Search results for: eigenvector

Authors: Dia I. Abu-Al-Nadi, M. J. Mismar, T. H. Ismail

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A technique for estimating the direction-of-arrival (DOA) of unknown number of source signals is presented using the eigen-approach. The eigenvector corresponding to the minimum eigenvalue of the autocorrelation matrix yields the minimum output power of the array. Also, the array polynomial with this eigenvector possesses roots on the unit circle. Therefore, the pseudo-spectrum is found by perturbing the phases of the roots one by one and calculating the corresponding array output power. The results indicate that the DOAs and the number of source signals are estimated accurately in the presence of a wide range of input noise levels.

Keywords: array signal processing, direction-of-arrival, antenna arrays, Eigenvalues, Eigenvectors, Lagrange multiplier

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Authors: Rashid Ahmed , John N. Avaritsiotis

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Many signal subspace-based approaches have already been proposed for determining the fixed Direction of Arrival (DOA) of plane waves impinging on an array of sensors. Two procedures for DOA estimation based neural networks are presented. First, Principal Component Analysis (PCA) is employed to extract the maximum eigenvalue and eigenvector from signal subspace to estimate DOA. Second, minor component analysis (MCA) is a statistical method of extracting the eigenvector associated with the smallest eigenvalue of the covariance matrix. In this paper, we will modify a Minor Component Analysis (MCA(R)) learning algorithm to enhance the convergence, where a convergence is essential for MCA algorithm towards practical applications. The learning rate parameter is also presented, which ensures fast convergence of the algorithm, because it has direct effect on the convergence of the weight vector and the error level is affected by this value. MCA is performed to determine the estimated DOA. Preliminary results will be furnished to illustrate the convergences results achieved.

Keywords: Direction of Arrival, neural networks, Principle Component Analysis, Minor Component Analysis

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Authors: Chimezie P. Nnanwa, Thomas C. Urama, Patrick O. Ezepue

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In this paper we use Random Matrix Theory to analyze the eigen-structure of the empirical correlations of 82 stocks which are consistently traded in the Nigerian Stock Exchange (NSE) over a 4-year study period 3 August 2009 to 26 August 2013. We apply the Marchenko-Pastur distribution of eigenvalues of a purely random matrix to investigate the presence of investment-pertinent information contained in the empirical correlation matrix of the selected stocks. We use hypothesised standard normal distribution of eigenvector components from RMT to assess deviations of the empirical eigenvectors to this distribution for different eigenvalues. We also use the Inverse Participation Ratio to measure the deviation of eigenvectors of the empirical correlation matrix from RMT results. These preliminary results on the dynamics of asset price correlations in the NSE are important for improving risk-return trade-offs associated with Markowitz’s portfolio optimization in the stock exchange, which is pursued in future work.

Keywords: correlation matrix, eigenvalue and eigenvector, inverse participation ratio, portfolio optimization, random matrix theory

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Authors: Abubakar Sadiq Mensah

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The Knowledge of the population growth of a nation is paramount to national planning. The population of a place is studied and a model developed over a period of time, Matrices is used to form model for population growth. The eigenvalue ƛ of the matrix A and its corresponding eigenvector X is such that AX = ƛX is calculated. The stable age distribution of the population is obtained using the eigenvalue and the characteristic polynomial. Hence, estimation could be made using eigenvalues and eigenvectors.

Keywords: eigenvalues, eigenvectors, population, growth/stability

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Authors: E. Tchandao Mangamana, V. Cariou, E. Vigneau, R. Glele Kakai, E. M. Qannari

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A new definition of a latent variable associated with a dataset makes it possible to propose variants of the PLS2 regression and the multi-block PLS (MB-PLS). We shall refer to these variants as Rd-PLS regression and Rd-MB-PLS respectively because they are inspired by both Redundancy analysis and PLS regression. Usually, a latent variable t associated with a dataset Z is defined as a linear combination of the variables of Z with the constraint that the length of the loading weights vector equals 1. Formally, t=Zw with ‖w‖=1. Denoting by Z' the transpose of Z, we define herein, a latent variable by t=ZZ’q with the constraint that the auxiliary variable q has a norm equal to 1. This new definition of a latent variable entails that, as previously, t is a linear combination of the variables in Z and, in addition, the loading vector w=Z’q is constrained to be a linear combination of the rows of Z. More importantly, t could be interpreted as a kind of projection of the auxiliary variable q onto the space generated by the variables in Z, since it is collinear to the first PLS1 component of q onto Z. Consider the situation in which we aim to predict a dataset Y from another dataset X. These two datasets relate to the same individuals and are assumed to be centered. Let us consider a latent variable u=YY’q to which we associate the variable t= XX’YY’q. Rd-PLS consists in seeking q (and therefore u and t) so that the covariance between t and u is maximum. The solution to this problem is straightforward and consists in setting q to the eigenvector of YY’XX’YY’ associated with the largest eigenvalue. For the determination of higher order components, we deflate X and Y with respect to the latent variable t. Extending Rd-PLS to the context of multi-block data is relatively easy. Starting from a latent variable u=YY’q, we consider its ‘projection’ on the space generated by the variables of each block Xk (k=1, ..., K) namely, tk= XkXk'YY’q. Thereafter, Rd-MB-PLS seeks q in order to maximize the average of the covariances of u with tk (k=1, ..., K). The solution to this problem is given by q, eigenvector of YY’XX’YY’, where X is the dataset obtained by horizontally merging datasets Xk (k=1, ..., K). For the determination of latent variables of order higher than 1, we use a deflation of Y and Xk with respect to the variable t= XX’YY’q. In the same vein, extending Rd-MB-PLS to the path modeling setting is straightforward. Methods are illustrated on the basis of case studies and performance of Rd-PLS and Rd-MB-PLS in terms of prediction is compared to that of PLS2 and MB-PLS.

Keywords: multiblock data analysis, partial least squares regression, path modeling, redundancy analysis

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Authors: Izuru Nomura, Tatsuya Takino, Yuji Kageyama, Shin Nagata, Hiroyuki Kamata

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We propose a method of crater detection from the image of the lunar surface captured by the small space probe. We use the principal component analysis (PCA) to detect craters. Nevertheless, considering　severe environment of the space, it is impossible to use generic computer in practice. Accordingly, we have to implement the method in FPGA. This paper compares FPGA and generic computer by the processing time of a method of crater detection using principal component analysis.

Keywords: crater, PCA, eigenvector, strength value, FPGA, processing time

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Authors: Ahmet Kaya

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Incoming cash flows and outgoing claims play an important role to determine how is companies’ profit or loss. In this matter, ruin probability provides to describe vulnerability of the companies against ruin. Quantum mechanism is one of the significant approaches to model ruin probability as stochastically. Using the Hamiltonian method, we have performed formalisation of quantum mechanics < x|e-ᵗᴴ|x' > and obtained the transition probability of 2x2 and 3x3 matrix as traditional and eigenvector basis where A is a ruin operator and H|x' > is a Schroedinger equation. This operator A and Schroedinger equation are defined by a Hamiltonian matrix H. As a result, probability of not to be in ruin can be simulated and calculated as stochastically.

Keywords: ruin probability, quantum mechanics, Hamiltonian technique, operator approach

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Authors: Ahmet Kaya

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Quantum mechanism is one of the most important approaches to calculating non-ruin probability. We apply standard Dirac notation to model given Hamiltonians. By using the traditional method and eigenvector basis, non-ruin probability is found for several examples. Also, non-ruin probability is calculated for two different Hamiltonian by using the tensor product. Finally, the path integral method is applied to the examples and comparison is made for stochastic simulations and path integral calculation.

Keywords: quantum physics, Hamiltonian system, path integral, tensor product, ruin probability

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Authors: Olesya Bolkhovskaya, Alexey Davydov, Alexander Maltsev

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In this paper two approaches to joint signal detection, time of arrival (ToA) and angle of arrival (AoA) estimation in multi-element antenna array are investigated. Two scenarios were considered: first one, when the waveform of the useful signal is known a priori and, second one, when the waveform of the desired signal is unknown. For first scenario, the antenna array signal processing based on multi-element matched filtering (MF) with the following non-coherent detection scheme and maximum likelihood (ML) parameter estimation blocks is exploited. For second scenario, the signal processing based on the antenna array elements covariance matrix estimation with the following eigenvector analysis and ML parameter estimation blocks is applied. The performance characteristics of both signal processing schemes are thoroughly investigated and compared for different useful signals and noise parameters.

Keywords: antenna array, signal detection, ToA, AoA estimation

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Authors: Ju-Hong Lee, Ching-Wei Liao, Kun-Che Lee

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This paper deals with the problem of using antenna sensors for adaptive beamforming in the presence of random steering mismatch. We present an efficient adaptive array beamformer with robustness to deal with the considered problem. The robustness of the proposed beamformer comes from the efficient designation of the steering vector. Using the received array data vector, we construct an appropriate correlation matrix associated with the received array data vector and a correlation matrix associated with signal sources. Then, the eigenvector associated with the largest eigenvalue of the constructed signal correlation matrix is designated as an appropriate estimate of the steering vector. Finally, the adaptive weight vector required for adaptive beamforming is obtained by using the estimated steering vector and the constructed correlation matrix of the array data vector. Simulation results confirm the effectiveness of the proposed method.

Keywords: adaptive beamforming, antenna array, linearly constrained minimum variance, robustness, steering vector

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Authors: Amrah Maryam

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The emergence of online social networks (OSNs) has transformed the way we pursue and share information. On the one hand, OSNs provide great ease for the spreading of positive information while, on the other hand, they may also become a channel for the spreading of malicious rumors and misinformation throughout the social network. Thus, to assure the trustworthiness of OSNs to its users, it is of vital importance to detect the misinformation propagation in the network by placing network monitors. In this paper, we aim to place monitors near the suspected nodes with the intent to limit the diffusion of misinformation in the social network, and then we also detect the most significant nodes in the network for propagating true information in order to minimize the effect of already diffused misinformation. Thus, we initiate two heuristic monitor placement using articulation points and truth propagation using eigenvector centrality. Furthermore, to provide real-time workings of the system, we integrate both the monitor placement and truth propagation entities as well. To signify the effectiveness of the approaches, we have carried out the experiment and evaluation of Stanford datasets of online social networks.

Keywords: online social networks, monitor placement, independent cascade model, spread of misinformation

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Authors: Alexander Hempfing

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The desire to understand business cycle fluctuations, trade interdependencies and co-movement has a long tradition in economic thinking. From input-output economics to business cycle theory, researchers aimed to find appropriate answers from an empirical as well as a theoretical perspective. This paper empirically analyses how the production structure of the global economy and several states developed over time, what their distributional properties are and if there are network specific metrics that allow identifying structurally important nodes, on a global, national and sectoral scale. For this, the World Input-Output Database was used, and different statistical methods were applied. Empirical evidence is provided that the importance of the Eastern hemisphere in the global production network has increased significantly between 2000 and 2014. Moreover, it was possible to show that the sectoral eigenvector centrality indices on a global level are power-law distributed, providing evidence that specific national sectors exist which are more critical to the world economy than others while serving as a hub within the global production network. However, further findings suggest, that global production cannot be characterized as a scale-free network.

Keywords: economic integration, industrial organization, input-output economics, network economics, production networks

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Authors: G. C. Tikkiwal, Mukesh Upadhyay

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During the surveillance operations at war or peace time, the Radar operator gets a scatter of targets over the screen. This may be a tracked vehicle like tank vis-à-vis T72, BMP etc, or it may be a wheeled vehicle like ALS, TATRA, 2.5Tonne, Shaktiman or moving the army, moving convoys etc. The radar operator selects one of the promising targets into single target tracking (STT) mode. Once the target is locked, the operator gets a typical audible signal into his headphones. With reference to the gained experience and training over the time, the operator then identifies the random target. But this process is cumbersome and is solely dependent on the skills of the operator, thus may lead to misclassification of the object. In this paper, we present a technique using mathematical and statistical methods like fast fourier transformation (FFT) and principal component analysis (PCA) to identify the random objects. The process of classification is based on transforming the audible signature of target into music octave-notes. The whole methodology is then automated by developing suitable software. This automation increases the efficiency of identification of the random target by reducing the chances of misclassification. This whole study is based on live data.

Keywords: radar target, FFT, principal component analysis, eigenvector, octave-notes, DSP

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Authors: G. C. Tikkiwal, Mukesh Upadhyay

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During the surveillance operations at war or peace time, the Radar operator gets a scatter of targets over the screen. This may be a tracked vehicle like tank vis-à-vis T72, BMP etc, or it may be a wheeled vehicle like ALS, TATRA, 2.5Tonne, Shaktiman or moving army, moving convoys etc. The Radar operator selects one of the promising targets into Single Target Tracking (STT) mode. Once the target is locked, the operator gets a typical audible signal into his headphones. With reference to the gained experience and training over the time, the operator then identifies the random target. But this process is cumbersome and is solely dependent on the skills of the operator, thus may lead to misclassification of the object. In this paper we present a technique using mathematical and statistical methods like Fast Fourier Transformation (FFT) and Principal Component Analysis (PCA) to identify the random objects. The process of classification is based on transforming the audible signature of target into music octave-notes. The whole methodology is then automated by developing suitable software. This automation increases the efficiency of identification of the random target by reducing the chances of misclassification. This whole study is based on live data.

Keywords: radar target, fft, principal component analysis, eigenvector, octave-notes, dsp

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Authors: Ali N. Suri, Ahmad A. Al-Makhlufi

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In this paper the problem of buckling of plates on foundation of finite length and with different side support is studied. The Finite Strip Method is used as tool for the analysis. This method uses finite strip elastic, foundation, and geometric matrices to build the assembly matrices for the whole structure, then after introducing boundary conditions at supports, the resulting reduced matrices is transformed into a standard Eigenvalue-Eigenvector problem. The solution of this problem will enable the determination of the buckling load, the associated buckling modes and the buckling wave length. To carry out the buckling analysis starting from the elastic, foundation, and geometric stiffness matrices for each strip a computer program FORTRAN list is developed. Since stiffness matrices are function of wave length of buckling, the computer program used an iteration procedure to find the critical buckling stress for each value of foundation modulus and for each boundary condition. The results showed the use of elastic medium to support plates subject to axial load increase a great deal the buckling load, the results found are very close with those obtained by other analytical methods and experimental work. The results also showed that foundation compensates the effect of the weakness of some types of constraint of side support and maximum benefit found for plate with one side simply supported the other free.

Keywords: buckling, finite strip, different sides support, plates on foundation

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Authors: Akinola Ikudayisi, Josiah Adeyemo

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The correct estimation of reference evapotranspiration (ETₒ) is required for effective irrigation water resources planning and management. However, there are some variables that must be considered while estimating and modeling ETₒ. This study therefore determines the multivariate analysis of correlated variables involved in the estimation and modeling of ETₒ at Vaalharts irrigation scheme (VIS) in South Africa using Principal Component Analysis (PCA) technique. Weather and meteorological data between 1994 and 2014 were obtained both from South African Weather Service (SAWS) and Agricultural Research Council (ARC) in South Africa for this study. Average monthly data of minimum and maximum temperature (°C), rainfall (mm), relative humidity (%), and wind speed (m/s) were the inputs to the PCA-based model, while ETₒ is the output. PCA technique was adopted to extract the most important information from the dataset and also to analyze the relationship between the five variables and ETₒ. This is to determine the most significant variables affecting ETₒ estimation at VIS. From the model performances, two principal components with a variance of 82.7% were retained after the eigenvector extraction. The results of the two principal components were compared and the model output shows that minimum temperature, maximum temperature and windspeed are the most important variables in ETₒ estimation and modeling at VIS. In order words, ETₒ increases with temperature and windspeed. Other variables such as rainfall and relative humidity are less important and cannot be used to provide enough information about ETₒ estimation at VIS. The outcome of this study has helped to reduce input variable dimensionality from five to the three most significant variables in ETₒ modelling at VIS, South Africa.

Keywords: irrigation, principal component analysis, reference evapotranspiration, Vaalharts

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Authors: Qiankun Zhong

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In a global cultural context, film festival awards become authorities to define the aesthetic value of films. To study which genres and producing countries are valued by different film festivals and how those evaluations interact with each other, this research explored the interactions between the film festivals through their selection of movies and the factors that lead to the tendency of film festivals to nominate the same movies. To do this, the author employed a two-mode network on the movies that won the highest awards at five international film festivals with the highest attendance in the past ten years (the Venice Film Festival, the Cannes Film Festival, the Toronto International Film Festival, Sundance Film Festival, and the Berlin International Film Festival) and the film festivals that nominated those movies. The title, genre, producing country and language of 50 movies, and the range (regional, national or international) and organizing country or area of 129 film festivals were collected. These created networks connected by nominating the same films and awarding the same movies. The author then assessed the density and centrality of these networks to answer the question: What are the film festivals that tend to have more shared values with other festivals? Based on the Eigenvector centrality of the two-mode network, Palm Springs, Robert Festival, Toronto, Chicago, and San Sebastian are the festivals that tend to nominate commonly appreciated movies. In contrast, Black Movie Film Festival has the unique value of generally not sharing nominations with other film festivals. A homophily test was applied to access the clustering effects of film and film festivals. The result showed that movie genres (E-I index=0.55) and geographic location (E-I index=0.35) are possible indicators of film festival clustering. A blockmodel was also created to examine the structural roles of the film festivals and their meaning in real-world context. By analyzing the same blocks with film festival attributes, it was identified that film festivals either organized in the same area, with the same history, or with the same attitude on independent films would occupy the same structural roles in the network. Through the interpretation of the blocks, language was identified as an indicator that contributes to the role position of a film festival. Comparing the result of blockmodeling in the different periods, it is seen that international film festivals contrast with the Hollywood industry’s dominant value. The structural role dynamics provide evidence for a multi-value film festival network.

Keywords: film festivals, film studies, media industry studies, network analysis

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Authors: Xianwei Zheng, Yuan Yan Tang

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Classical window Fourier transform has been widely used in signal processing, image processing, machine learning and pattern recognition. The related Gabor transform is powerful enough to capture the texture information of any given dataset. Recently, in the emerging field of graph signal processing, researchers devoting themselves to develop a graph signal processing theory to handle the so-called graph signals. Among the new developing theory, windowed graph Fourier transform has been constructed to establish a time-frequency analysis framework of graph signals. The windowed graph Fourier transform is defined by using the translation and modulation operators of graph signals, following the similar calculations in classical windowed Fourier transform. Specifically, the translation and modulation operators of graph signals are defined by using the Laplacian eigenvectors as follows. For a given graph signal, its translation is defined by a similar manner as its definition in classical signal processing. Specifically, the translation operator can be defined by using the Fourier atoms; the graph signal translation is defined similarly by using the Laplacian eigenvectors. The modulation of the graph can also be established by using the Laplacian eigenvectors. The windowed graph Fourier transform based on these two operators has been applied to obtain time-frequency representations of graph signals. Fundamentally, the modulation operator is defined similarly to the classical modulation by multiplying a graph signal with the entries in each Fourier atom. However, a single Laplacian eigenvector entry cannot play a similar role as the Fourier atom. This definition ignored the relationship between the translation and modulation operators. In this paper, a new definition of the modulation operator is proposed and thus another time-frequency framework for graph signal is constructed. Specifically, the relationship between the translation and modulation operations can be established by the Fourier transform. Specifically, for any signal, the Fourier transform of its translation is the modulation of its Fourier transform. Thus, the modulation of any signal can be defined as the inverse Fourier transform of the translation of its Fourier transform. Therefore, similarly, the graph modulation of any graph signal can be defined as the inverse graph Fourier transform of the translation of its graph Fourier. The novel definition of the graph modulation operator established a relationship of the translation and modulation operations. The new modulation operation and the original translation operation are applied to construct a new framework of graph signal time-frequency analysis. Furthermore, a windowed graph Fourier frame theory is developed. Necessary and sufficient conditions for constructing windowed graph Fourier frames, tight frames and dual frames are presented in this paper. The novel graph signal time-frequency analysis framework is applied to signals defined on well-known graphs, e.g. Minnesota road graph and random graphs. Experimental results show that the novel framework captures new features of graph signals.

Keywords: graph signals, windowed graph Fourier transform, windowed graph Fourier frames, vertex frequency analysis

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Authors: Shimeles Terefe Mengistue, Ascensión Del Olmo, Paola Marziani, Mirjana Pović, María Angeles Martínez-Carballo, Jaime Perea, Isabel M. Árquez

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Quasars have historically been classified into two distinct classes, radio-loud (RL) and radio-quiet (RQ), taking into account the presence and absence of relativistic radio jets, respectively. The absence of spectra with a high S/N ratio led to the impression that all quasars (QSOs) are spectroscopically similar. Although different attempts were made to unify these two classes, there is a long-standing open debate involving the possibility of a real physical dichotomy between RL and RQ quasars. In this work, we present new high S/N spectra of 11 extremely powerful jetted quasars with radio-to-optical flux density ratio > 1000 that concomitantly cover the low-ionization emission of Mgii𝜆2800 and Hbeta𝛽 as well as the Feii blends in the redshift range 0.35 < z < 1, observed at Calar Alto Observatory (Spain). This work aims to quantify broad emission line differences between RL and RQ quasars by using the four-dimensional eigenvector 1 (4DE1) parameter space and its main sequence (MS) and to check the effect of powerful radio ejection on the low ionization broad emission lines. Emission lines are analysed by making two complementary approaches, a multicomponent non-linear fitting to account for the individual components of the broad emission lines and by analysing the full profile of the lines through parameters such as total widths, centroid velocities at different fractional intensities, asymmetry, and kurtosis indices. It is found that broad emission lines show large reward asymmetry both in Hbeta𝛽 and Mgii2800A. The location of our RL sources in a UV plane looks similar to the optical one, with weak Feii UV emission and broad Mgii2800A. We supplement the 11 sources with large samples from previous work to gain some general inferences. The result shows, compared to RQ, our extreme RL quasars show larger median Hbeta full width at half maximum (FWHM), weaker Feii emission, larger 𝑀BH, lower 𝐿bol/𝐿Edd, and a restricted space occupation in the optical and UV MS planes. The differences are more elusive when the comparison is carried out by restricting the RQ population to the region of the MS occupied by RL quasars, albeit an unbiased comparison matching 𝑀BH and 𝐿bol/𝐿Edd suggests that the most powerful RL quasars show the highest redward asymmetries in Hbeta.

Keywords: galaxies, active, line, profiles, quasars, emission lines, supermassive black holes

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