-biclusters clustering (KBC) algorithm for the microarray biclustering issue. Besides minimizing the dissimilarities between genes and bicluster centers within all biclusters, the objective function of the KBC algorithm additionally takes into account how to minimize the residues within all biclusters based on the mean square residue model. In addition, the objective function also maximizes the entropy of conditions to stimulate more conditions to contribute the identification of biclusters. The KBC algorithm adopts the K-means type clustering process to efficiently make the partition of K biclusters be optimized. A set of experiments on a practical microarray dataset are demonstrated to show the performance of the proposed KBC algorithm.

Keywords: Microarray, Biclustering, Subspace clustering, Meansquare residue model.

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8393 Multiple Moving Talker Tracking by Integration of Two Successive Algorithms

Authors: Kenji Suyama, Masahiro Oshida, Noboru Owada

Abstract:

In this paper, an estimation accuracy of multiple moving talker tracking using a microphone array is improved. The tracking can be achieved by the adaptive method in which two algorithms are integrated, namely, the PAST (Projection Approximation Subspace Tracking) algorithm and the IPLS (Interior Point Least Square) algorithm. When either talker begins to speak again after a silent period, an appropriate feasible region for an evaluation function of the IPLS algorithm might not be set. Then, the tracking fails due to the incorrect updating. Therefore, if an increment of the number of active talkers is detected, the feasible region must be reset. Then, a low cost realization is required for the high speed tracking and a high accuracy realization is desired for the precise tracking. In this paper, the directions roughly estimated using the delayed-sum-array method are used for the resetting. Several results of experiments performed in an actual room environment show the effectiveness of the proposed method.

Keywords: moving talkers tracking, microphone array, signal subspace

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8392 Optimal Economic Restructuring Aimed at an Increase in GDP Constrained by a Decrease in Energy Consumption and CO2 Emissions

Authors: Alexander Y. Vaninsky

Abstract:

The objective of this paper is finding the way of economic restructuring - that is, change in the shares of sectoral gross outputs - resulting in the maximum possible increase in the gross domestic product (GDP) combined with decreases in energy consumption and CO2 emissions. It uses an input-output model for the GDP and factorial models for the energy consumption and CO2 emissions to determine the projection of the gradient of GDP, and the antigradients of the energy consumption and CO2 emissions, respectively, on a subspace formed by the structure-related variables. Since the gradient (antigradient) provides a direction of the steepest increase (decrease) of the objective function, and their projections retain this property for the functions' limitation to the subspace, each of the three directional vectors solves a particular problem of optimal structural change. In the next step, a type of factor analysis is applied to find a convex combination of the projected gradient and antigradients having maximal possible positive correlation with each of the three. This convex combination provides the desired direction of the structural change. The national economy of the United States is used as an example of applications.

Keywords: Economic restructuring, Input-Output analysis, Divisia index, Factorial decomposition, E3 models.

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8391 An Improved Adaptive Dot-Shape Beamforming Algorithm Research on Frequency Diverse Array

Authors: Yanping Liao, Zenan Wu, Ruigang Zhao

Abstract:

Frequency diverse array (FDA) beamforming is a technology developed in recent years, and its antenna pattern has a unique angle-distance-dependent characteristic. However, the beam is always required to have strong concentration, high resolution and low sidelobe level to form the point-to-point interference in the concentrated set. In order to eliminate the angle-distance coupling of the traditional FDA and to make the beam energy more concentrated, this paper adopts a multi-carrier FDA structure based on proposed power exponential frequency offset to improve the array structure and frequency offset of the traditional FDA. The simulation results show that the beam pattern of the array can form a dot-shape beam with more concentrated energy, and its resolution and sidelobe level performance are improved. However, the covariance matrix of the signal in the traditional adaptive beamforming algorithm is estimated by the finite-time snapshot data. When the number of snapshots is limited, the algorithm has an underestimation problem, which leads to the estimation error of the covariance matrix to cause beam distortion, so that the output pattern cannot form a dot-shape beam. And it also has main lobe deviation and high sidelobe level problems in the case of limited snapshot. Aiming at these problems, an adaptive beamforming technique based on exponential correction for multi-carrier FDA is proposed to improve beamforming robustness. The steps are as follows: first, the beamforming of the multi-carrier FDA is formed under linear constrained minimum variance (LCMV) criteria. Then the eigenvalue decomposition of the covariance matrix is ​​performed to obtain the diagonal matrix composed of the interference subspace, the noise subspace and the corresponding eigenvalues. Finally, the correction index is introduced to exponentially correct the small eigenvalues ​​of the noise subspace, improve the divergence of small eigenvalues ​​in the noise subspace, and improve the performance of beamforming. The theoretical analysis and simulation results show that the proposed algorithm can make the multi-carrier FDA form a dot-shape beam at limited snapshots, reduce the sidelobe level, improve the robustness of beamforming, and have better performance.

Keywords: Multi-carrier frequency diverse array, adaptive beamforming, correction index, limited snapshot, robust.

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8390 Random Subspace Neural Classifier for Meteor Recognition in the Night Sky

Authors: Carlos Vera, Tetyana Baydyk, Ernst Kussul, Graciela Velasco, Miguel Aparicio

Abstract:

This article describes the Random Subspace Neural Classifier (RSC) for the recognition of meteors in the night sky. We used images of meteors entering the atmosphere at night between 8:00 p.m.-5: 00 a.m. The objective of this project is to classify meteor and star images (with stars as the image background). The monitoring of the sky and the classification of meteors are made for future applications by scientists. The image database was collected from different websites. We worked with RGB-type images with dimensions of 220x220 pixels stored in the BitMap Protocol (BMP) format. Subsequent window scanning and processing were carried out for each image. The scan window where the characteristics were extracted had the size of 20x20 pixels with a scanning step size of 10 pixels. Brightness, contrast and contour orientation histograms were used as inputs for the RSC. The RSC worked with two classes and classified into: 1) with meteors and 2) without meteors. Different tests were carried out by varying the number of training cycles and the number of images for training and recognition. The percentage error for the neural classifier was calculated. The results show a good RSC classifier response with 89% correct recognition. The results of these experiments are presented and discussed.

Keywords: Contour orientation histogram, meteors, night sky, RSC neural classifier, stars.

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8389 Ensemble Learning with Decision Tree for Remote Sensing Classification

Authors: Mahesh Pal

Abstract:

In recent years, a number of works proposing the combination of multiple classifiers to produce a single classification have been reported in remote sensing literature. The resulting classifier, referred to as an ensemble classifier, is generally found to be more accurate than any of the individual classifiers making up the ensemble. As accuracy is the primary concern, much of the research in the field of land cover classification is focused on improving classification accuracy. This study compares the performance of four ensemble approaches (boosting, bagging, DECORATE and random subspace) with a univariate decision tree as base classifier. Two training datasets, one without ant noise and other with 20 percent noise was used to judge the performance of different ensemble approaches. Results with noise free data set suggest an improvement of about 4% in classification accuracy with all ensemble approaches in comparison to the results provided by univariate decision tree classifier. Highest classification accuracy of 87.43% was achieved by boosted decision tree. A comparison of results with noisy data set suggests that bagging, DECORATE and random subspace approaches works well with this data whereas the performance of boosted decision tree degrades and a classification accuracy of 79.7% is achieved which is even lower than that is achieved (i.e. 80.02%) by using unboosted decision tree classifier.

Keywords: Ensemble learning, decision tree, remote sensingclassification.

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8388 A Comparison of Recent Methods for Solving a Model 1D Convection Diffusion Equation

Authors: Ashvin Gopaul, Jayrani Cheeneebash, Kamleshsing Baurhoo

Abstract:

In this paper we study some numerical methods to solve a model one-dimensional convection–diffusion equation. The semi-discretisation of the space variable results into a system of ordinary differential equations and the solution of the latter involves the evaluation of a matrix exponent. Since the calculation of this term is computationally expensive, we study some methods based on Krylov subspace and on Restrictive Taylor series approximation respectively. We also consider the Chebyshev Pseudospectral collocation method to do the spatial discretisation and we present the numerical solution obtained by these methods.

Keywords: Chebyshev Pseudospectral collocation method, convection-diffusion equation, restrictive Taylor approximation.

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8387 Constructing of Classifier for Face Recognition on the Basis of the Conjugation Indexes

Authors: Vladimir A. Fursov, Nikita E. Kozin

Abstract:

In this work the opportunity of construction of the qualifiers for face-recognition systems based on conjugation criteria is investigated. The linkage between the bipartite conjugation, the conjugation with a subspace and the conjugation with the null-space is shown. The unified solving rule is investigated. It makes the decision on the rating of face to a class considering the linkage between conjugation values. The described recognition method can be successfully applied to the distributed systems of video control and video observation.

Keywords: Conjugation, Eigenfaces, Recognition.

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8386 Approximate Solutions to Large Stein Matrix Equations

Authors: Khalide Jbilou

Abstract:

In the present paper, we propose numerical methods for solving the Stein equation AXC - X - D = 0 where the matrix A is large and sparse. Such problems appear in discrete-time control problems, filtering and image restoration. We consider the case where the matrix D is of full rank and the case where D is factored as a product of two matrices. The proposed methods are Krylov subspace methods based on the block Arnoldi algorithm. We give theoretical results and we report some numerical experiments.

Keywords: IEEEtran, journal, LATEX, paper, template.

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8385 An Iterative Algorithm to Compute the Generalized Inverse A(2) T,S Under the Restricted Inner Product

Authors: Xingping Sheng

Abstract:

Let T and S be a subspace of Cn and Cm, respectively. Then for A ∈ Cm×n satisfied AT ⊕ S = Cm, the generalized inverse A(2) T,S is given by A(2) T,S = (PS⊥APT )†. In this paper, a finite formulae is presented to compute generalized inverse A(2) T,S under the concept of restricted inner product, which defined as < A,B >T,S=< PS⊥APT,B > for the A,B ∈ Cm×n. By this iterative method, when taken the initial matrix X0 = PTA∗PS⊥, the generalized inverse A(2) T,S can be obtained within at most mn iteration steps in absence of roundoff errors. Finally given numerical example is shown that the iterative formulae is quite efficient.

Keywords: Generalized inverse A(2) T, S, Restricted inner product, Iterative method, Orthogonal projection.

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8384 Extending Global Full Orthogonalization method for Solving the Matrix Equation AXB=F

Authors: Fatemeh Panjeh Ali Beik

Abstract:

In the present work, we propose a new method for solving the matrix equation AXB=F . The new method can be considered as a generalized form of the well-known global full orthogonalization method (Gl-FOM) for solving multiple linear systems. Hence, the method will be called extended Gl-FOM (EGl- FOM). For implementing EGl-FOM, generalized forms of block Krylov subspace and global Arnoldi process are presented. Finally, some numerical experiments are given to illustrate the efficiency of our new method.

Keywords: Matrix equations, Iterative methods, Block Krylovsubspace methods.

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8383 The BGMRES Method for Generalized Sylvester Matrix Equation AXB − X = C and Preconditioning

Authors: Azita Tajaddini, Ramleh Shamsi

Abstract:

In this paper, we present the block generalized minimal residual (BGMRES) method in order to solve the generalized Sylvester matrix equation. However, this method may not be converged in some problems. We construct a polynomial preconditioner based on BGMRES which shows why polynomial preconditioner is superior to some block solvers. Finally, numerical experiments report the effectiveness of this method.

Keywords: Linear matrix equation, Block GMRES, matrix Krylov subspace, polynomial preconditioner.

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8382 High Resolution Methods Based On Rank Revealing Triangular Factorizations

Authors: M. Bouri, S. Bourennane

Abstract:

In this paper, we propose a novel method for subspace estimation used high resolution method without eigendecomposition where the sample Cross-Spectral Matrix (CSM) is replaced by upper triangular matrix obtained from LU factorization. This novel method decreases the computational complexity. The method relies on a recently published result on Rank-Revealing LU (RRLU) factorization. Simulation results demonstrates that the new algorithm outperform the Householder rank-revealing QR (RRQR) factorization method and the MUSIC in the low Signal to Noise Ratio (SNR) scenarios.

Keywords: Factorization, Localization, Matrix, Signalsubspace.

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