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covariance-matrix
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Classification of Different Mental Activities Based on Riemannian Geometry
,
M.Sc. Thesis
Sharif University of Technology
;
Babaiezadeh, Massoud
(Supervisor)
Abstract
Brain-Computer Interface (BCI) presents a way for brain’s direct connection with external world. BCI system is composed of three parts: 1) Signal acquisition, 2) Signal processing and 3) External device control. The main part of this system is signal processing which includes three subparts: 1) Feature extraction, 2) Dimension reduction and 3) Signal separation and classification. In this thesis, we focus on the signal processing section in BCI systems. One of the most successful works done in signal processing is the use of covariance matrices in feature extraction from brain signals. Since covariance matrices are positive semi-definite and symmetric, they belong to certain manifolds called...
Limiting spectral distribution of the sample covariance matrix of the windowed array data
, Article Eurasip Journal on Advances in Signal Processing ; Volume 2013, Issue 1 , 2013 ; 16876172 (ISSN) ; Gazor, S ; Bastani, M. H ; Sharif University of Technology
2013
Abstract
In this article, we investigate the limiting spectral distribution of the sample covariance matrix (SCM) of weighted/windowed complex data. We use recent advances in random matrix theory and describe the distribution of eigenvalues of the doubly correlated Wishart matrices. We obtain an approximation for the spectral distribution of the SCM obtained from windowed data. We also determine a condition on the coefficients of the window, under which the fragmentation of the support of noise eigenvalues can be avoided, in the noise-only data case. For the commonly used exponential window, we derive an explicit expression for the l.s.d of the noise-only data. In addition, we present a method to...
Spectral distribution of the exponentially windowed sample covariance matrix
, Article ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, 25 March 2012 through 30 March 2012, Kyoto ; 2012 , Pages 3529-3532 ; 15206149 (ISSN) ; 9781467300469 (ISBN) ; Bastani, M. H ; Gazor, S ; Sharif University of Technology
IEEE
2012
Abstract
In this paper, we investigate the effect of applying an exponential window on the limiting spectral distribution (l.s.d.) of the exponentially windowed sample covariance matrix (SCM) of complex array data. We use recent advances in random matrix theory which describe the distribution of eigenvalues of the doubly correlated Wishart matrices. We derive an explicit expression for the l.s.d. of the noise-only data. Simulations are performed to support our theoretical claims
Optomechanical entanglement in the presence of laser phase noise
, Article Physical Review A - Atomic, Molecular, and Optical Physics ; Volume 84, Issue 6 , 2011 ; 10502947 (ISSN) ; Bahrampour, A. R ; Simon, C ; Sharif University of Technology
2011
Abstract
We study the simplest optomechanical system in the presence of laser phase noise (LPN) using the covariance matrix formalism. We show that for any LPN model with a finite correlation time, the destructive effect of the phase noise is especially strong in the bistable regime. This explains why ground-state cooling is still possible in the presence of phase noise, as it happens far away from the bistable regime. We also show that the optomechanical entanglement is strongly affected by phase noise
Quantum optomechanics in the bistable regime
, Article Physical Review A - Atomic, Molecular, and Optical Physics ; Volume 84, Issue 3 , September , 2011 ; 10502947 (ISSN) ; Bahrampour, A. R ; Simon, C ; Sharif University of Technology
2011
Abstract
We study the simplest optomechanical system with a focus on the bistable regime. The covariance matrix formalism allows us to study both cooling and entanglement in a unified framework. We identify two key factors governing entanglement; namely, the bistability parameter (i.e., the distance from the end of a stable branch in the bistable regime) and the effective detuning, and we describe the optimum regime where entanglement is greatest. We also show that, in general, entanglement is a nonmonotonic function of optomechanical coupling. This is especially important in understanding the optomechanical entanglement of the second stable branch
Robust and rapid converging adaptive beamforming via a subspace method for the signal-plusinterferences covariance matrix estimation
, Article IET Signal Processing ; Vol. 8, Issue. 5 , July , 2014 , pp. 507-520 ; ISSN: 17519675 ; Bastani, M. H ; Sharif University of Technology
Abstract
The presence of the desired signal (DS) in the training snapshots makes the adaptive beamformer sensitive to any steering vector mismatch and dramatically reduces the convergence rate. Even the performance of the most of the existing robust adaptive beamformers is degraded when the signal-to-noise ratio (SNR) is increased. In this study, a high converging rate robust adaptive beamformer is proposed. This method is a promoted eigenspace-based beamformer. In this paper, a new signal-plus-interferences (SPI) covariance matrix estimator is proposed. The subspace of the ideal SPI covariance matrices is exploited and the estimated covariance matrix is projected into this subspace. This projection...
Source enumeration in large arrays based on moments of eigenvalues in sample starved conditions
, Article IEEE Workshop on Signal Processing Systems, SiPS: Design and Implementation, 17 October 2012 through 19 October 2012, Quebec ; October , 2012 , Pages 79-84 ; 15206130 (ISSN) ; 9780769548562 (ISBN) ; Bastani, M. H ; Gazor, S ; Sharif University of Technology
2012
Abstract
This paper presents a scheme to enumerate the incident waves impinging on a high dimensional uniform linear array using relatively few samples. The approach is based on Minimum Description Length (MDL) criteria and statistical properties of eigenvalues of the Sample Covariance Matrix (SCM). We assume that several models, with each model representing a certain number of sources, will compete and MDL criterion will select the best model with the minimum model complexity and maximum model decision. Statistics of noise eigenvalue of SCM can be approximated by the distributional properties of the eigenvalues given by Marcenko-Pastur distribution in the signal-free SCM. In this paper we use random...
Using empirical covariance matrix in enhancing prediction accuracy of linear models with missing information
, Article 2017 12th International Conference on Sampling Theory and Applications, SampTA 2017, 3 July 2017 through 7 July 2017 ; 2017 , Pages 446-450 ; 9781538615652 (ISBN) ; Shahsavari, S ; Esmaeili, A ; Marvasti, F ; Sharif University of Technology
Abstract
Inference and Estimation in Missing Information (MI) scenarios are important topics in Statistical Learning Theory and Machine Learning (ML). In ML literature, attempts have been made to enhance prediction through precise feature selection methods. In sparse linear models, LASSO is well-known in extracting the desired support of the signal and resisting against noisy systems. When sparse models are also suffering from MI, the sparse recovery and inference of the missing models are taken into account simultaneously. In this paper, we will introduce an approach which enjoys sparse regression and covariance matrix estimation to improve matrix completion accuracy, and as a result enhancing...
Effect of unitary transformation on Bayesian information criterion for source numbering in array processing
, Article IET Signal Processing ; Volume 13, Issue 7 , 2019 , Pages 670-678 ; 17519675 (ISSN) ; Aref, M. R ; Razzazi, F ; Sharif University of Technology
Institution of Engineering and Technology
2019
Abstract
An approach based on unitary transformation for the problem of estimating the number of signals is proposed in this study. Among the information theoretic criteria, the authors focus on the conventional Bayesian information criterion (BIC) in the presence of a uniform linear array. The sample covariance matrix of this array is transformed into the real symmetric one by using a unitary transformation. This real symmetric matrix has real eigenvalues and eigenvectors. Therefore its eigenvalue decomposition needs only real computations. Since the eigenvalues of this real symmetric matrix are equal to the eigenvalues of the sample covariance matrix, by replacing them in BIC formula, the term...
Covariance-based multiple-impulse rendezvous design
, Article IEEE Transactions on Aerospace and Electronic Systems ; Volume 55, Issue 5 , 2019 , Pages 2128-2137 ; 00189251 (ISSN) ; Kiani, M ; Pourtakdoust, S. H ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2019
Abstract
A novel trajectory design methodology is proposed in the current work to minimize the state uncertainty in the crucial mission of spacecraft rendezvous. The trajectory is shaped under constraints utilizing a multiple-impulse approach. State uncertainty is characterized in terms of covariance, and the impulse time as the only effective parameter in uncertainty propagation is selected to minimize the trace of the covariance matrix. Furthermore, the impulse location is also adopted as the other design parameter to satisfy various translational constraints of the space mission. Efficiency and viability of the proposed idea have been investigated through some scenarios that include constraints on...
Optimal design of truss structures with frequency constraints: a comparative study of DE, IDE, LSHADE, and CMAES algorithms
, Article Engineering with Computers ; 2021 ; 01770667 (ISSN) ; Mesbahi, P ; Moosavian, N ; Daliri, H ; Sharif University of Technology
Springer Science and Business Media Deutschland GmbH
2021
Abstract
The present study examines the performance of three powerful methods including the original differential evolution (DE), the improved differential evolution (IDE), and the winner of the CEC-2014 competition, LSHADE, in addition to the covariance matrix adaptation evolution strategy (CMAES) for size optimization of truss structures under natural frequency constraints. Despite the abundant researches on novel meta-heuristic algorithms in the literature, the application of CMAES, one of the most powerful and reliable optimization algorithms, on the optimal solution of the truss structures has received scant attention. For consistent comparison between these algorithms, four stopping criteria...
Beampattern Design in Non-uniform MIMO Radars
, M.Sc. Thesis Sharif University of Technology ; Bastani, Mohammad Hassan (Supervisor)
Abstract
Multiple Input Multiple Output (MIMO) radar is an emerging technology which has attracted many researchers recently. The problem of beampattern design of a MIMO radar in uniform arrays and with the covariance based method of point targets has been investigated by many papers so far. In this thesis it is desirable to consider this problem in non-uniform arrays. Many authors have designed the transmitted beampattern by means of designing the cross correlation matrix of transmitted signals elements, but in this paper optimizing the locations of transmitted antennas will be done as well as cross correlation matrix of transmitted signals to achieve a better results
Design and Implementation of Distributed Dimensionality Reduction Algorithms under Communication Constraints
, M.Sc. Thesis Sharif University of Technology ; Maddah Ali, Mohammad Ali (Supervisor) ; Salehkaleybar, Saber (Supervisor)
Abstract
Nowadays we are witnessing the emergence of machine learning in various applications. One of the key problems in data science and machine learning is the problem of dimensionality reduction, which deals with finding a mapping that embeds samples to a lower-dimensional space such that, the relationships between the samples and their properties are preserved in the secondary space as much as possible. Obtaining such mapping is essential in today's high-dimensional settings. Moreover, due to the large volume of data and high-dimensional samples, it is infeasible or insecure to process and store all data in a single machine. As a result, we need to process data in a distributed manner.In this...
Effect of laser phase noise on the fidelity of optomechanical quantum memory
, Article Physical Review A - Atomic, Molecular, and Optical Physics ; Volume 91, Issue 3 , March , 2015 ; 10502947 (ISSN) ; Bahrampour, A. R ; Sharif University of Technology
American Physical Society
2015
Abstract
Optomechanical and electromechanical cavities have been widely used in quantum memories and quantum transducers. We theoretically investigate the robustness of optomechanical and electromechanical quantum memories against the noise of the control laser. By solving the Langevin equations and using the covariance matrix formalism in the presence of laser noise, the storing fidelity of Gaussian states is obtained. It is shown that the destructive effect of phase noise is more significant in higher values of coupling laser amplitude and optomechanical coupling strength G. However, by further increasing the coupling coefficient, the interaction time between photons and phonons decreases below the...
Robust Huber similarity measure for image registration in the presence of spatially-varying intensity distortion
, Article Signal Processing ; Volume 109 , April , 2015 , Pages 54-68 ; 01651684 (ISSN) ; Fatemizadeh, E ; Sharif University of Technology
Elsevier
2015
Abstract
Similarity measure is an important part of image registration. The main challenge of similarity measure is lack of robustness to different distortions. A well-known distortion is spatially-varying intensity distortion. Its main characteristic is correlation among pixels. Most traditional intensity based similarity measures (e.g., SSD, MI) assume stationary image and pixel to pixel independence. Hence, these similarity measures are not robust against spatially-varying intensity distortion. Here, we suppose that non-stationary intensity distortion has a sparse representation in transform domain, i.e. its distribution has high peak at origin and a long tail. We use two viewpoints of Maximum...
An attribute learning method for zero-shot recognition
, Article 2017 25th Iranian Conference on Electrical Engineering, ICEE 2017, 2 May 2017 through 4 May 2017 ; 2017 , Pages 2235-2240 ; 9781509059638 (ISBN) ; Shojaee, S. M ; Soleymani Baghshah, M ; Sharif University of Technology
Abstract
Recently, the problem of integrating side information about classes has emerged in the learning settings like zero-shot learning. Although using multiple sources of information about the input space has been investigated in the last decade and many multi-view and multi-modal learning methods have already been introduced, the attribute learning for classes (output space) is a new problem that has been attended in the last few years. In this paper, we propose an attribute learning method that can use different sources of descriptions for classes to find new attributes that are more proper to be used as class signatures. Experimental results show that the learned attributes by the proposed...
Extended two-dimensional PCA for efficient face representation and recognition
, Article 2008 IEEE 4th International Conference on Intelligent Computer Communication and Processing, ICCP 2008, Cluj-Napoca, 28 August 2008 through 30 August 2008 ; October , 2008 , Pages 295-298 ; 9781424426737 (ISBN) ; Manzuri Shalmani, M. T ; Khademi, M ; Sharif University of Technology
2008
Abstract
In this paper a novel method called Extended Two-Dimensional PCA (E2DPCA) is proposed which is an extension to the original 2DPCA. We state that the covariance matrix of 2DPCA is equivalent to the average of the main diagonal of the covariance matrix of PCA. This implies that 2DPCA eliminates some covariance information that can be useful for recognition. E2DPCA instead of just using the main diagonal considers a radius of r diagonals around it and expands the averaging so as to include the covariance information within those diagonals. The parameter r unifies PCA and 2DPCA. r=1 produces the covariance of 2DPCA, r=n that of PCA. Hence, by controlling r it is possible to control the...
Skewness reduction approach in multi-attribute process monitoring
, Article Communications in Statistics - Theory and Methods ; Volume 36, Issue 12 , 2007 , Pages 2313-2325 ; 03610926 (ISSN) ; Abbasi, B ; Sharif University of Technology
2007
Abstract
Since the product quality of many industrial processes depends upon more than one dependent variable or attribute, they are either multivariate or multi-attribute in nature. Although multivariate statistical process control is receiving increased attention in the literature, little work has been done to deal with multi-attribute processes. In this article, we develop a new methodology to monitor multi-attribute processes. To do this, first we transform multi-attribute data in a way that their marginal probability distributions have almost zero skewness. Then, we estimate the transformed covariance matrix and apply the well-known T2 control chart. In order to illustrate the proposed method...
Seizure detection in EEG signals: a comparison of different approaches
, Article 28th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS'06, New York, NY, 30 August 2006 through 3 September 2006 ; 2006 , Pages 6724-6727 ; 05891019 (ISSN); 1424400325 (ISBN); 9781424400324 (ISBN) ; Maghsoudi, A ; Shamsollahi, M. B ; Sharif University of Technology
2006
Abstract
In this paper, the performance of traditional variance-based method for detection of epileptic seizures in EEG signals are compared with various methods based on nonlinear time series analysis, entropies, logistic regression, discrete wavelet transform and time frequency distributions. We noted that variance-based method in compare to the mentioned methods had the best result (100%) applied on the same database. © 2006 IEEE
Source enumeration in large arrays using moments of eigenvalues and relatively few samples
, Article IET Signal Processing ; Volume 6, Issue 7 , 2012 , Pages 689-696 ; 17519675 (ISSN) ; Gazor, S ; Bastani, H ; Sharif University of Technology
IET
2012
Abstract
This study presents a method based on minimum description length criterion to enumerate the incident waves impinging on a large array using a relatively small number of samples. The proposed scheme exploits the statistical properties of eigenvalues of the sample covariance matrix (SCM) of Gaussian processes. The authors use a number of moments of noise eigenvalues of the SCM in order to separate noise and signal subspaces more accurately. In particular, the authors assume a Marcenko-Pastur probability density function (pdf) for the eigenvalues of SCM associated with the noise subspace. We also use an enhanced noise variance estimator to reduce the bias leakage between the subspaces....