The Experts below are selected from a list of 69219 Experts worldwide ranked by ideXlab platform
Pascal Frossard - One of the best experts on this subject based on the ideXlab platform.
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learning Heat Diffusion graphs
IEEE Transactions on Signal and Information Processing over Networks, 2017Co-Authors: Dorina Thanou, Daniel Kressner, Xiaowen Dong, Pascal FrossardAbstract:Information analysis of data often boils down to properly identifying their hidden structure. In many cases, the data structure can be described by a graph representation that supports signals in the dataset. In some applications, this graph may be partly determined by design constraints or predetermined sensing arrangements. In general though, the data structure is not readily available nor easily defined. In this paper, we propose to represent structured data as a sparse combination of localized functions that live on a graph. This model is more appropriate to represent local data arrangements than the classical global smoothness prior. We focus on the problem of inferring the connectivity that best explains the data samples at different vertices of a graph that is a priori unknown. We concentrate on the case where the observed data are actually the sum of Heat Diffusion processes, which is a widely used model for data on networks or other irregular structures. We cast a new graph learning problem and solve it with an efficient nonconvex optimization algorithm. Experiments on both synthetic and real world data finally illustrate the benefits of the proposed graph learning framework and confirm that the data structure can be efficiently learned from data observations only. We believe that our algorithm will help solving key questions in diverse application domains such as social and biological network analysis where it is crucial to unveil proper data structure for understanding and inference.
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Learning Heat Diffusion graphs
IEEE Transactions on Signal and Information Processing over Networks, 2017Co-Authors: Dorina Thanou, Daniel Kressner, Xiaowen Dong, Pascal FrossardAbstract:Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or pre-determined sensing arrangements, like in road transportation networks for example. In general though, the data structure is not readily available and becomes pretty difficult to define. In particular, the global smoothness assumptions, that most of the existing works adopt, are often too general and unable to properly capture localized properties of data. In this paper, we go beyond this classical data model and rather propose to represent information as a sparse combination of localized functions that live on a data structure represented by a graph. Based on this model, we focus on the problem of inferring the connectivity that best explains the data samples at different vertices of a graph that is a priori unknown. We concentrate on the case where the observed data is actually the sum of Heat Diffusion processes, which is a quite common model for data on networks or other irregular structures. We cast a new graph learning problem and solve it with an efficient nonconvex optimization algorithm. Experiments on both synthetic and real world data finally illustrate the benefits of the proposed graph learning framework and confirm that the data structure can be efficiently learned from data observations only. We believe that our algorithm will help solving key questions in diverse application domains such as social and biological network analysis where it is crucial to unveil proper geometry for data understanding and inference.
Shinichi Aihara - One of the best experts on this subject based on the ideXlab platform.
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consistency property of extended least squares parameter estimation for stochastic Diffusion equation
Systems & Control Letters, 1998Co-Authors: Shinichi AiharaAbstract:The extended least-squares parameter estimate for stochastic Heat Diffusion equations is considered. The unknown parameter is a Heat Diffusion coefficient which is a function of a spatial variable. Almost sure convergence for the estimated parameter is proved. A numerical example is demonstrated for supporting the theoretical results developed here.
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consistency of extended least square parameter estimate for stochastic distributed parameter systems
European Control Conference, 1997Co-Authors: Shinichi AiharaAbstract:The extended least square parameter estimate for stochastic Heat Diffusion equations is considered. The unknown parameter is a Heat Diffusion coefficient which is a function of a spatial variable. Almost sure convergence for the estimated parameter is proved. A numerical example is demonstrated for supporting the theoretical resluts developed here.
Dorina Thanou - One of the best experts on this subject based on the ideXlab platform.
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learning Heat Diffusion graphs
IEEE Transactions on Signal and Information Processing over Networks, 2017Co-Authors: Dorina Thanou, Daniel Kressner, Xiaowen Dong, Pascal FrossardAbstract:Information analysis of data often boils down to properly identifying their hidden structure. In many cases, the data structure can be described by a graph representation that supports signals in the dataset. In some applications, this graph may be partly determined by design constraints or predetermined sensing arrangements. In general though, the data structure is not readily available nor easily defined. In this paper, we propose to represent structured data as a sparse combination of localized functions that live on a graph. This model is more appropriate to represent local data arrangements than the classical global smoothness prior. We focus on the problem of inferring the connectivity that best explains the data samples at different vertices of a graph that is a priori unknown. We concentrate on the case where the observed data are actually the sum of Heat Diffusion processes, which is a widely used model for data on networks or other irregular structures. We cast a new graph learning problem and solve it with an efficient nonconvex optimization algorithm. Experiments on both synthetic and real world data finally illustrate the benefits of the proposed graph learning framework and confirm that the data structure can be efficiently learned from data observations only. We believe that our algorithm will help solving key questions in diverse application domains such as social and biological network analysis where it is crucial to unveil proper data structure for understanding and inference.
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Learning Heat Diffusion graphs
IEEE Transactions on Signal and Information Processing over Networks, 2017Co-Authors: Dorina Thanou, Daniel Kressner, Xiaowen Dong, Pascal FrossardAbstract:Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or pre-determined sensing arrangements, like in road transportation networks for example. In general though, the data structure is not readily available and becomes pretty difficult to define. In particular, the global smoothness assumptions, that most of the existing works adopt, are often too general and unable to properly capture localized properties of data. In this paper, we go beyond this classical data model and rather propose to represent information as a sparse combination of localized functions that live on a data structure represented by a graph. Based on this model, we focus on the problem of inferring the connectivity that best explains the data samples at different vertices of a graph that is a priori unknown. We concentrate on the case where the observed data is actually the sum of Heat Diffusion processes, which is a quite common model for data on networks or other irregular structures. We cast a new graph learning problem and solve it with an efficient nonconvex optimization algorithm. Experiments on both synthetic and real world data finally illustrate the benefits of the proposed graph learning framework and confirm that the data structure can be efficiently learned from data observations only. We believe that our algorithm will help solving key questions in diverse application domains such as social and biological network analysis where it is crucial to unveil proper geometry for data understanding and inference.
Moo K Chung - One of the best experts on this subject based on the ideXlab platform.
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fast polynomial approximation of Heat kernel convolution on manifolds and its application to brain sulcal and gyral graph pattern analysis
IEEE Transactions on Medical Imaging, 2020Co-Authors: Shihgu Huang, Ilwoo Lyu, Anqi Qiu, Moo K ChungAbstract:Heat Diffusion has been widely used in brain imaging for surface fairing, mesh regularization and cortical data smoothing. Motivated by Diffusion wavelets and convolutional neural networks on graphs, we present a new fast and accurate numerical scheme to solve Heat Diffusion on surface meshes. This is achieved by approximating the Heat kernel convolution using high degree orthogonal polynomials in the spectral domain. We also derive the closed-form expression of the spectral decomposition of the Laplace-Beltrami operator and use it to solve Heat Diffusion on a manifold for the first time. The proposed fast polynomial approximation scheme avoids solving for the eigenfunctions of the Laplace-Beltrami operator, which is computationally costly for large mesh size, and the numerical instability associated with the finite element method based Diffusion solvers. The proposed method is applied in localizing the male and female differences in cortical sulcal and gyral graph patterns obtained from MRI in an innovative way. The MATLAB code is available at http://www.stat.wisc.edu/~mchung/chebyshev .
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fast polynomial approximation of Heat kernel convolution on manifolds and its application to brain sulcal and gyral graph pattern analysis
arXiv: Computer Vision and Pattern Recognition, 2019Co-Authors: Shihgu Huang, Ilwoo Lyu, Anqi Qiu, Moo K ChungAbstract:Heat Diffusion has been widely used in brain imaging for surface fairing, mesh regularization and cortical data smoothing. Motivated by Diffusion wavelets and convolutional neural networks on graphs, we present a new fast and accurate numerical scheme to solve Heat Diffusion on surface meshes. This is achieved by approximating the Heat kernel convolution using high degree orthogonal polynomials in the spectral domain. We also derive the closed-form expression of the spectral decomposition of the Laplace-Beltrami operator and use it to solve Heat Diffusion on a manifold for the first time. The proposed fast polynomial approximation scheme avoids solving for the eigenfunctions of the Laplace-Beltrami operator, which is computationally costly for large mesh size, and the numerical instability associated with the finite element method based Diffusion solvers. The proposed method is applied in localizing the male and female differences in cortical sulcal and gyral graph patterns obtained from MRI in an innovative way. The MATLAB code is available at this http URL
Alexander V Priezzhev - One of the best experts on this subject based on the ideXlab platform.
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self localization of laser induced tumour coagulation limited by Heat Diffusion through active tissue
Journal of Medical Engineering & Technology, 2006Co-Authors: Bohdan Datsko, Igor A Lubashevsky, Vasyl V Gafiychuk, Alexander V PriezzhevAbstract:We analyse necrosis growth due to thermal coagulation induced by laser light absorption and limited by Heat Diffusion into the surrounding live tissue. The tissue is assumed to contain a tumour in the undamaged tissue where the blood perfusion rate does not change during the action. By contrast, normal tissue responds strongly to an increase in the tissue temperature and the blood perfusion rate can grow by tenfold. We study in detail necrosis formation under conditions typical of a real course of thermal therapy treatment. The duration of the treatment is about 5 minutes when a necrosis domain of about 1 cm or above is formed. In particular, if the tumour size is sufficiently large, i.e. it exceeds 1 cm, and the tissue response is not too delayed, i.e. the delay time does not exceed 1 min, then there are conditions under which the relative volume of the damaged normal tissue is small in comparison with the tumour volume after the tumour is totally coagulated.
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laser induced Heat Diffusion limited tissue coagulation as a laser therapy mode
Laser-Tissue Interaction XI: Photochemical Photothermal and Photomechanical, 2000Co-Authors: Igor A Lubashevsky, Alexander V Priezzhev, Vasyl V GafiychukAbstract:Previously we have developed a free boundary model for local thermal coagulation induced by laser light absorption when the tissue region affected directly by laser light is sufficiently small and Heat Diffusion into the surrounding tissue governs the necrosis growth. In the present paper keeping in mind the obtained results we state the point of view on the necrosis formation under these conditions as the basis of an individual laser therapy mode exhibiting specific properties. In particular, roughly speaking, the size of the resulting necrosis domain is determined by the physical characteristics of the tissue and its response to local Heating, and by the applicator form rather than the treatment duration and the irradiation power.
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effect of blood vessel discreteness on necrosis formation during laser induced thermal coagulation limited by Heat Diffusion
Journal of Biomedical Optics, 1999Co-Authors: Igor A Lubashevsky, Alexander V PriezzhevAbstract:When Heated, living tissue exhibits random nonuniformities in temperature that are due to the discreteness of vessel arrangement. Because of the strong temperature dependence of the thermal coagulation rate these nonuniformities should substantially affect the necrosis growth induced by local Heating. In the present work we study the effect of vessel discreteness on the form of a necrosis domain when its growth is limited by Heat Diffusion into the surrounding tissue. Namely, we analyze the characteristics of the necrosis boundary that are due to vessel discreteness. In particular, we find the mean amplitude d G and the correlation length l G of the necrosis boundary perturbations depending on the main tissue parameters. In addition, it is shown that there are universal relations between the mean size R of the necrosis domain and the characteristics d G , l G of the boundary perturbations, which are due to the fractal structure of the vascular network. © 1999 Society of Photo-Optical Instrumentation Engineers. [S1083-3668(99)00702-9]
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laser induced Heat Diffusion limited tissue coagulation ii effect of random temperature nonuniformities on the form of a spherical and cylindrical necrosis domain
BiOS '98 International Biomedical Optics Symposium, 1998Co-Authors: Igor A Lubashevsky, Alexander V PriezzhevAbstract:When Heated the living tissue exhibits temperature nonuniformities due to the vessel discreetness. On small scales the particular details of the vessel arraignments are practically unknown, so we regard such nonuniformities as random. When the tissue region affected directly by laser light is sufficiently small Heat Diffusion into the surrounding tissue is responsible for the necrosis growth. In this case strong temperature dependence of the thermal coagulation rate gives rise to the substantial perturbations the necrosis boundary due to the random temperature nonuniformities. In the previous papers we have analyzed this effect assuming the necrosis boundary quasiplane. In particular, we have found that for typical values of the tissue parameters the correlation length of such perturbations can be comparable with the necrosis size in magnitude. Therefore, the present paper studies the effect of the random temperature nonuniformities for a necrosis domain of spherical and cylindrical form. In this way we are able to analyze this effect for a more realistic situation, namely, depending on the form of an applicator delivering laser light inside the tissue. In particular, we have shown that for cylindrical applicators the effect of the vessel discreetness can be described by the developed previously model. For spherical applicators of small size (about several millimeters) this effect is depressed because in this case blood perfusion does not affect substantially the necrosis growth.
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laser induced Heat Diffusion limited tissue coagulation i form of the necrosis boundary caused by random temperature nonuniformities
Laser-tissue interaction tissue optics and laser welding. Conference, 1998Co-Authors: Igor A Lubashevsky, Alexander V PriezzhevAbstract:ABSTRACT When Heated the living tissue exhibits random nonuniformities in the temperature that are due to the discreteness ofvessel arrangement. Because of strong temperature dependence of the thermal coagulation rate these nonuniformitiesshould substantially affect the necrosis growth induced by local Heating. In the present work we study their effect on the form of a necrosis domain when its growth is limited by Heat Diffusion into the surrounding tissue. In particular, we analyze the mean amplitude and the correlation length of the interface perturbations depending on the main characteristics of the random temperature nonuniformites.Keywords: Necrosis domain, Thermal coagulation, Vessel discreteness, Random temperature nonuniformities 1. PROBLEM BACKGROUND. RANDOM TEMPERATURE NONUNIFORMITES Blood flowing through the vascular network in living tissue forms paths of fast Heat transport and under typical conditions it is blood flow that governs Heat propagation on scales exceeding several millimeters (for an introduction
